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Go Math Grade 4 Chapter 9 Answer Key Pdf Relate Fractions and Decimals

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Relate Fractions and Decimals Go Math Grade 4 Chapter 9 Answer Key Pdf

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Lesson 1: Relate Tenths and Decimals

Lesson 2: Relate Hundredths and Decimals

Lesson 3: Equivalent Fractions and Decimals

Lesson 4: Relate Fractions, Decimals, and Money

Lesson 5: Problem Solving • Money

Mid-Chapter Checkpoint

Lesson 6: Add Fraction Parts of 10 and 100

Lesson 7: Compare Decimals

Review/Test

Common Core – New – Page No. 499

Relate Tenths and Decimals

Write the fraction or mixed number and the decimal shown by the model.

Question 1
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 1

Answer:
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 1

Question 2.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 2
Type below:
________

Answer:
1\(\frac{2}{10}\)

Explanation:
The model is divided into 10 equal parts. Each part represents one-tenth.
1 2/10 is 1 whole and 2 tenths.

Question 3.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 3
Type below:
________

Answer:
2\(\frac{3}{10}\) = 2.3

Explanation:
grade 4 chapter 9 Common Core Image 1 499

Question 4.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 4
Type below:
________

Answer:
4\(\frac{8}{10}\) = 4.8

Explanation:
grade 4 chapter 9 Common Core Image 2 499

Write the fraction or mixed number as a decimal.

Question 5.
\(\frac{4}{10}\)
_____

Answer:
0.4

Explanation:
Write down 4 with the decimal point 1 space from the right (because 10 has 1 zero)
0.4

Compare Fractions and Decimals Lesson 1 Answer Key Question 6.
3 \(\frac{1}{10}\)
_____

Answer:
3.1

Explanation:
Multiply 3 x 10 = 30.
Add 30 + 1 = 31.
So, 31/10.
Write down 31 with the decimal point 1 space from the right (because 10 has 1 zero)
3.1

Question 7.
\(\frac{7}{10}\)
_____

Answer:
0.7

Explanation:
Write down 7 with the decimal point 1 space from the right (because 10 has 1 zero)
0.7

Question 8.
6 \(\frac{5}{10}\)
_____

Answer:
6.5

Explanation:
Multiply 6 x 10 = 60.
Add 60 + 5 = 65.
So, 65/10.
Write down 35 with the decimal point 1 space from the right (because 10 has 1 zero)
6.5

Question 9.
\(\frac{9}{10}\)
_____

Answer:
0.9

Explanation:
Write down 9 with the decimal point 1 space from the right (because 10 has 1 zero)
0.9

Problem Solving

Question 10.
There are 10 sports balls in the equipment closet. Three are kickballs. Write the portion of the balls that are kickballs as a fraction, as a decimal, and in word form.
Type below:
_________

Answer:
\(\frac{3}{10}\) = 0.3 = three tenths

Explanation:
There are 10 sports balls in the equipment closet. Three are kickballs. So, 3/10 kickballs are available.

Question 11.
Peyton has 2 pizzas. Each pizza is cut into 10 equal slices. She and her friends eat 14 slices. What part of the pizzas did they eat? Write your answer as a decimal.
_________

Answer:
1.4 pizzas

Explanation:
Peyton has 2 pizzas. Each pizza is cut into 10 equal slices.
So, the total number of slices = 2 x 10 = 20.
She and her friends eat 14 slices.
So, they ate 1 whole pizza and 4 parts out of 10 slices in the second pizza.
1 4/10 = 14/10 = 1.4 pizzas

Common Core – New – Page No. 500

Lesson Check

Question 1.
Valerie has 10 CDs in her music case. Seven of the CDs are pop music CDs. What is this amount written as a decimal?
Options:
a. 70.0
b. 7.0
c. 0.7
d. 0.07

Answer:
c. 0.7

Explanation:
Valerie has 10 CDs in her music case. Seven of the CDs are pop music CDs.
Seven CDs out of 10 CDs = 7/10 =0.7

Question 2.
Which decimal amount is modeled below?
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 5
Options:
a. 140.0
b. 14.0
c. 1.4
d. 0.14

Answer:
c. 1.4

Explanation:
1\(\frac{4}{10}\)
Multiply 10 x 1 = 10.
Add 10 + 4 = 14.
So, 14/10 = 1.4.

Spiral Review

Question 3.
Which number is a factor of 13?
Options:
a. 1
b. 3
c. 4
d. 7

Answer:
a. 1

Explanation:
13 has 1 and 13 as its factors.

Question 4.
An art gallery has 18 paintings and 4 photographs displayed in equal rows on a wall, with the same number of each type of art in each row. Which of the following could be the number of rows?
Options:
a. 2 rows
b. 3 rows
c. 4 rows
d. 6 rows

Answer:
a. 2 rows

Explanation:
An art gallery has 18 paintings and 4 photographs displayed in equal rows on a wall, with the same number of each type of art in each row. So, 18 paintings and 4 photographs need to be divided into equal parts.
18/2 = 9; 4/2 = 2.
2 rows can be possible with 9 pictures and 2 pictures in each row.

Question 5.
How do you write the mixed number shown as a fraction greater than 1?
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 6
Options:
a. \(\frac{32}{5}\)
b. \(\frac{14}{4}\)
c. \(\frac{6}{4}\)
d. \(\frac{4}{4}\)

Answer:
b. \(\frac{14}{4}\)

Explanation:
3\(\frac{2}{4}\) = 14/4. 14 divided by 4 is equal to 3 with a remainder of 2. The 3 is greater than 1. So, 14/4 > 1.

Question 6.
Which of the following models has an amount shaded that is equivalent to the fraction \(\frac{1}{5}\)?
a. Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 7
b. Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 8
c. Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 9
d. Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 10

Answer:
c. Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 9

Explanation:
a. \(\frac{2}{3}\)
b. \(\frac{5}{10}\) = \(\frac{1}{2}\)
c. \(\frac{2}{10}\) = \(\frac{1}{5}\)
d. \(\frac{1}{10}\)

Page No. 503

Question 1.
Shade the model to show \(\frac{31}{100}\).
Write the amount as a decimal.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 11
_____

Answer:
grade 4 chapter 9 Relate Fractions and Decimals Image 1 503

Write the fraction or mixed number and the decimal shown by the model.

Question 2.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 12
Type below:
_________

Answer:
\(\frac{68}{100}\) = 0.68

Explanation:
68 boxes are shaded out of 100 boxes.

Question 3.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 13
Type below:
_________

Answer:
\(\frac{8}{100}\) = 0.08

Explanation:
8 boxes are shaded out of 100 boxes.

Question 4.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 14
Type below:
_________

Answer:
6\(\frac{19}{100}\) = 6.19

Explanation:
0.5 is 5 tenths and 0.50 is 5 tenths 0 hundredths. Since both 0.5 and 0.50 have 5 tenths and no hundredths, they are equivalent

Write the fraction or mixed number and the decimal shown by the model.

Question 5.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 15
Type below:
_________

Answer:
1\(\frac{83}{100}\) = 1.83

Explanation:
1 whole number(all the square boxes are shaded) and 83 square boxes shaded out from 100 boxes.

Go Math Book Grade 4 Lesson 9.2 Relate Hundredths and Decimals Question 6.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 16
Type below:
_________

Answer:
\(\frac{75}{100}\)

Explanation:
75 boxes are shaded out of 100 boxes.

Question 7.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 17
Type below:
_________

Answer:
\(\frac{47}{100}\) = 0.47

Explanation:
The point lies between \(\frac{40}{100}\) and \(\frac{50}{100}\). The number of lines in between \(\frac{40}{100}\) and \(\frac{50}{100}\) are 10. The point is placed at the 7th line. So, 40 + 7 = 47. Answer = \(\frac{47}{100}\)

Practice: Copy and Solve Write the fraction or mixed number as a decimal.

Question 8.
\(\frac{9}{100}\) = _____

Answer:
0.09

Explanation:
Write down 9 with the decimal point 2 spaces from the right (because 100 has 2 zeros)

Question 9.
4 \(\frac{55}{100}\) = _____

Answer:
4.55

Explanation:
4 \(\frac{55}{100}\) = \(\frac{455}{100}\)
Write down 455 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, 4.55 is the answer

Question 10.
\(\frac{10}{100}\) = _____

Answer:
0.10 = 0.1

Explanation:
Write down 10 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, 0.10 =0.1 is the answer

Question 11.
9 \(\frac{33}{100}\) = _____

Answer:
9.33

Explanation:
9 \(\frac{33}{100}\) = \(\frac{933}{100}\)
Write down 933 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, 9.33 is the answer.

Go Math Grade 4 Chapter 9 Pdf Question 12.
\(\frac{92}{100}\) = _____

Answer:
0.92

Explanation:
Write down 92 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, 0.92 is the answer

Question 13.
14 \(\frac{16}{100}\) = _____

Answer:
14.16

Explanation:
14 \(\frac{16}{100}\) = \(\frac{1416}{100}\)
Write down 1416 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, 14.16 is the answer.

Page No. 504

Question 14.
Shade the grids to show three different ways to represent \(\frac{16}{100}\) using models.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 18
Type below:
_________

Answer:
grade 4 chapter 9 Relate Fractions and Decimals Image 1 504

Question 15.
Describe Relationships Describe how one whole, one-tenth, and one hundredth are related.
Type below:
_________

Answer:
One whole = 1.00
One tenth: 0.1
One hundredth: 0.01
One whole is 10 times the one-tenth, and one-tenth is 10 times the one hundredth.

Question 16.
Shade the model to show 1 \(\frac{24}{100}\). Then write the mixed number in decimal form.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 19
_____

Answer:
grade 4 chapter 9 Relate Fractions and Decimals Image 2 504
1\(\frac{24}{100}\) = \(\frac{124}{100}\) = 1.24

Question 17.
The Memorial Library is 0.3 mile from school. Whose statement makes sense? Whose statement is nonsense? Explain your reasoning.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 20
Type below:
_________

Answer:
The boy’s statement makes sense. Because The Memorial Library is 0.3 miles from the school. Digit 3 in the tenths place after the first place of decimal.
The girl’s statement makes non-sense. Because there she said 3 miles that is not equal to 0.3 miles.

Common Core – New – Page No. 505

Relate Hundredths and Decimals

Write the fraction or mixed number and the decimal shown by the model.

Question 1.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 21

Answer:
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 21

Question 2.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 22
Type below:
_________

Answer:
\(\frac{29}{100}\) = 0.29

Explanation:
0.20 names the same amount as 20/100. So, the given point is at 29/100 = 0.29

Question 3.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 23
Type below:
_________

Answer:
1\(\frac{54}{100}\) = 1.54

Explanation:
From the given image, one model is one whole and another model 54 boxes shaded out of 100. So, the answer is 1\(\frac{54}{100}\) = 1.54

Question 4.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 24
Type below:
_________

Answer:
4\(\frac{62}{100}\) = 4.62

Explanation:
4.60 names the same amount as 4\(\frac{60}{100}\). So, the given point is at 4\(\frac{62}{100}\) = 4.62

Write the fraction or mixed number as a decimal.

Question 5.
\(\frac{37}{100}\)
_____

Answer:
0.37

Explanation:
Write down 37 with the decimal point 2 spaces from the right (because 100 has 2 zeros). 0.37

Question 6.
8 \(\frac{11}{100}\)
_____

Answer:
8.11

Explanation:
8\(\frac{11}{100}\) = \(\frac{811}{100}\)
Write down 811 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, 8.11 is the answer.

Question 7.
\(\frac{98}{100}\)
_____

Answer:
0.98

Explanation:
Write down 98 with the decimal point 2 spaces from the right (because 100 has 2 zeros). 0.98

Question 8.
25 \(\frac{50}{100}\)
_____

Answer:
25.50

Explanation:
25\(\frac{50}{100}\) = \(\frac{2550}{100}\)
Write down 2550 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, 25.50 is the answer.

Question 9.
\(\frac{6}{100}\)
_____

Answer:
0.06

Explanation:
Write down 6 with the decimal point 2 spaces from the right (because 100 has 2 zeros). 0.06

Problem Solving

Question 10.
There are 100 pennies in a dollar. What fraction of a dollar is 61 pennies? Write it as a fraction, as a decimal, and in word form.
Type below:
_________

Answer:
\(\frac{61}{100}\) pennies = 0.61 = sixty-one hundredths

Explanation:
There are 100 pennies in a dollar. So, for 61 pennies, there are \(\frac{61}{100}\) pennies = 0.61 = sixty-one hundredths.

Question 11.
Kylee has collected 100 souvenir thimbles from different places she has visited with her family. Twenty of the thimbles are carved from wood. Write the fraction of thimbles that are wooden as a decimal.
_________

Answer:
It is easier to work with decimals then fractions because it is like adding whole numbers in a normal way.

Common Core – New – Page No. 506

Lesson Check

Question 1.
Which decimal represents the shaded section of the model below?
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 25
Options:
a. 830.0
b. 83.0
c. 8.30
d. 0.83

Answer:
d. 0.83

Explanation:
The model is divided into 100 equal parts. Each part represents one hundredth. 83 boxes are shaded out of 100. So, the answer is \(\frac{83}{100}\) = 0.83

Question 2.
There were 100 questions on the unit test. Alondra answered 97 of the questions correctly. What decimal represents the fraction of questions Alondra answered correctly?
Options:
a. 0.97
b. 9.70
c. 90.70
d. 970.0

Answer:
a. 0.97

Explanation:
There were 100 questions on the unit test. Alondra answered 97 of the questions correctly. So, \(\frac{97}{100}\) questions answered correctly. = 0.97

Spiral Review

Question 3.
Which is equivalent to \(\frac{7}{8}\)?
Options:
a. \(\frac{5}{8}+\frac{3}{8}\)
b. \(\frac{4}{8}+\frac{1}{8}+\frac{1}{8}\)
c. \(\frac{3}{8}+\frac{2}{8}+\frac{2}{8}\)
d. \(\frac{2}{8}+\frac{2}{8}+\frac{1}{8}+\frac{1}{8}\)

Answer:
c. \(\frac{3}{8}+\frac{2}{8}+\frac{2}{8}\)

Explanation:
c. \(\frac{3}{8}+\frac{2}{8}+\frac{2}{8}\) = \(\frac{7}{8}\)

Question 4.
What is \(\frac{9}{10}-\frac{6}{10}\)?
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 26
Options:
a. \(\frac{1}{10}\)
b. \(\frac{3}{10}\)
c. \(\frac{4}{10}\)
d. \(\frac{6}{10}\)

Answer:
b. \(\frac{3}{10}\)

Explanation:
\(\frac{9}{10}-\frac{6}{10}\). From 9 parts, 6 parts are removed. So, the remaining positions are 3.

4th Grade Go Math Relate Tenths and Decimals Question 5.
Misha used \(\frac{1}{4}\) of a carton of 12 eggs to make an omelet. How many eggs did she use?
Options:
a. 2
b. 3
c. 4
d. 6

Answer:
b. 3

Explanation:
Misha used \(\frac{1}{4}\) of a carton of 12 eggs to make an omelet. \(\frac{1}{4}\) x 12 = 3 eggs.

Question 6.
Kurt used the rule add 4, subtract 1 to generate a pattern. The first term in his pattern is 5. Which number could be in Kurt’s pattern?
Options:
a. 4
b. 6
c. 10
d. 14

Answer:
d. 14

Explanation:
Kurt used the rule add 4, subtract 1 to generate a pattern. The first term in his pattern is 5. The pattern numbers are 5, 8, 11, 14, 17, 20, etc. So, the answer is 14.

Page No. 509

Question 1.
Write \(\frac{4}{10}\) as hundredths.
Write \(\frac{4}{10}\) as an equivalent fraction.
\(\frac{4}{10}\) =\(\frac{4 × ■}{10× ■}\)
Write \(\frac{4}{10}\) as a decimal.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 27
Type below:
_________

Answer:
\(\frac{40}{100}\)
grade 4 chapter 9 Relate Fractions and Decimals Image 1 509
0.40

Explanation:
Write \(\frac{4}{10}\) as an equivalent fraction.
\(\frac{4}{10}\) =\(\frac{4 × 10}{10× 10}\) = \(\frac{40}{100}\)
6 tenths is the same as 6 tenths 0 hundredths. So the decimal form = 0.40

Write the number as hundredths in fraction form and decimal form.

Question 2.
\(\frac{7}{10}\)
Type below:
_________

Answer:
\(\frac{70}{100}\)
grade 4 chapter 9 Relate Fractions and Decimals Image 2 509
0.70

Explanation:
Write \(\frac{7}{10}\) as an equivalent fraction.
\(\frac{7}{10}\) =\(\frac{7 × 10}{10× 10}\) = \(\frac{70}{100}\)
7 tenths is the same as 7 tenths 0 hundredths. So the decimal form = 0.70

Question 3.
0.5
Type below:
_________

Answer:
\(\frac{50}{100}\)
grade 4 chapter 9 Relate Fractions and Decimals Image 3 509
0.50

Explanation:
Write 0.5 = \(\frac{5}{10}\) as an equivalent fraction.
\(\frac{5}{10}\) =\(\frac{5 × 10}{10× 10}\) = \(\frac{50}{100}\)
5 tenths is the same as 5 tenths 0 hundredths and also 0.5

Question 4.
\(\frac{3}{10}\)
Type below:
_________

Answer:
\(\frac{30}{100}\)
grade 4 chapter 9 Relate Fractions and Decimals Image 4 509
0.30

Explanation:
Write \(\frac{3}{10}\) as an equivalent fraction.
\(\frac{3}{10}\) =\(\frac{3 × 10}{10× 10}\) = \(\frac{30}{100}\)
3 tenths is the same as 3 tenths 0 hundredths. So the decimal form = 0.30

Write the number as tenths in fraction form and decimal form.

Question 5.
0.40
Type below:
_________

Answer:
\(\frac{4}{10}\) = 0.4

Explanation:
grade 4 chapter 9 Relate Fractions and Decimals Image 1 509
There are no hundredths.
0.40 is equivalent to 4 tenths.
Write 0.40 as 4 tenths = 0.4 = \(\frac{4}{10}\)

Question 6.
\(\frac{80}{100}\)
Type below:
_________

Answer:
\(\frac{8}{10}\)
grade 4 chapter 9 Relate Fractions and Decimals Image 5 509
0.8

Explanation:
10 is a common factor of the numerator and the denominator.
\(\frac{80}{100}\) = \(\frac{80 ÷ 10}{100 ÷ 10}\) = \(\frac{8}{10}\)
0.8

Question 7.
\(\frac{20}{100}\)
Type below:
_________

Answer:
\(\frac{2}{10}\)
grade 4 chapter 9 Relate Fractions and Decimals Image 6 509
0.2

Explanation:
10 is a common factor of the numerator and the denominator.
\(\frac{20}{100}\) = \(\frac{20 ÷ 10}{100 ÷ 10}\) = \(\frac{2}{10}\)
0.2

Practice: Copy and Solve Write the number as hundredths in fraction form and decimal form.

Question 8.
\(\frac{8}{10}\)
Type below:
_________

Answer:
\(\frac{80}{100}\)
grade 4 chapter 9 Relate Fractions and Decimals Image 5 509
0.8

Explanation:
Write \(\frac{8}{10}\) as an equivalent fraction.
\(\frac{8}{10}\) =\(\frac{8 × 10}{10× 10}\) = \(\frac{80}{100}\)
8 tenths is the same as 8 tenths 0 hundredths. So the decimal form = 0.8

Question 9.
\(\frac{2}{10}\)
Type below:
_________

Answer:
\(\frac{20}{100}\)
grade 4 chapter 9 Relate Fractions and Decimals Image 6 509
0.2

Explanation:
Write \(\frac{2}{10}\) as an equivalent fraction.
\(\frac{2}{10}\) =\(\frac{2 × 10}{10× 10}\) = \(\frac{20}{100}\)
2 tenths is the same as 2 tenths 0 hundredths. So the decimal form = 0.2

Question 10.
0.1
Type below:
_________

Answer:
\(\frac{50}{100}\)
grade 4 chapter 9 Relate Fractions and Decimals Image 7 509
0.50

Explanation:
Write 0.1 = \(\frac{1}{10}\) as an equivalent fraction.
\(\frac{1}{10}\) =\(\frac{1 × 10}{10× 10}\) = \(\frac{10}{100}\)
1 tenth is the same as 1 tenth 0 hundredths and also 0.1

Practice: Copy and Solve Write the number as tenths in fraction form and decimal form.

Question 11.
\(\frac{60}{100}\)
Type below:
_________

Answer:
\(\frac{6}{10}\)
grade 4 chapter 9 Relate Fractions and Decimals Image 8 509
0.6

Explanation:
10 is a common factor of the numerator and the denominator.
\(\frac{60}{100}\) = \(\frac{60 ÷ 10}{100 ÷ 10}\) = \(\frac{6}{10}\)
0.6

Question 12.
\(\frac{90}{100}\)
Type below:
_________

Answer:
\(\frac{9}{10}\)
grade 4 chapter 9 Relate Fractions and Decimals Image 9 509
0.9

Explanation:
10 is a common factor of the numerator and the denominator.
\(\frac{90}{100}\) = \(\frac{90 ÷ 10}{100 ÷ 10}\) = \(\frac{9}{10}\)
= 0.9

Question 13.
0.70
Type below:
_________

Answer:
\(\frac{7}{10}\)
grade 4 chapter 9 Relate Fractions and Decimals Image 2 509
0.7

Explanation:
grade 4 chapter 9 Relate Fractions and Decimals Image 2 509
There are no hundredths.
0.70 is equivalent to 7 tenths.
Write 0.70 as 7 tenths = 0.7 = \(\frac{7}{10}\)

Write the number as an equivalent mixed number with hundredths.

Question 14.
1 \(\frac{4}{10}\) = _____

Answer:
1 \(\frac{40}{100}\)

Explanation:
1 \(\frac{4 x 10}{10 x 10}\) = 1 \(\frac{40}{100}\)

Question 15.
3 \(\frac{5}{10}\) = _____

Answer:
3 \(\frac{50}{100}\)

Explanation:
3 \(\frac{5}{10}\) = 3 \(\frac{5 x 10}{10 x 10}\) = 3 \(\frac{50}{100}\)

Question 16.
2 \(\frac{9}{10}\) = _____

Answer:
2 \(\frac{90}{100}\)

Explanation:
2 \(\frac{9}{10}\) = 2 \(\frac{9 x 10}{10 x 10}\) = 2 \(\frac{90}{100}\)

Page No. 510

Question 17.
Carter says that 0.08 is equivalent to \(\frac{8}{10}\). Describe and correct Carter’s error.
Type below:
_________

Answer:
grade 4 chapter 9 Relate Fractions and Decimals Image 1 510
8 hundredths = \(\frac{8}{100}\)
The decimal point is before the 2 numbers. So, the denominator should be 100.

Question 18.
For numbers 18a–18e, choose True or False for the statement.
a. 0.6 is equivalent to \(\frac{6}{100}\).
i. True
ii. False

Answer:
ii. False

Explanation:
grade 4 chapter 9 Relate Fractions and Decimals Image 8 509
0.60 = 6 tenths.
6 tenths = \(\frac{6}{10}\)

Question 18.
b. \(\frac{3}{10}\) is equivalent to 0.30.
i. True
ii. False

Answer:
i. True

Explanation:
grade 4 chapter 9 Relate Fractions and Decimals Image 4 509
0.30 = 3 tenths.
3 tenths = \(\frac{3}{10}\)

Question 18.
c. \(\frac{40}{100}\) is equivalent to \(\frac{4}{10}\).
i. True
ii. False

Answer:
i. True

Explanation:
10 is a common factor of the numerator and the denominator.
\(\frac{40}{100}\) = \(\frac{40 ÷ 10}{100 ÷ 10}\) = \(\frac{4}{10}\)

Question 18.
d. 0.40 is equivalent to \(\frac{4}{100}\).
i. True
ii. False

Answer:
ii. False

Explanation:
grade 4 chapter 9 Relate Fractions and Decimals Image 1 509
4 tenths and 0 hundreds = \(\frac{4}{10}\)

Question 18.
e. 0.5 is equivalent to 0.50.
i. True
ii. False

Answer:
i. True

Explanation:
If you add any zeros after the 5 it will be equal to 0.5. So, 0.5 is equivalent to 0.50

Inland Water
How many lakes and rivers does your state have? The U.S. Geological Survey defines inland water as water that is surrounded by land. The Atlantic Ocean, the Pacific Ocean, and the Great Lakes are not considered inland water.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 28

Question 19.
Just over \(\frac{2}{100}\) of the entire United States is inland water. Write \(\frac{2}{100}\) as a decimal.
_____

Answer:
0.02

Explanation:
Write down 2 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, \(\frac{2}{100}\) = 0.02 is the answer

Question 20.
Can you write 0.02 as tenths? Explain.
_____ tenth

Answer:
0.2 tenth

Explanation:
0.02 = \(\frac{2}{100}\) = \(\frac{2 ÷ 10}{100 ÷ 10}\) = \(\frac{0.2}{10}\)

Question 21.
About 0.17 of the area of Rhode Island is inland water. Write 0.17 as a fraction.
\(\frac{□}{□}\)

Answer:
\(\frac{17}{100}\)

Explanation:
grade 4 chapter 9 Relate Fractions and Decimals Image 2 510
1 tenth and 7 hundred.
So, write 0.17 as \(\frac{17}{100}\)

Question 22.
Louisiana’s lakes and rivers cover about \(\frac{1}{10}\) of the state. Write \(\frac{1}{10}\) as hundredths in words, fraction form, and decimal form.
Type below:
_________

Answer:
Ten hundredths = \(\frac{10}{100}\) = 0.10

Explanation:
1 tenth is the same as the 1 tenth and 0 hundred
grade 4 chapter 9 Relate Fractions and Decimals Image 7 509
0.1 = 0.10 = \(\frac{10}{100}\)

Common Core – New – Page No. 511

Equivalent Fractions and Decimals

Write the number as hundredths in fraction form and decimal form.

Question 1.
\(\frac{5}{10}\) \(\frac{5}{10}\) = \(\frac{5 \times 10}{10 \times 10}\) = \(\frac{50}{100}\)
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 29
Think: 5 tenths is the same as 5 tenths and 0 hundredths. Write 0.50.

Question 2.
\(\frac{9}{10}\)
Type below:
_________

Answer:
\(\frac{90}{100}\); 0.90

Explanation:
\(\frac{9}{10}\) = \(\frac{9 \times 10}{10 \times 10}\) = \(\frac{90}{100}\)
9 tenths is the same as 9 tenths and 0 hundredths. Write 0.90

Question 3.
0.2
Type below:
_________

Answer:
\(\frac{20}{100}\)
0.20

Explanation:
2 tenths is the same as 2 tenths and 0 hundredths. Write 0.20.
grade 4 chapter 9 Relate Fractions and Decimals Image 6 509
\(\frac{2}{10}\) = \(\frac{2 x 10}{10 x 10}\) = \(\frac{20}{100}\)

Question 4.
0.8
Type below:
_________

Answer:
\(\frac{80}{100}\) = 0.80

Explanation:
8 tenths is the same as 8 tenths and 0 hundredths. Write 0.80.
grade 4 chapter 9 Relate Fractions and Decimals Image 5 509
\(\frac{8}{10}\) = \(\frac{8 x 10}{10 x 10}\) = \(\frac{80}{100}\)

Write the number as tenths in fraction form and decimal form.

Question 5.
\(\frac{40}{100}\)
Type below:
_________

Answer:
\(\frac{4}{10}\) = 0.4

Explanation:
10 is a common factor of the numerator and the denominator.
\(\frac{40}{100}\) = \(\frac{40 ÷ 10}{100 ÷ 10}\) = \(\frac{4}{10}\)
= 0.4

Relate Fractions and Decimals 4th Grade Question 6.
\(\frac{10}{100}\)
Type below:
_________

Answer:
\(\frac{1}{10}\) = 0.1

Explanation:
10 is a common factor of the numerator and the denominator.
\(\frac{10}{100}\) = \(\frac{10 ÷ 10}{100 ÷ 10}\) = \(\frac{1}{10}\)
= 0.1

Question 7.
0.60
Type below:
_________

Answer:
\(\frac{6}{10}\) = 0.6

Explanation:
0.60 is 60 hundredths.
\(\frac{60}{100}\).
10 is a common factor of the numerator and the denominator.
\(\frac{60}{100}\) = \(\frac{60 ÷ 10}{100 ÷ 10}\) = \(\frac{6}{10}\)
= 0.6

Problem Solving

Question 8.
Billy walks \(\frac{6}{10}\) mile to school each day. Write \(\frac{6}{10}\) as hundredths in fraction form and in decimal form.
Type below:
________

Answer:
\(\frac{60}{100}\)
0.60

Explanation:
Billy walks \(\frac{6}{10}\) mile to school each day.
\(\frac{6}{10}\) = \(\frac{6 x 10}{10 x 10}\) = \(\frac{60}{100}\)
grade 4 chapter 9 Relate Fractions and Decimals Image 8 509
0.60

Question 9.
Four states have names that begin with the letter A. This represents 0.08 of all the states. Write 0.08 as a fraction.
\(\frac{□}{□}\)

Answer:
\(\frac{8}{100}\)

Explanation:
0.08 is 8 hundredths. So, the fraction is \(\frac{8}{100}\)

Common Core – New – Page No. 512

Lesson Check

Question 1.
The fourth-grade students at Harvest School make up 0.3 of all students at the school. Which fraction is equivalent to 0.3?
Options:
a. \(\frac{3}{10}\)
b. \(\frac{30}{10}\)
c. \(\frac{3}{100}\)
d. \(\frac{33}{100}\)

Answer:
a. \(\frac{3}{10}\)

Explanation:
0.3 is same as the 3 tenths. So, the answer is \(\frac{3}{10}\)

Question 2.
Kyle and his brother have a marble set. Of the marbles, 12 are blue. This represents \(\frac{50}{100}\) of all the marbles. Which decimal is equivalent to \(\frac{50}{100}\)?
Options:
a. 50
b. 5.0
c. 0.50
d. 5,000

Answer:
c. 0.50

Explanation:

Write down 50 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, 0.50 is the answer

Spiral Review

Question 3.
Jesse won his race by 3 \(\frac{45}{100}\) seconds. What is this number written as a decimal?
Options:
a. 0.345
b. 3.45
c. 34.5
d. 345

Answer:
b. 3.45

Explanation:
3 \(\frac{45}{100}\) = \(\frac{345}{100}\). Write down 345 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, 3.45 is the answer

Question 4.
Marge cut 16 pieces of tape for mounting pictures on poster board. Each piece of tape was \(\frac{3}{8}\) inch long. How much tape did Marge use?
Options:
a. 2 inches
b. 4 inches
c. 5 inches
d. 6 inches

Answer:
d. 6 inches

Explanation:
\(\frac{3}{8}\) x 16 = 6 inches

Question 5.
Of Katie’s pattern blocks, \(\frac{9}{12}\) are triangles. What is \(\frac{9}{12}\) in simplest form?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{2}{3}\)
c. \(\frac{3}{4}\)
d. \(\frac{9}{12}\)

Answer:
c. \(\frac{3}{4}\)

Explanation:
\(\frac{9}{12}\) is divided by 3. So, \(\frac{3}{4}\) is the answer.

Question 6.
A number pattern has 75 as its first term. The rule for the pattern is to subtract 6. What is the sixth term?
Options:
a. 39
b. 45
c. 51
d. 69

Answer:
b. 45

Explanation:
75 is the first term.
75 – 6 =69
69 – 6 = 63
63 – 6 = 57
57 – 6 = 51
51 – 6 = 45.
The sixth term is 45.

Page No. 515

Question 1.
Write the amount of money as a decimal in terms of dollars.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 30
5 pennies = \(\frac{5}{100}\) of a dollar = _____ of a dollar.
_____ of a dollar

Answer:
5 pennies = \(\frac{5}{100}\) of a dollar = 0.05 of a dollar.
0.05 of a dollar

Explanation:
Write down 5 with the decimal point 2 spaces from the right (because 100 has 2 zeros). 0.05

Write the total money amount. Then write the amount as a fraction or a mixed number and as a decimal in terms of dollars.

Question 2.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 31
Type below:
_________

Answer:
\(\frac{109}{100}\) = 1.09

Explanation:
1 dollar = 1/10 dimes
1 dollar = 1/100 pennies
1 dollar = 25/100 quarters
(3 x 1/10) + (4 x 1/100) + (3 x 25/100)
3/10 + 4/100 + 75/100
30/100 + 4/100 + 75/100 = 109/100 = 1.09

Question 3.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 32
Type below:
_________

Answer:
\(\frac{60}{100}\) = 0.60

Explanation:
Given that 1 quarter, 2 dimes, and 3 cents.
10 dimes = 1 dollars
100 pennies = 1 dollar
4 quarters = 1 dollar
2 cents = 1 dollar
(25/100) + (2 x 1/10) + (3 x 5/100) = 25/100 + 20/100 + 15/100 = 60/100 = 0.60

Write as a money amount and as a decimal in terms of dollars.

Question 4.
\(\frac{92}{100}\)
amount: _____ decimal: _____of a dollar

Answer:
amount: $0.92 decimal: 0.92 of a dollar

Explanation:
\(\frac{92}{100}\) = 0.92

Question 5.
\(\frac{7}{100}\)
money amount: $ _____ decimal: _____ of a dollar

Answer:
money amount: $0.07 decimal: 0.07 of a dollar

Explanation:
\(\frac{7}{100}\) = 0.07

Question 6.
\(\frac{16}{100}\)
money amount: $ _____ decimal: _____ of a dollar

Answer:
money amount: $0.16 decimal: 0.16 of a dollar

Explanation:
\(\frac{16}{100}\) = 0.16

Question 7.
\(\frac{53}{100}\)
money amount: $ _____ decimal: _____ of a dollar

Answer:
money amount: $0.53 decimal: 0.53 of a dollar

Explanation:
\(\frac{53}{100}\) = 0.53

Write the total money amount. Then write the amount as a fraction or a mixed number and as a decimal in terms of dollars.

Question 8.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 33
Type below:
_________

Answer:
\(\frac{46}{100}\) = 0.46

Explanation:
Given that 3 dimes, 3 nickels, 1 pennies
(3 x 10/100) + (3 x 5/100) + 1/100 = 30/100 + 15/100 + 1/100 = 46/100 = 0.46

Question 9.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 34
Type below:
_________

Answer:
\(\frac{136}{100}\) = 1.36

Explanation:
Given that 1 dollar, 1 quarter, 1 pennies, 2 nickels
1 + 25/100 + 1/100 + (2 x 5/100)
1 + 25/100 + 1/100 + 10/100
1 + 36/100
136/100 = 1.36

Write as a money amount and as a decimal in terms of dollars.

Question 10.
\(\frac{27}{100}\)
money amount: $ _____ decimal: _____ of a dollar

Answer:
amount: $0.27 decimal: 0.27 of a dollar

Explanation:
\(\frac{27}{100}\) = 0.27

Question 11.
\(\frac{4}{100}\)
money amount: $ _____ decimal: _____ of a dollar

Answer:
amount: $0.04 decimal: 0.04 of a dollar

Explanation:
\(\frac{4}{100}\) = 0.04

Go Math Grade 4 Chapter 9 Test Answer Key Question 12.
\(\frac{75}{100}\)
money amount: $ _____ decimal: _____ of a dollar

Answer:
amount: $0.75 decimal: 0.75 of a dollar

Explanation:
\(\frac{75}{100}\) = 0.75

Question 13.
\(\frac{100}{100}\)
money amount: $ _____ decimal:_____ of a dollar

Answer:
money amount: $1 decimal: 1 of a dollar

Explanation:
\(\frac{100}{100}\) = 1

Write the total money amount. Then write the amount as a fraction and as a decimal in terms of dollars.

Question 14.
1 quarter 6 dimes 8 pennies
Type below:
_________

Answer:
money amount: $0.39; fraction: \(\frac{39}{100}\) decimal: 0.39 of a dollar

Explanation:
1 dollar = 100 cents
1 quarter = 25 cents
1 dime = 10 cents
1 penny = 1 cent
1 quarter 6 dimes 8 pennies = (25/100) + (6 x 10/100) + (8 x 1/100)
25/100 + 60/100 + 8/100 = 39/100 = 0.39

Question 15.
3 dimes 5 nickels 20 pennies
Type below:
_________

Answer:
money amount: $0.75; fraction: \(\frac{75}{100}\) decimal: 0.75 of a dollar

Explanation:
1 dollar = 100 cents
1 quarter = 25 cents
1 dime = 10 cents
1 penny = 1 cent
3 dimes 5 nickels 20 pennies = (3 x 10/100) + (5 x 5/100) + (20 x 1/100)
30/100 + 25/100 + 20/100 = 75/100 = 0.75

Page No. 516

Make Connections Algebra Complete to tell the value of each digit.

Question 16.
a.
$1.05 = _____ dollar + _____ pennies;

Answer:
$1.05 = 1 dollar + 5 pennies

Explanation:
grade 4 chapter 9 Relate Fractions and Decimals Image 1 516
$1.05 = 1 dollar and 05 pennies
There are 100 pennies in 1 dollar.
So, $1.05 = 105 pennies.

Question 16.
b.
1.05 = _____ one + _____ hundredths

Answer:
1.05 = 1 one and 05 hundredths

Explanation:
grade 4 chapter 9 Relate Fractions and Decimals Image 2 516
1.05 = 1 one and 05 hundredths
There are 100 hundredths in 1 one.
So, 1.05 = 105 hundredths.

Question 17.
a.
$5.18 = _____ dollars + _____ dime + _____ pennies;

Answer:
$5.18 = 5 dollars + 1 dime + 8 pennies;

Explanation:
grade 4 chapter 9 Relate Fractions and Decimals Image 3 516
$5.18 = 5 dollar and 1 dime and 8 pennies
There are 500 pennies in 5 dollars.
1 dime = 10 pennies
So, $5.18 = 518 pennies.

Question 17.
b.
5.18 = _____ ones + _____ tenth + _____ pennies

Answer:
5.18 = 5 ones + 1 tenths + 8 pennies

Explanation:
grade 4 chapter 9 Relate Fractions and Decimals Image 4 516
5.18 = 5 ones and 1 tenths and 8 pennies
There are 100 hundredths in 1 one. So, 500 hundredths in 5 ones.
So, 5.18 = 518 hundredths.

Use the table for 18–19.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 35

Question 18.
The table shows the coins three students have. Write Nick’s total amount as a fraction in terms of dollars.
\(\frac{□}{□}\) of a dollar

Answer:
\(\frac{92}{100}\) of a dollar

Explanation:
Nick’s total amount = 2 quarters + 4 dimes + 0 Nickels + 2 pennies
= (2 x 25/100) + (4 x 10/100) + (2 x 1/100) = 50/100 + 40/100 + 2/100 = 92/100

Question 19.
Kim spent \(\frac{40}{100}\) of a dollar on a snack. Write as a money amount the amount she has left.
$ _____

Answer:
$0.28

Explanation:
Kim’s total amount = 1 quarter + 3 dimes + 2 nickels + 3 pennies
= 25/100 + (3 x 10/100) + (2 x 5/100) + (3 x 1/100) = 25/100 + 30/100 + 10/100 + 3/100 = 68/100.
Kim spent \(\frac{40}{100}\) of a dollar on a snack. So, 68/100 – 40/100 = 28/100 = 0.28

Question 20.
Travis has \(\frac{1}{2}\) of a dollar. He has at least two different types of coins in his pocket. Draw two possible sets of coins that Travis could have.
Type below:
_________

Answer:
grade 4 chapter 9 Relate Fractions and Decimals Image 6 516

Explanation:
1 Quarter + 2 dimes + 5 Pennies = 25/100 + 10/100 + 10/100 + 5/100 = 50/100 = 1/2 of a dollar
1 Quarter + 2 dimes + 1 Nickel = 25/100 + 10/100 + 10/100 + 5/100 = 50/100 = 1/2 of a dollar

Question 21.
Complete the table.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 36
Type below:
_________

Answer:
grade 4 chapter 9 Relate Fractions and Decimals Image 7 516

Common Core – New – Page No. 517

Relate Fractions, Decimals, and Money

Write the total money amount. Then write the amount as a fraction or a mixed number and as a decimal in terms of dollars.

Question 1.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 37

Answer:
$0.18 = \(\frac{18}{100}\) = 0.18

Explanation:
Given that 3 Pennies + 3 Nickels = 3/100 + 15/100 = 18/100

Question 2.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 38
Type below:
_________

Answer:
$0.56 = \(\frac{56}{100}\) = 0.56

Explanation:
Given that 1 Quarter + 3 dime + 1 Pennies = 25/100 + 30/100 + 1/100 = 56/100

Write as a money amount and as a decimal in terms of dollars.

Question 3.
\(\frac{25}{100}\)
Dollars: _____ Decimal: _____

Answer:
Dollars: 1 quarter = $0.25; Decimal: 0.25

Explanation:
25 our of 100 dollars = 1 quarter.
So, 25/100 = 0.25

Question 4.
\(\frac{79}{100}\)
Dollars: _____ Decimal: _____

Answer:
amount: $0.79 decimal: 0.79 of a dollar

Explanation:
\(\frac{79}{100}\) = 0.79

Question 5.
\(\frac{31}{100}\)
Dollars: _____ Decimal: _____

Answer:
amount: $0.31 decimal: 0.31 of a dollar

Explanation:
\(\frac{31}{100}\) = 0.31

Question 6.
\(\frac{8}{100}\)
Dollars: _____ Decimal: _____

Answer:
amount: $0.08 decimal: 0.08 of a dollar

Explanation:
\(\frac{8}{100}\) = 0.08

Question 7.
\(\frac{42}{100}\)
Dollars: _____ Decimal: _____

Answer:
amount: $0.42 decimal: 0.42 of a dollar

Explanation:
\(\frac{42}{100}\) = 0.42

Write the money amount as a fraction in terms of dollars.

Question 8.
$0.87
\(\frac{□}{□}\)

Answer:
\(\frac{87}{100}\) of a dollar

Explanation:
grade 4 chapter 9 Relate Fractions and Decimals Image 1 517
$0.87 = 87 pennies
There are 100 pennies in 1 dollar.
So, $0.87 = \(\frac{87}{100}\) of a dollar.

Question 9.
$0.03
\(\frac{□}{□}\)

Answer:
\(\frac{3}{100}\)

Explanation:
grade 4 chapter 9 Relate Fractions and Decimals Image 2 517
$0.03 = 3 pennies
There are 100 pennies in 1 dollar.
So, $0.03 = \(\frac{3}{100}\).

Question 10.
$0.66
\(\frac{□}{□}\)

Answer:
\(\frac{66}{100}\)

Explanation:
grade 4 chapter 9 Relate Fractions and Decimals Image 3 517
$0.66 = 66 pennies
There are 100 pennies in 1 dollar.
So, $0.66 = \(\frac{66}{100}\).

Question 11.
$0.95
\(\frac{□}{□}\)

Answer:
\(\frac{95}{100}\)

Explanation:
grade 4 chapter 9 Relate Fractions and Decimals Image 4 517
$0.95 = 95 pennies
There are 100 pennies in 1 dollar.
So, $0.95 = \(\frac{95}{100}\).

Question 12.
$1.00
\(\frac{□}{□}\)

Answer:
\(\frac{100}{100}\)

Explanation:
grade 4 chapter 9 Relate Fractions and Decimals Image 5 517
$1.00 = 1 dollar
There are 100 pennies in 1 dollar.
So, $1.00 = \(\frac{100}{100}\).

Write the total money amount. Then write the amount as a fraction and as a decimal in terms of dollars.

Question 13.
2 quarters 2 dimes
Type below:
_________

Answer:
money amount: $0.70; fraction: \(\frac{70}{100}\); decimal: 0.70

Explanation:
Given that 2 quarters 2 dimes = (2 x 25/100) + (2 x 10/100) = 50/100 + 20/100 = 70/100

Question 14.
3 dimes 4 pennies
Type below:
_________

Answer:
money amount: $0.34; fraction: \(\frac{34}{100}\); decimal: 0.34

Explanation:
Given that 3 dimes 4 pennies = (3 x 10/100) + (4 x 1/100) = 30/100 + 4/100 = 34/100

4th Grade Go Math Pdf Lesson 9.5 Answer Key Question 15.
8 nickels 12 pennies
Type below:
_________

Answer:
money amount: $0.57; fraction: \(\frac{57}{100}\); decimal: 0.57

Explanation:
Given that 8 nickels 12 pennies = (8 x 5/100) + (12 x 1/100) = 45/100 + 12/100 = 57/100

Problem Solving

Question 16.
Kate has 1 dime, 4 nickels, and 8 pennies. Write Kate’s total amount as a fraction in terms of a dollar.
\(\frac{□}{□}\)

Answer:
fraction: \(\frac{38}{100}\)

Explanation:
Kate has 1 dime, 4 nickels, and 8 pennies.
10/100 + (4 x 5/100) + (8/100) = 10/100 + 20/100 + 8/100 = 38/100

Question 17.
Nolan says he has \(\frac{75}{100}\) of a dollar. If he only has 3 coins, what are the coins?
_________

Answer:
3 quarters

Explanation:
3 quarters = \(\frac{25}{100}\) + \(\frac{25}{100}\) + \(\frac{25}{100}\) = \(\frac{75}{100}\)

Common Core – New – Page No. 518

Lesson Check

Question 1.
Which of the following names the total money amount shown as a fraction in terms of a dollar?
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 39
Options:
a. \(\frac{43}{1}\)
b. \(\frac{43}{10}\)
c. \(\frac{43}{57}\)
d. \(\frac{43}{100}\)

Answer:
d. \(\frac{43}{100}\)

Explanation:
Given that 1 quarter + 1 nickel + 1 dime + 3 pennies = 25/100 + 5/100 + 10/100 + 3/100 = 43/100

Question 2.
Crystal has \(\frac{81}{100}\) of a dollar. Which of the following could be the coins Crystal has?
Options:
a. 3 quarters, 1 dime, 1 penny
b. 2 quarters, 6 nickels, 1 penny
c. 2 quarters, 21 pennies
d. 1 quarter, 4 dimes, 1 nickel, 1 penny

Answer:
b. 2 quarters, 6 nickels, 1 penny

Explanation:
2 quarters, 6 nickels, 1 penny = (2 x 25/100) + (6 x 5/100) + 1/100 = 50/100 + 30/100 + 1/100 = 81/100

Spiral Review

Question 3.
Joel gives \(\frac{1}{3}\) of his baseball cards to his sister. Which fraction is equivalent to \(\frac{1}{3}\)?
Options:
a. \(\frac{3}{5}\)
b. \(\frac{2}{6}\)
c. \(\frac{8}{9}\)
d. \(\frac{4}{10}\)

Answer:
b. \(\frac{2}{6}\)

Explanation:
\(\frac{2}{6}\) is divided by 2. The remaining answer after the dividion is \(\frac{1}{3}\).

Question 4.
Penelope bakes pretzels. She salts \(\frac{3}{8}\) of the pretzels. Which fraction is equivalent to \(\frac{3}{8}\)?
Options:
a. \(\frac{9}{24}\)
b. \(\frac{15}{20}\)
c. \(\frac{3}{16}\)
d. \(\frac{1}{5}\)

Answer:
a. \(\frac{9}{24}\)

Explanation:
a. \(\frac{9}{24}\) is divided by 3. The remaining fraction after the division is \(\frac{3}{8}\).

Question 5.
Which decimal is shown by the model?
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 40
Options:
a. 10.0
b. 1.0
c. 0.1
d. 0.01

Answer:
d. 0.01

Explanation:
1 box is shaded out of 100. So, the fraction is 1/100 = 0.01.

Question 6.
Mr. Guzman has 100 cows on his dairy farm. Of the cows, 57 are Holstein. What decimal represents the portion of cows that are Holstein?
Options:
a. 0.43
b. 0.57
c. 5.7
d. 57.0

Answer:
b. 0.57

Explanation:
Mr. Guzman has 100 cows on his dairy farm. Of the cows, 57 are Holstein. So, 57/100 Holstein cows are available.
57/100 = 0.57

Page No. 521

Question 1.
Juan has $3.43. He is buying a paint brush that costs $1.21 to paint a model race car. How much will Juan have after he pays for the paint brush?
First, use bills and coins to model $3.43.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 41
Next, you need to subtract. Remove bills and coins that have a value of $1.21. Mark Xs to show what you remove.
Last, count the value of the bills and coins that are left. How much will Juan have left?
$ _____

Answer:
Juan has $3.43. He is buying a paint brush that costs $1.21 to paint a model race car. Subtract $3.43 – $1.21
grade 4 chapter 9 Relate Fractions and Decimals Image 1 521
2 dollars, 2 dimes, and 2 pennies left.
2 + (2 x 10/100) + (2/100) = 2 + 20/100 + 2/100 = 2 + 22/100 = 2.22.
Juan has left $2.22

Question 2.
What if Juan has $3.43, and he wants to buy a paint brush that costs $2.28? How much money will Juan have left then? Explain.
$ _____

Answer:
$1.15

Explanation:
Juan has $3.43. He wants to buy a paint brush that costs $2.28.
$3.43 – $2.28 = $1.15

Question 3.
Sophia has $2.25. She wants to give an equal amount to each of her 3 young cousins. How much will each cousin receive?
$ _____ each cousin receive

Answer:
$0.75 each cousin receive

Explanation:
Sophia has $2.25. She wants to give an equal amount to each of her 3 young cousins.
Divide $2.25 with 3 = $2.25/3 = $0.75

Page No. 522

Question 4.
Marcus saves $13 each week. In how many weeks will he have saved at least $100?
_____ weeks

Answer:
8 weeks

Explanation:
Marcus saves $13 each week. He saves $100 in $100/$13 weeks = 7.96 weeks that is nearly equal to 8 weeks.

Question 5.
Analyze Relationships Hoshi has $50. Emily has $23 more than Hoshi. Karl has $16 less than Emily. How much money do they have all together?
$ _____

Answer:
$180

Explanation:
Hoshi has $50.
Emily has $23 more than Hoshi = $50 + $23 = $73.
Karl has $16 less than Emily = $73 – $16 = $57.
All together = $50 +$73 + $57 = $180.

Question 6.
Four girls have $5.00 to share equally. How much money will each girl get? Explain.
$ _____ each girl

Answer:
$1.25 for each girl

Explanation:
Four girls have $5.00 to share equally. So, each girl get $5.00/4 = $1.25

Question 7.
What if four girls want to share $5.52 equally? How much money will each girl get? Explain.
$ _____

Answer:
$1.38

Explanation:
Four girls have $5.52 to share equally. So, each girl get $5.52/4 = $1.38. If the amount shares equally, each girl get 1 dollar, 1 dime, 8 pennies.

Question 8.
Aimee and three of her friends have three quarters and one nickel. If Aimee and her friends share the money equally, how much will each person get? Explain how you found your answer.
$ _____

Answer:
$0.2

Explanation:
Aimee and three of her friends have three quarters and one nickel. If Aimee and her friends share the money equally. Four members shared (3 x 25/100) + 5/100 = 75/100 + 5/100 = 80/100 = 0.8.
Four members shared $0.8 equally, $0.8/4 = $0.2.

Common Core – New – Page No. 523

Problem Solving Money

Use the act it out strategy to solve.

Question 1.
Carl wants to buy a bicycle bell that costs $4.50. Carl has saved $2.75 so far. How much more money does he need to buy the bell?
Use 4 $1 bills and 2 quarters to model $4.50. Remove bills and coins that have a value of $2.75. First, remove 2 $1 bills and 2 quarters.
Next, exchange one $1 bill for 4 quarters and remove 1 quarter.
Count the amount that is left. So, Carl needs to save $1.75 more.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 42

Answer:
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 42

Question 2.
Together, Xavier, Yolanda, and Zachary have $4.44. If each person has the same amount, how much money does each person have?
$ __________

Answer:
$1.11

Explanation:
Together, Xavier, Yolanda, and Zachary have $4.44. If each person has the same amount, $4.44/4 = $1.11

Question 3.
Marcus, Nan, and Olive each have $1.65 in their pockets. They decide to combine the money. How much money do they have altogether?
$ __________

Answer:
$4.95

Explanation:
Marcus, Nan, and Olive each have $1.65 in their pockets. They decide to combine the money. So, $1.65 + $1.65 + $1.65 = $4.95

Question 4.
Jessie saves $6 each week. In how many weeks will she have saved at least $50?
__________ weeks

Answer:
9 weeks

Explanation:
Jessie saves $6 each week. To save $50, $50/$6 = 9 weeks (approximately)

Question 5.
Becca has $12 more than Cece. Dave has $3 less than Cece. Cece has $10. How much money do they have altogether?
$ __________

Answer:
$39

Explanation:
Cece has $10.
Becca has $12 more than Cece = $10 + $12 = $22.
Dave has $3 less than Cece = $10 – $3 = $7.
All together = $10 + $22 + $7 = $39.

Common Core – New – Page No. 524

Lesson Check

Question 1.
Four friends earned $5.20 for washing a car. They shared the money equally. How much did each friend get?
Options:
a. $1.05
b. $1.30
c. $1.60
d. $20.80

Answer:
b. $1.30

Explanation:
Four friends earned $5.20 for washing a car. They shared the money equally.
$5.20/4 = $1.30

Question 2.
Which represents the value of one $1 bill and 5 quarters?
Options:
a. $1.05
b. $1.25
c. $1.50
d. $2.25

Answer:
d. $2.25

Explanation:
one $1 bill and 5 quarters. 5 quarters = 5 x 0.25 = 1.25.
$1 + $1.25 = $2.25

Spiral Review

Question 3.
Bethany has 9 pennies. What fraction of a dollar is this?
Options:
a. \(\frac{9}{100}\)
b. \(\frac{9}{10}\)
c. \(\frac{90}{100}\)
d. \(\frac{99}{100}\)

Answer:
a. \(\frac{9}{100}\)

Explanation:
1 dollar = 100 pennies.
So, 9 pennies = 9/100 of a dollar

Question 4.
Michael made \(\frac{9}{12}\) of his free throws at practice. What is \(\frac{9}{12}\) in simplest form?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{3}{9}\)
c. \(\frac{1}{2}\)
d. \(\frac{3}{4}\)

Answer:
d. \(\frac{3}{4}\)

Explanation:
\(\frac{9}{12}\) is divided by 3 that is equal to d. \(\frac{3}{4}\).

Question 5.
I am a prime number between 30 and 40. Which number could I be?
Options:
a. 31
b. 33
c. 36
d. 39

Answer:
a. 31

Explanation:
31 has fractions 1 and 31.

Question 6.
Georgette is using the benchmark \(\frac{1}{2}\) to compare fractions. Which statement is correct?
Options:
a. \(\frac{3}{8}>\frac{1}{2}\)
b. \(\frac{2}{5}<\frac{1}{2}\)
c. \(\frac{7}{12}<\frac{1}{2}\)
d. \(\frac{9}{10}=\frac{1}{2}\)

Answer:
b. \(\frac{2}{5}<\frac{1}{2}\)

Explanation:
From the given details, \(\frac{2}{5}<\frac{1}{2}\) is the correct answer.

Page No. 525

Choose the best term from the box to complete the sentence.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 43

Question 1.
A symbol used to separate the ones and the tenths place is called a __________.
__________

Answer:
decimal point

Question 2.
The number 0.4 is written as a ____________.
__________

Answer:
4 tenths or 40 hundredths

Question 3.
A ______________ is one of one hundred equal parts of a whole.
__________

Answer:
hundredth

Write the fraction or mixed number and the decimal shown by the model.

Question 4.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 44
Type below:
________

Answer:
\(\frac{4}{10}\) = 0.4

Explanation:
From the given model, 4 boxes are shaded out of 10 boxes. So, the fraction is \(\frac{4}{10}\) = 0.4

Question 5.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 45
Type below:
________

Answer:
1\(\frac{3}{100}\) = 1.03

Explanation:
The model is divided into 100 equal parts. Each part represents the one-hundredth.
1\(\frac{3}{100}\) is 1 whole and 3 hundredths.

Write the number as hundredths in fraction form and decimal form.

Question 6.
\(\frac{8}{10}\)
Type below:
________

Answer:
\(\frac{80}{100}\)
grade 4 chapter 9 Relate Fractions and Decimals Image 5 509
0.80

Explanation:
Write \(\frac{8}{10}\) as an equivalent fraction.
\(\frac{8}{10}\) =\(\frac{8 × 10}{10× 10}\) = \(\frac{80}{100}\)
8 tenths is the same as 8 tenths 0 hundredths. So the decimal form = 0.80

Question 7.
0.5
Type below:
________

Answer:
\(\frac{50}{100}\)
grade 4 chapter 9 Relate Fractions and Decimals Image 3 509
0.50

Explanation:
Write 0.5 = \(\frac{5}{10}\) as an equivalent fraction.
\(\frac{5}{10}\) =\(\frac{5 × 10}{10× 10}\) = \(\frac{50}{100}\)
5 tenths is the same as 5 tenths 0 hundredths and also 0.50

Question 8.
Type below:
________

Answer:
b. \(\frac{2}{5}<\frac{1}{2}\)

Explanation:

Write the fraction or mixed number as a money amount, and as a decimal in terms of dollars.

Question 9.
\(\frac{95}{100}\)
amount: $ _____ decimal: _____ of a dollar

Answer:
amount: $0.95; decimal: 0.95

Explanation:
Write down 95 with the decimal point 2 spaces from the right (because 100 has 2 zeros)

Question 10.
1 \(\frac{48}{100}\)
amount: $ _____ decimal: _____ of a dollar

Answer:
amount: $1.48; decimal: 1.48

Explanation:
1\(\frac{48}{100}\) = \(\frac{148}{100}\)
Write down 148 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, 1.48 is the answer

Question 11.
\(\frac{4}{100}\)
amount: $ _____ decimal: _____ of a dollar

Answer:
amount: $0.04; decimal: 0.04

Explanation:
Write down 4 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, the answer is 0.04

Page No. 526

Question 12.
Ken’s turtle competed in a 0.50-meter race. His turtle had traveled \(\frac{4}{100}\)
meter when the winning turtle crossed the finish line. What is \(\frac{4}{100}\) written as a decimal?
_____

Answer:
decimal: 0.04

Explanation:
Write down 4 with the decimal point 2 spaces from the right (because 100 has 2 zeros). So, the answer is 0.04

Question 13.
Alex lives eight tenths of a mile from Sarah. What is eight tenths written as a decimal?
_____

Answer:
decimal: 0.8

Explanation:
Write down 8 with the decimal point 1 space from the right (because 100 has 1 zero). The decimal value of eight-tenths is 0.8

Go Math 4th Grade Lesson 9.6 Answer Key Question 14.
What fraction and decimal, in hundredths, is equivalent to \(\frac{7}{10}\)?
Type below:
________

Answer:
\(\frac{7 x 10}{10 x 10}\) = 0.70

Explanation:
\(\frac{7}{10}\) = \(\frac{7 x 10}{10 x 10}\) = 0.70

Question 15.
Elaine found the following in her pocket. How much money was in her pocket?
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 46
$ _____

Answer:
$\(\frac{140}{100}\)

Explanation:
Given that 1 dollar, 1 quarter, 1 dime, 1 Nickel.
1 + 25/100 + 10/100 + 5/100 = 1 + 40/100 = 140/100

Question 16.
Three girls share $0.60. Each girl gets the same amount. How much money does each girl get?
$ _____

Answer:
$0.20

Explanation:
Three girls share $0.60. Each girl gets the same amount. So, $0.60/3 = $0.20

Question 17.
The deli scale weighs meat and cheese in hundredths of a pound. Sam put \(\frac{5}{10}\) pound of pepperoni on the deli scale. What weight does the deli scale show?
_____ hundredths

Answer:
50 hundredths

Explanation:
\(\frac{5}{10}\) = \(\frac{5 x 10}{10 x 10}\) = \(\frac{50}{100}\).
\(\frac{50}{100}\) written as 50 hundredths.

Page No. 529

Question 1.
Find \(\frac{7}{10}+\frac{5}{100}\)
Think: Write the addends as fractions with a common denominator.
\(\frac{■}{100}\) + \(\frac{■}{100}\) = \(\frac{■}{■}\)
\(\frac{□}{□}\)

Answer:
\(\frac{75}{100}\)

Explanation:
\(\frac{7}{10}+\frac{5}{100}\).
Write the addends as fractions with a common denominator
\(\frac{7}{10}\) = \(\frac{7 X 10}{10 X 10}\) = \(\frac{70}{100}\).
\(\frac{70}{100}+\frac{5}{100}\) = \(\frac{75}{100}\)

Find the sum.

Question 2.
\(\frac{1}{10}+\frac{11}{100}\) = \(\frac{□}{□}\)

Answer:
\(\frac{21}{100}\)

Explanation:
\(\frac{1}{10}+\frac{11}{100}\).
Write the addends as fractions with a common denominator
\(\frac{1}{10}\) = \(\frac{1 X 10}{10 X 10}\) = \(\frac{10}{100}\).
\(\frac{10}{100}+\frac{11}{100}\) = \(\frac{21}{100}\)

Question 3.
\(\frac{36}{100}+\frac{5}{10}\) = \(\frac{□}{□}\)

Answer:
\(\frac{86}{100}\)

Explanation:
\(\frac{36}{100}+\frac{5}{10}\).
Write the addends as fractions with a common denominator
\(\frac{5}{10}\) = \(\frac{5 X 10}{10 X 10}\) = \(\frac{50}{100}\).
\(\frac{36}{100}+\frac{50}{100}\) = \(\frac{86}{100}\).

Question 4.
$0.16 + $0.45 = $ _____

Answer:
$0.61

Explanation:
Think 0.16 as 16 hundredths = \(\frac{16}{100}\).
Think 0.45 as 45 hundredths = \(\frac{45}{100}\).
Write the addends as fractions with a common denominator
\(\frac{16}{100}\) + \(\frac{45}{100}\) = \(\frac{61}{100}\) = 0.61

Question 5.
$0.08 + $0.88 = $ _____

Answer:
$0.96

Explanation:
Think 0.08 as 8 hundredths = \(\frac{8}{100}\).
Think 0.88 as 88 hundredths = \(\frac{88}{100}\).
Write the addends as fractions with a common denominator.
\(\frac{8}{100}\) + \(\frac{88}{100}\) = \(\frac{96}{100}\) = 0.96

Question 6.
\(\frac{6}{10}+\frac{25}{100}\) = \(\frac{□}{□}\)

Answer:
\(\frac{85}{100}[/latex

Explanation:
[latex]\frac{6}{10}+\frac{25}{100}\)
Write the addends as fractions with a common denominator.
\(\frac{6}{10}\) = \(\frac{6 X 10}{10 X 10}\) = \(\frac{60}{100}\).
\(\frac{60}{100}+\frac{25}{100}\) = \(\frac{85}{100}\).

Question 7.
\(\frac{7}{10}+\frac{7}{100}\) = \(\frac{□}{□}\)

Answer:
50 hundredths

Explanation:
\(\frac{7}{10}+\frac{7}{100}\)
Write the addends as fractions with a common denominator.
\(\frac{7}{10}\) = \(\frac{7 X 10}{10 X 10}\) = \(\frac{70}{100}\).
\(\frac{70}{100}+\frac{7}{100}\) = \(\frac{77}{100}\).

Question 8.
$0.55 + $0.23 = $ _____

Answer:
$0.78

Explanation:
Think 0.55 as 55 hundredths = \(\frac{55}{100}\).
Think 0.23 as 23 hundredths = \(\frac{23}{100}\).
Write the addends as fractions with a common denominator.
\(\frac{55}{100}\) + \(\frac{23}{100}\) = \(\frac{78}{100}\) = 0.78.

Question 9.
$0.19 + $0.13 = $ _____

Answer:
$0.32

Explanation:
Think 0.19 as 19 hundredths = \(\frac{19}{100}\).
Think 0.13 as 13 hundredths = \(\frac{13}{100}\).
Write the addends as fractions with a common denominator.
\(\frac{19}{100}\) + \(\frac{13}{100}\) = \(\frac{32}{100}\) = 0.32.

Reason Quantitatively Algebra Write the number that makes the equation true.

Question 10.
\(\frac{20}{100}+\frac{■}{10}\) = \(\frac{60}{100}\)
■ = _____

Answer:
■ = 4

Explanation:
\(\frac{20}{100}+\frac{■}{10}\) = \(\frac{60}{100}\).
Let the unknown number = s.
If s = 4,
\(\frac{20}{100}+\frac{4}{10}\).
Write the addends as fractions with a common denominator.
\(\frac{4}{10}\) = \(\frac{4 X 10}{10 X 10}\) = \(\frac{40}{100}\).
\(\frac{20}{100}+\frac{40}{100}\) = \(\frac{60}{100}\).
So, the unknown number is 4.

Question 11.
\(\frac{2}{10}+\frac{■}{100}\) = \(\frac{90}{100}\)
■ = _____

Answer:
■ = 70

Explanation:
\(\frac{2}{10}+\frac{■}{100}\) = \(\frac{90}{100}\).
Let the unknown number = s.
If s = 70,
\(\frac{2}{10}+\frac{7}{100}\).
Write the addends as fractions with a common denominator.
\(\frac{2}{10}\) = \(\frac{2 X 10}{10 X 10}\) = \(\frac{20}{100}\).
\(\frac{20}{100}+\frac{70}{100}\) = \(\frac{90}{100}\).
So, the unknown number is 70.

Question 12.
Jerry had 1 gallon of ice cream. He used \(\frac{3}{10}\) gallon to make chocolate milkshakes and 0.40 gallon to make vanilla milkshakes. How much ice cream does Jerry have left after making the milkshakes?
_____ gallon

Answer:
0.30 gallon

Explanation:
Jerry had 1 gallon of ice cream. He used \(\frac{3}{10}\) gallon to make chocolate milkshakes and 0.40 gallon to make vanilla milkshakes.
So, write 0.40 as \(\frac{40}{100}\) gallon.
She used \(\frac{3}{10}\) + \(\frac{40}{100}\).
\(\frac{3}{10}\) = \(\frac{3 X 10}{10 X 10}\) = \(\frac{30}{100}\).
\(\frac{30}{100}\) + \(\frac{40}{100}\) = \(\frac{70}{100}\)
Jerry have left 1 – \(\frac{70}{100}\) = \(\frac{30}{100}\) = 0.30 gallon

Page No. 530

Use the table for 13−16.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 47

Question 13.
Dean selects Teakwood stones and Buckskin stones to pave a path in front of his house. How many meters long will each set of one Teakwood stone and one Buckskin stone be?
_____ meter

Answer:
\(\frac{71}{100}\) meter

Explanation:
Dean selects Teakwood stones and Buckskin stones to pave a path in front of his house.
Teakwood stone and one Buckskin stone = \(\frac{3}{10}\) + \(\frac{41}{100}\).
Write the addends as fractions with a common denominator.
\(\frac{3}{10}\) = \(\frac{3 X 10}{10 X 10}\) = \(\frac{30}{100}\).
\(\frac{30}{100}\) + \(\frac{41}{100}\) = \(\frac{71}{100}\)

Go Math 4th Grade Lesson 9.7 Compare Decimals Question 14.
The backyard patio at Nona’s house is made from a repeating pattern of one Rose stone and one Rainbow stone. How many meters long is each pair of stones?
_____ meter

Answer:
\(\frac{68}{100}\) meter

Explanation:
The backyard patio at Nona’s house is made from a repeating pattern of one Rose stone and one Rainbow stone.
Each pair of stone = \(\frac{8}{100}\) + \(\frac{6}{10}\).
\(\frac{6}{10}\) = \(\frac{6 X 10}{10 X 10}\) = \(\frac{60}{100}\).
Each pair of stone = \(\frac{8}{100}\) + \(\frac{60}{100}\) = \(\frac{68}{100}\).

Question 15.
For a stone path, Emily likes the look of a Rustic stone, then a Rainbow stone, and then another Rustic stone. How long will the three stones in a row be? Explain.
_____ meter

Answer:
\(\frac{90}{100}\) meter

Explanation:
For a stone path, Emily likes the look of a Rustic stone, then a Rainbow stone, and then another Rustic stone. If three stones in a row, then
\(\frac{15}{100}\) + \(\frac{6}{10}\) + \(\frac{15}{100}\).
\(\frac{30}{100}\) + \(\frac{6}{10}\).
\(\frac{6}{10}\) = \(\frac{6 X 10}{10 X 10}\) = \(\frac{60}{100}\).
\(\frac{30}{100}\) + \(\frac{60}{100}\) = \(\frac{90}{100}\).

Question 16.
Which two stones can you place end-to-end to get a length of 0.38 meter? Explain how you found your answer.
Type below:
________

Answer:
If you add Teakwood stones and Rose stones, then you get a length of 0.38 meter.
\(\frac{3}{10}\) + \(\frac{8}{100}\).
\(\frac{3}{10}\) = \(\frac{3 X 10}{10 X 10}\) = \(\frac{30}{100}\).
\(\frac{30}{100}\) + \(\frac{8}{100}\) = latex]\frac{38}{100}[/latex] = 0.38.
If you add any other two stones, the answer will not equal to 0.38.

Question 17.
Christelle is making a dollhouse. The dollhouse is \(\frac{6}{10}\) meter tall without the roof. The roof is \(\frac{15}{100}\) meter high. What is the height of the dollhouse with the roof? Choose a number from each column to complete an equation to solve.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 48
\(\frac{□}{□}\) meter

Answer:
\(\frac{60}{100}\) + \(\frac{15}{100}\) = \(\frac{75}{100}\) meter

Explanation:
\(\frac{6}{10}\) + \(\frac{15}{100}\).
\(\frac{6}{10}\) = \(\frac{6 X 10}{10 X 10}\) = \(\frac{60}{100}\).
\(\frac{60}{100}\) + \(\frac{15}{100}\) = \(\frac{75}{100}\).

Common Core – New – Page No. 531

Add Fractional Parts of 10 and 100

Find the sum.

Question 1.
\(\frac{2}{10}+\frac{43}{100}\) Think: Write \(\frac{2}{10}\) as a fraction with a denominator of 100: \(\frac{2 \times 10}{10 \times 10}=\frac{20}{100}\)
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 49

Answer:
\(\frac{63}{100}\)

Explanation:
Think: Write \(\frac{2}{10}\) as a fraction with a denominator of 100: \(\frac{2 \times 10}{10 \times 10}=\frac{20}{100}\)
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 49

Question 2.
\(\frac{17}{100}+\frac{6}{10}\)
\(\frac{□}{□}\)

Answer:
\(\frac{77}{100}\)

Explanation:
\(\frac{17}{100}+\frac{6}{10}\).
\(\frac{6 \times 10}{10 \times 10}=\frac{60}{100}\)
\(\frac{17}{100}+\frac{60}{100}\) = \(\frac{77}{100}\)

Question 3.
\(\frac{9}{100}+\frac{4}{10}\)
\(\frac{□}{□}\)

Answer:
\(\frac{49}{100}\)

Explanation:
\(\frac{9}{100}+\frac{4}{10}\).
\(\frac{4 \times 10}{10 \times 10}=\frac{40}{100}\)
\(\frac{9}{100}+\frac{40}{100}\) = \(\frac{49}{100}\)

Question 4.
\(\frac{7}{10}+\frac{23}{100}\)
\(\frac{□}{□}\)

Answer:
\(\frac{93}{100}\)

Explanation:
\(\frac{7}{10}+\frac{23}{100}\).
\(\frac{7 \times 10}{10 \times 10}=\frac{70}{100}\)
\(\frac{70}{100}+\frac{23}{100}\) = \(\frac{93}{100}\)

Question 5.
$0.48 + $0.30
$ _____

Answer:
$0.78

Explanation:
Think $0.48 as \(\frac{48}{100}\).
Think $0.30 as \(\frac{30}{100}\).
\(\frac{48}{100}+\frac{30}{100}\) = \(\frac{78}{100}\) = $0.78

Question 6.
$0.25 + $0.34
$ _____

Answer:
$0.59

Explanation:
Think $0.25 as \(\frac{25}{100}\).
Think $0.34 as \(\frac{34}{100}\).
\(\frac{25}{100}+\frac{34}{100}\) = \(\frac{59}{100}\) = $0.59

Question 7.
$0.66 + $0.06
$ _____

Answer:
$0.72

Explanation:
Think $0.66 as \(\frac{66}{100}\).
Think $0.06 as \(\frac{6}{100}\).
\(\frac{66}{100}+\frac{6}{100}\) = \(\frac{72}{100}\) = $0.72

Problem Solving

Question 8.
Ned’s frog jumped \(\frac{38}{100}\) meter. Then his frog jumped \(\frac{4}{10}\) meter. How far did Ned’s frog jump in all?
\(\frac{□}{□}\)

Answer:
\(\frac{78}{100}\) meter

Explanation:
Ned’s frog jumped \(\frac{38}{100}\) meter. Then his frog jumped \(\frac{4}{10}\) meter.
So, together \(\frac{38}{100}\) + \(\frac{4}{10}\) jumped.
\(\frac{4}{10}\) = \(\frac{4 \times 10}{10 \times 10}=\frac{40}{100}\).
\(\frac{38}{100}\) + \(\frac{40}{100}\) = \(\frac{78}{100}\).

Question 9.
Keiko walks \(\frac{5}{10}\) kilometer from school to the park. Then she walks \(\frac{19}{100}\) kilometer from the park to her home. How far does Keiko walk in all?
\(\frac{□}{□}\)

Answer:
\(\frac{69}{100}\) kilometer

Explanation:
Keiko walks \(\frac{5}{10}\) kilometer from school to the park. Then she walks \(\frac{19}{100}\) kilometer from the park to her home.
Total = \(\frac{5}{10}\) + \(\frac{19}{100}\) kilometer.
\(\frac{5}{10}\) = \(\frac{5 \times 10}{10 \times 10}=\frac{50}{100}\).
\(\frac{50}{100}\) + \(\frac{19}{100}\) = \(\frac{69}{100}\).

Common Core – New – Page No. 532

Lesson Check

Question 1.
In a fish tank, \(\frac{2}{10}\) of the fish were orange and \(\frac{5}{100}\) of the fish were striped. What fraction of the fish were orange or striped?
Options:
a. \(\frac{7}{10}\)
b. \(\frac{52}{100}\)
c. \(\frac{25}{100}\)
d. \(\frac{7}{100}\)

Answer:
c. \(\frac{25}{100}\)

Explanation:
In a fish tank, \(\frac{2}{10}\) of the fish were orange and \(\frac{5}{100}\) of the fish were striped.
To find the raction of the fish were orange or striped Add \(\frac{2}{10}\) and \(\frac{5}{100}\).
\(\frac{2}{10}\) = \(\frac{2 \times 10}{10 \times 10}=\frac{20}{100}\).
\(\frac{20}{100}\) + \(\frac{5}{100}\) = \(\frac{25}{100}\).

Question 2.
Greg spends $0.45 on an eraser and $0.30 on a pen. How much money does Greg spend in all?
Options:
a. $3.45
b. $0.75
c. $0.48
d. $0.15

Answer:
b. $0.75

Explanation:
Think $0.45 as \(\frac{45}{100}\).
Think $0.30 as \(\frac{30}{100}\).
\(\frac{45}{100}+\frac{30}{100}\) = \(\frac{75}{100}\) = $0.75.

Spiral Review

Question 3.
Phillip saves $8 each month. How many months will it take him to save at least $60?
Options:
a. 6 months
b. 7 months
c. 8 months
d. 9 months

Answer:
c. 8 months

Explanation:
Phillip saves $8 each month.
To save at least $60, \(\frac{60}{8}\) = 8 months (approximately)

Question 4.
Ursula and Yi share a submarine sandwich. Ursula eats \(\frac{2}{8}\) of the sandwich. Yi eats \(\frac{3}{8}\) of the sandwich. How much of the sandwich do the two friends eat?
Options:
a. \(\frac{1}{8}\)
b. \(\frac{4}{8}\)
c. \(\frac{5}{8}\)
d. \(\frac{6}{8}\)

Answer:
c. \(\frac{5}{8}\)

Explanation:
Ursula and Yi share a submarine sandwich. Ursula eats \(\frac{2}{8}\) of the sandwich. Yi eats \(\frac{3}{8}\) of the sandwich.
Two friends eat \(\frac{2}{8}\) + \(\frac{3}{8}\) = \(\frac{5}{8}\)

Question 5.
A carpenter has a board that is 8 feet long. He cuts off two pieces. One piece is 3 \(\frac{1}{2}\) feet long and the other is 2 \(\frac{1}{3}\) feet long. How much of the board is left?
Options:
a. 2 \(\frac{1}{6}\)
b. 2 \(\frac{5}{6}\)
c. 3 \(\frac{1}{6}\)
d. 3 \(\frac{5}{6}\)

Answer:
a. 2 \(\frac{1}{6}\)

Explanation:
3 \(\frac{1}{2}\) = \(\frac{7}{2}\).
2 \(\frac{1}{3}\) = \(\frac{7}{3}\).
A carpenter has a board that is 8 feet long. He cuts off two pieces. One piece is 3 \(\frac{1}{2}\) feet long and the other is 2 \(\frac{1}{3}\) feet long.
\(\frac{7}{2}\) + \(\frac{7}{3}\) = \(\frac{7 \times 3}{2\times 3} + [latex]\frac{7 \times 2}{3\times 2} = [latex]\frac{21}{6}\) + \(\frac{14}{6}\) = \(\frac{35}{6}\) = 5\(\frac{5}{6}\).
He left 8 – 5\(\frac{5}{6}\).
7\(\frac{6}{6}\) – 5\(\frac{5}{6}\) = 2\(\frac{1}{6}\)

Question 6.
Jeff drinks \(\frac{2}{3}\) of a glass of juice. Which fraction is equivalent to \(\frac{2}{3}\)?
Options:
a. \(\frac{1}{3}\)
b. \(\frac{3}{2}\)
c. \(\frac{3}{6}\)
d. \(\frac{8}{12}\)

Answer:
d. \(\frac{8}{12}\)

Explanation:
\(\frac{8}{12}\) is divided by 4. So, \(\frac{8}{12}\) = \(\frac{2}{3}\).

Page No. 535

Question 1.
Compare 0.39 and 0.42. Write <, >, or =.
Shade the model to help.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 50
0.39 ____ 0.42

Answer:
grade 4 chapter 9 Relate Fractions and Decimals Image 1 535
0.39 < 0.42

Compare. Write <, >, or =.

Question 2.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 51
0.26 ____ 0.23

Answer:
0.26 > 0.23

Explanation:
grade 4 chapter 9 Relate Fractions and Decimals Image 2 535
The digits in the one’s and tenths place are the same. Compare the digits in the hundredths place. 6 > 3. So, 0.26 > 0.23.

Question 3.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 52
0.7 ____ 0.54

Answer:
0.7 > 0.54

Explanation:
grade 4 chapter 9 Relate Fractions and Decimals Image 3 535
The digits in the ones place are the same. Compare the digits in the tenths place. 0.7 = 0.70. 7 > 5. So, 0.70 > 0.54.

Question 4.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 53
1.15 ____ 1.3

Answer:
1.15 < 1.3

Explanation:
grade 4 chapter 9 Relate Fractions and Decimals Image 4 535
The digits in the ones place are the same. Compare the digits in the tenths place. 1 < 3. So, 1.15 < 1.3

Question 5.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 54
4.5 ____ 2.89

Answer:
4.5 > 2.89

Explanation:
grade 4 chapter 9 Relate Fractions and Decimals Image 5 535
Compare one’s digits. 4 > 2 . So, 4.5 > 2.89

Compare. Write <, >, or =.

Question 6.
0.9 ____ 0.81

Answer:
0.9 > 0.81

Explanation:
0.9 is 9 tenths, which is equivalent to 90 hundredths.
0.81 is 81 hundredths.
90 hundredths > 81 hundredths. So, 0.9 > 0.81.

Question 7.
1.06 ____ 0.6

Answer:
1.06 > 0.6

Explanation:
1.06 is 106 hundredths.
0.6 is 6 tenths, which is equivalent to 60 hundredths.
106 hundredths > 60 hundredths. So, 1.06 > 0.6.

Question 8.
0.25 ____ 0.3

Answer:
0.25 < 0.3

Explanation:
0.25 is 25 hundredths.
0.3 is 3 tenths, which is equivalent to 30 hundredths.
25 hundredths < 30 hundredths. So, 0.25 < 0.3.

Question 9.
2.61 ____ 3.29

Answer:
2.61 < 3.29

Explanation:
2.61 is 261 hundredths.
3.29 is 329 hundredths.
261 hundredths < 329 hundredths. So, 2.61 < 3.29.

Reason Quantitatively Compare. Write <, >, or =.

Question 10.
0.30 ____ \(\frac{3}{10}\)

Answer:
0.30 = \(\frac{3}{10}\)

Explanation:
0.30 is 30 hundredths.
\(\frac{3}{10}\) is 3 tenths, which is equal to 30 hundredths.
30 hundredths = 30 hundredths. So, 0.30 = \(\frac{3}{10}\).

Question 11.
\(\frac{4}{100}\) ____ 0.2

Answer:
\(\frac{4}{100}\) < 0.2

Explanation:
\(\frac{4}{100}\) is 4 hundredths.
0.2 is 2 tenths, which is equal to 20 hundredths.
4 hundredths < 20 hundredths. So, \(\frac{4}{100}\) < 0.2

Question 12.
0.15 ____ \(\frac{1}{10}\)

Answer:
0.15 > \(\frac{1}{10}\)

Explanation:
0.15 is 15 hundredths.
\(\frac{1}{10}\) is 1 tenths, which is equal to 10 hundredths.
15 hundredths > 10 hundredths. So, 0.15 > \(\frac{1}{10}\).

Question 13.
\(\frac{1}{8}\) ____ 0.8

Answer:
latex]\frac{1}{8}[/latex] < 0.8

Explanation:
\(\frac{1}{8}\) = 0.25 is 25 hundredths.
0.8 is 8 tenths, which is equal to 80 hundredths.
25 hundredths < 80 hundredths. So, \(\frac{1}{8}\) < 0.8

Question 14.
Robert had $14.53 in his pocket. Ivan had $14.25 in his pocket. Matt had $14.40 in his pocket. Who had more money, Robert or Matt? Did Ivan have more money than either Robert or Matt?
________

Answer:
Robert had more money.
No, Ivan didn’t have more money than either Robert or Matt.

Explanation:
Compare Robert, Ivan, and Matt money to know who had more money.
The digits in the one’s place are the same. Compare the digits in the tenths place. 5 > 4 > 2. So, Robert had more money.

Page No. 536

Question 15.
Ricardo and Brandon ran a 1500-meter race. Ricardo finished in 4.89 minutes. Brandon finished in 4.83 minutes. What was the time of the runner who finished first?
a. What are you asked to find?–
Type below:
________

Answer:
The time of the runner who finished first.

Question 15.
b. What do you need to do to find the answer?
Type below:
________

Answer:
I have to compare the times to find the time that is less.

Question 15.
c. Solve the problem.
Type below:
________

Answer:
Use place-value chart
grade 4 chapter 9 Relate Fractions and Decimals Image 1 536
The digits of the one’s and tenths are equal. So, compare hundredths to find greater time.
9 > 3.
4.83 minutes are less than 4.89.

Question 15.
d. What was the time of the runner who finished first?
______ minutes

Answer:
4.83 minutes

Question 15.
e. Look back. Does your answer make sense? Explain.
_____

Answer:
Yes. The time of the runner who finished first is the lesser time of the two. Since 4.83, 4.89, then 4.83 minutes is the time of the runner who finished first.

Question 16.
The Venus flytrap closes in 0.3 second and the waterwheel plant closes in 0.2 second. What decimal is halfway between 0.2 and 0.3? Explain.
_____

Answer:
0.2 is 2 tenths, which is equal to the 20 hundredths.
0.3 is 3 tenths, which is equal to 30 hundredths.
The halfway between 20 hundredths and 30 hundredths is 25 hundredths.
So, the answer is 0.25.

Question 17.
For numbers 17a–17c, select True or False for the inequality.
a. 0.5 > 0.53
i. True
ii. False

Answer:
ii. False

Explanation:
0.5 is 50 hundredths.
0.53 is 53 hundredths.
50 hundredths < 53 hundredths. So, 0.5 < 0.53. So, the answer is false.

Question 17.
b. 0.35 < 0.37
i. True
ii. False

Answer:
i. True

Explanation:
0.35 is 35 hundredths.
0.37 is 37 hundredths.
35 hundredths < 37 hundredths.
0.35 < 0.37.
So, the answer is true.

Question 17. c. $1.35 > $0.35
i. True
ii. False

Answer:
i. True

Explanation:
$1.35 is 135 hundredths.
$0.35 is 35 hundredths.
135 hundredths > 35 hundredths.
$1.35 > $0.35.
So, the answer is correct.

Common Core – New – Page No. 537

Compare Decimals

Compare. Write <. >, or =.

Question 1.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 55
Think: 3 tenths is less than 5 tenths. So, 0.35 < 0.53

Answer:
0.35 < 0.53

Explanation:
3 tenths is less than 5 tenths. So, 0.35 < 0.53

Question 2.
0.6 ______ 0.60

Answer:
0.6 = 0.60

Explanation:
0.6 is 6 tenths can write as 6 tenths and 0 hundredths. So, 0.6 = 0.60.

Question 3.
0.24 ______ 0.31

Answer:
0.24 < 0.31

Explanation:
2 tenths is less than 3 tenths. So, 0.24 < 0.31.

Question 4.
0.94 ______ 0.9

Answer:
0.94 > 0.9

Explanation:
The digits of tenths are equal. So, compare hundredths. 4 hundredths is greater than 0 hundredths. So, 0.94 > 0.9.

Go Math 4th Grade Chapter 9 Test Answer Key Question 5.
0.3 ______ 0.32

Answer:
0.3 < 0.32

Explanation:
The digits of tenths are equal. So, compare hundredths. 0 hundredths is less than 2 hundredths. So, 0.3 < 0.32.

Question 6.
0.45 ______ 0.28

Answer:
0.45 > 0.28

Explanation:
4 tenths is greater than 2 tenths. So, 0.45 > 0.28.

Question 7.
0.39 ______ 0.93

Answer:
0.39 < 0.93

Explanation:
3 tenths is less than 9 tenths. So, 0.39 < 0.93.

Use the number line to compare. Write true or false.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals Common Core - New img 56

Question 8.
0.8 > 0.78
______

Answer:
true

Explanation:
0.78 is in between 0.7 and 0.8 that is less than 0.8. So, 0.8 > 0.78.

Question 9.
0.4 > 0.84
______

Answer:
false

Explanation:
0.4 is less than 0.84 and the left side of the number line. So, 0.4 < 0.84. The answer is false.

Question 10.
0.7 > 0.70
______

Answer:
false

Explanation:
0.7 is 7 tenths and 70 hundredths. 0.7 = 0.70. So, the answer is false.

Question 11.
0.4 > 0.04
______

Answer:
true

Explanation:
0.04 is less than 0.4 and it is left side of the 0.1 on the number line. 0.1 is less than 0.4. So, the given answer is true.

Compare. Write true or false.

Question 12.
0.09 > 0.1
______

Answer:
false

Explanation:
0 tenths is less than 1 tenths. So, 0.09 < 0.1. So, the answer is false.

Question 13.
0.24 = 0.42
______

Answer:
false

Explanation:
2 tenths is less than 4 tenths. So, 0.24 < 0.42. So, the answer is false.

Question 14.
0.17 < 0.32 ______

Answer:
true

Explanation:
1 tenths is less than 3 tenths. So, 0.17 < 0.32. So, the answer is true.

Question 15.
0.85 > 0.82
______

Answer:
true

Explanation:
The digits of tenths are equal. So, compare hundredths. 5 hundredths is greater than 2 hundredths. So, 0.85 > 0.82.

Question 16.
Kelly walks 0.7 mile to school. Mary walks 0.49 mile to school. Write an inequality using <, > or = to compare the distances they walk to school.
0.7 ______ 0.49

Answer:
0.7 > 0.49

Explanation:
7 tenths is greater than 4 tenths. So, 0.7 > 0.49.

Question 17.
Tyrone shades two decimal grids. He shades 0.03 of the squares on one grid blue. He shades 0.3 of another grid red. Which grid has the greater part shaded?
0.03 ______ 0.3

Answer:
0.03 < 0.3

Explanation:
0.03 is 3 hundredths.
0.3 is 3 tenths, which is equal to 30 hundredths.
3 hundredths < 30 hundredths. So, 0.03 < 0.3.

Common Core – New – Page No. 538

Lesson Check

Question 1.
Bob, Cal, and Pete each made a stack of baseball cards. Bob’s stack was 0.2 meter high. Cal’s stack was 0.24 meter high. Pete’s stack was 0.18 meter high.
Which statement is true?
Options:
a. 0.02 > 0.24
b. 0.24 > 0.18
c. 0.18 > 0.2
d. 0.24 = 0.2

Answer:
b. 0.24 > 0.18

Explanation:
2 tenths is greater than 1 tenth. So, 0.24 > 0.18.

Question 2.
Three classmates spent money at the school supplies store. Mark spent 0.5 dollar, Andre spent 0.45 dollar, and Raquel spent 0.52 dollar. Which
statement is true?
Options:
a. 0.45 > 0.5
b. 0.52 < 0.45
c. 0.5 = 0.52
d. 0.45 < 0.5

Answer:
d. 0.45 < 0.5

Explanation:
4 tenths is less than 5 tenth. So, 0.45 > 0.5.

Spiral Review

Question 3.
Pedro has $0.35 in his pocket. Alice has $0.40 in her pocket. How much money do Pedro and Alice have in their pockets altogether?
Options:
a. $0.05
b. $0.39
c. $0.75
d. $0.79

Answer:
c. $0.75

Explanation:
Pedro has $0.35 in his pocket. Alice has $0.40 in her pocket.
Together = $0.35 + $0.40 = $0.75.

Question 4.
The measure 62 centimeters is equivalent to \(\frac{62}{100}\) meter. What is this measure written as a decimal?
Options:
a. 62.0 meters
b. 6.2 meters
c. 0.62 meter
d. 0.6 meter

Answer:
c. 0.62 meter

Explanation:
\(\frac{62}{100}\) = 0.62 meter.

Question 5.
Joel has 24 sports trophies. Of the trophies, \(\frac{1}{8}\) are soccer trophies. How many soccer trophies does Joel have?
Options:
a. 2
b. 3
c. 4
d. 6

Answer:
b. 3

Explanation:
Joel has 24 sports trophies. Of the trophies, \(\frac{1}{8}\) are soccer trophies.
So, \(\frac{1}{8}\) X 24 = 3 soccer trophies.

Question 6.
Molly’s jump rope is 6 \(\frac{1}{3}\) feet long. Gail’s jump rope is 4 \(\frac{2}{3}\) feet long. How much longer is Molly’s jump rope?
Options:
a. 1 \(\frac{1}{3}\) feet
b. 1 \(\frac{2}{3}\) feet
c. 2 \(\frac{1}{3}\) feet
d. 2 \(\frac{2}{3}\) feet

Answer:
b. 1 \(\frac{2}{3}\) feet

Explanation:
6 \(\frac{1}{3}\) feet = \(\frac{19}{3}\) feet.
4 \(\frac{2}{3}\) feet = \(\frac{14}{3}\) feet.
\(\frac{19}{3}\) – \(\frac{14}{3}\) = \(\frac{5}{3}\) feet = b. 1 \(\frac{2}{3}\) feet.

Page No. 539

Question 1.
Select a number shown by the model. Mark all that apply.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 57
Type below:
________

Answer:
1 \(\frac{4}{10}\) = \(\frac{14}{10}\) = 1.4

Explanation:
from the given image, there is one whole number and \(\frac{4}{10}\) of another model. So, 1 \(\frac{4}{10}\) = \(\frac{14}{10}\) = 1.4

Question 2.
Rick has one dollar and twenty-seven cents to buy a notebook. Which names this money amount in terms of dollars? Mark all that apply.
Options:
a. 12.7
b. 1.027
c. $1.27
d. 1.27
e. 1 \(\frac{27}{100}\)
f. \(\frac{127}{10}\)

Answer:
c. $1.27
d. 1.27
e. 1 \(\frac{27}{100}\)

Explanation:
one dollar and twenty-seven cents = 1 \(\frac{27}{100}\) = 1.27 = $1.27

Question 3.
For numbers 3a–3e, select True or False for the statement.
a. 0.9 is equivalent to 0.90.
i. True
ii. False

Answer:
i. True

Explanation:
0.9 is 9 tenths, which is equal to 90 hundredths. 0.9 = 0.90. So, the answer is true.

Question 3.
b. 0.20 is equivalent to \(\frac{2}{100}\)
i. True
ii. False

Answer:
ii. False

Explanation:
\(\frac{2}{100}\) = 0.02. So, the given answer is false.

Question 3.
c. \(\frac{80}{100}\) is equivalent to \(\frac{8}{10}\).
i. True
ii. False

Answer:
i. True

Explanation:
Divide \(\frac{80}{100}\) by 10 = \(\frac{8}{10}\). So, the answer is true.

Question 3.
d. \(\frac{6}{10}\) is equivalent to 0.60.
i. True
ii. False

Answer:
i. True

Explanation:
\(\frac{6}{10}\) is 0.6. 0.6 is 6 tenths, which is equal to 6 tenths and 0 hundredths. 0.60. So, 0.6 =0.60. The answer is true.

Question 3.
e. 0.3 is equivalent to \(\frac{3}{100}\)
i. True
ii. False

Answer:
ii. False

Explanation:
0.3 is 3 tenths, which is equal to 3 tenths and 0 hundredths. \(\frac{3}{100}\) is 0 tenths. So, the answer is false.

Page No. 540

Question 4.
After selling some old books and toys, Gwen and her brother Max had 5 one-dollar bills, 6 quarters, and 8 dimes. They agreed to divide the money equally.
Part A
Wat is the total amount of money that Gwen and Max earned?
Explain.
$ _____

Answer:
$7.30

Explanation:
After selling some old books and toys, Gwen and her brother Max had 5 one-dollar bills, 6 quarters, and 8 dimes.
5 + (6 X 25/100) + (8 X 10/100) = 5 + 150/100 + 80/100 = 5 + 230/100 = 730/100 = 7.30

Question 4.
Part B
Max said that he and Gwen cannot get equal amounts of money because 5 one-dollar bills cannot be divided evenly. Do you agree with Max?
Explain.
_____

Answer:
ii. False

Explanation:
No; they can share the 3 quarters and 4 dimes each. Then, they can change the 5 dollar bills into quarters. 1 dollar = 4 quarters. So, 5 dollars = 5 X 4 or 20 quarters. They can each get 10 quarters. So, each person has a total of 13 quarters and 4 dimes. $3.25 + $0.40 = $3.65

Question 5.
Harrison rode his bike \(\frac{6}{10}\) of a mile to the park. Shade the model. Then write the decimal to show how far Harrison rode his bike.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 58
Harrison rode his bike _______ mile to the park.
_____

Answer:
grade 4 chapter 9 Relate Fractions and Decimals Image 1 540
Harrison rode his bike 0.6 mile to the park.

Explanation:
6 boxes are shaded out of 10.

Question 6.
Amaldo spent \(\frac{88}{100}\) of a dollar on a souvenir pencil from Zion National Park in Utah. What is \(\frac{88}{100}\) written as a decimal in terms of dollars?
_____

Answer:
0.88

Explanation:
Write down 88 with the decimal point 2 spaces from the right (because 100 has 2 zeros). 0.88

Question 7.
Tran has $5.82. He is saving for a video game that costs $8.95.
Tran needs _______ more to have enough money for the game.
_____

Answer:
$3.13

Explanation:
Tran has $5.82. He is saving for a video game that costs $8.95. To know more amount need to buy a video game = $8.95 – $5.82 = $3.13

Page No. 541

Question 8.
Cheyenne lives \(\frac{7}{10}\) mile from school. A fraction in hundredths equal to \(\frac{7}{10}\) is
\(\frac{□}{□}\)

Answer:
\(\frac{70}{100}\)

Explanation:
\(\frac{7}{10}\) = \(\frac{7 \times 10}{10 \times 10}\) = \(\frac{70}{100}\)

Question 9.
Write a decimal in tenths that is less than 2.42 but greater than 2.0.
Type below:
__________

Answer:
2.1, 2.2, 2.3, 2.4

Explanation:
The decimal in greater than 2.0 and below the 2.4 are 2.1, 2.2, 2.3, 2.4

Question 10.
Kylee and two of her friends are at a museum. They find two quarters and one dime on the ground.
Part A
If Kylee and her friends share the money equally, how much will each person get? Explain how you found your answer.
$ _____
Explain:
__________

Answer:
$0.20; Two quarters and one dime are equal to $0.50 + $0.10 = $0.60. Take $0.60 as 6 dimes. When 6 dimes divide equally, each person will receive 2 dimes or $0.20.

Question 10.
Part B
Kylee says that each person will receive \(\frac{2}{10}\) of the money that was found. Do you agree? Explain.
__________

Answer:
No; Each person receives $0.20, which is 2/10 of a dollar, not 2/10 of the money that was found. Since there are 3 people who share the money equally, each person will receive 1/3 of the money.

Question 11.
Shade the model to show 1 \(\frac{52}{100}\). Then write the mixed number in decimal form.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 59
_____

Answer:
grade 4 chapter 9 Relate Fractions and Decimals Image 2 541
1.52

Page No. 542

Question 12.
Henry is making a recipe for biscuits. A recipe calls for \(\frac{5}{10}\) kilogram flour and \(\frac{9}{100}\) kilogram sugar.
Part A
If Henry measures correctly and combines the two amounts, how much flour and sugar will he have? Show your work.
\(\frac{□}{□}\) kilogram

Answer:
\(\frac{59}{100}\) kilogram

Explanation:
Henry is making a recipe for biscuits. A recipe calls for \(\frac{5}{10}\) kilogram flour and \(\frac{9}{100}\) kilogram sugar. So, add \(\frac{5}{10}\) kilogram flour and \(\frac{9}{100}\) kilogram flour.
\(\frac{5}{10}\) = \(\frac{5 \times 10}{10 \times 10}\) = \(\frac{50}{100}\).
\(\frac{50}{100}\) + \(\frac{9}{100}\) = \(\frac{59}{100}\).

Question 12.
Part B
How can you write your answer as a decimal?
__________ kilogram

Answer:
0.59 kilogram

Explanation:
\(\frac{59}{100}\) = 0.59

Question 13.
An orchestra has 100 musicians. \(\frac{4}{10}\) of them play string instruments—violin, viola, cello, double bass, guitar, lute, and harp. What decimal is equivalent to \(\frac{4}{10}\)?
__________

Answer:
0.4 or 0.40

Explanation:
\(\frac{4}{10}\) = 0.4 = 0.40

Question 14.
Complete the table.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 60

Answer:
grade 4 chapter 9 Relate Fractions and Decimals Image 3 541

Question 15.
The point on the number line shows the number of seconds it took an athlete to run the forty-yard dash. Write the decimal that correctly names the point.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 61

Answer:
\(\frac{70}{100}\)

Explanation:
The point is in between 5\(\frac{5}{10}\) and 6.0. The point after the 5\(\frac{5}{10}\) is 5\(\frac{6}{10}\) = 5.6

Page No. 543

Question 16.
Ingrid is making a toy car. The toy car is \(\frac{5}{10}\) meter high without the roof. The roof is \(\frac{18}{100}\) meter high. What is the height of the toy car with the roof? Choose a number from each column to complete an equation to solve.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 62
Type below:
__________

Answer:
\(\frac{50}{100}\) + \(\frac{18}{100}\) = \(\frac{68}{100}\) meter high

Explanation:
\(\frac{5}{10}\) = \(\frac{5 \times 10}{10 \times 10}\) = \(\frac{50}{100}\).
\(\frac{50}{100}\) + \(\frac{18}{100}\) = \(\frac{68}{100}\).

Question 17.
Callie shaded the model to represent the questions she answered correctly on a test. What decimal represents the part of the model that is shaded?
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 63
represents _____

Answer:
0.81

Explanation:
81 boxes are shaded out of 100. So, \(\frac{81}{100}\) = 0.81

Question 18.
For numbers 18a–18f, select True or False for the inequality.
a. 0.21 < 0.27
i. True
ii. False

Answer:
i. True

Explanation:
The digits in the one’s and tenths place are the same. Compare the digits in the hundredths place. 1 < 7. So, 0.21 < 0.27. The answer is true.

Question 18. b. 0.4 > 0.45

i. True
ii. False

Answer:
ii. False

Explanation:
0.4 = 0.40
The digits in the one’s and tenths place are the same. Compare the digits in the hundredths place. 0 < 5. So, 0.4 < 0.46. The answer is false.

Question 18.
c. $3.21 > $0.2
i. True
ii. False

Answer:
i. True

Explanation:
3 ones is greater than 0’s. So, $3.21 > $0.2

Question 18.
d. 1.9 < 1.90
i. True
ii. False

Answer:
ii. False

Explanation:
1.9 = 1.90. So, the answer is false

Question 18. e. 0.41 = 0.14
i. True
ii. False

Answer:
ii. False

Explanation:
The digits in the one’s are the same. Compare the digits in the tenths place. 4 > 1. So, 0.41 > 0.14. The answer is false.

Question 18. f. 6.2 > 6.02
i. True
ii. False

Answer:
i. True

Explanation:
2 tenths is greater than 0 tenths. So, 6.2 > 6.02. The answer is true.

Question 19.
Fill in the numbers to find the sum.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 64
Type below:
__________

Answer:
\(\frac{4}{10}\) + \(\frac{40}{100}\) = \(\frac{8}{10}\)

Explanation:
Let the unknown numbers are A and B.
\(\frac{4}{10}\) + \(\frac{A}{100}\) = \(\frac{8}{B}\)
If A = 40 and B = 10, then \(\frac{4}{10}\) + \(\frac{40}{100}\) = \(\frac{8}{10}\).

Page No. 544

Question 20.
Steve is measuring the growth of a tree. He drew this model to show the tree’s growth in meters. Which fraction, mixed number, or decimal does the model show? Mark all that apply.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 65
Options:
a. 1.28
b. 12.8
c. 0.28
d. 2 \(\frac{8}{100}\)
e. 1 \(\frac{28}{100}\)
f. 1 \(\frac{28}{10}\)

Answer:
a. 1.28
e. 1 \(\frac{28}{100}\)

Explanation:
From the given image, it has one model of 1 whole number and other model is shades 24 boxes out of 100. So, 1 \(\frac{28}{100}\) = \(\frac{128}{100}\) = 1.28 is the answer.

Question 21.
Luke lives 0.4 kilometer from a skating rink. Mark lives 0.25 kilometer from the skating rink.
Part A
Who lives closer to the skating rink? Explain.
_____

Answer:
Mark lives closer to the skating rink

Explanation:
0.4 is 4 tenths and 0.25 is 2 tenths 5 hundredths. Compare the tenths, since
4 tenths > 2 tenths. Luke lives farther from the rink. So, Mark lives closer.

Question 21.
Part B
How can you write each distance as a fraction? Explain.
Type below:
__________

Answer:
\(\frac{4}{10}\) and \(\frac{25}{100}\)

Explanation:
0.4 is 4 tenths. So, \(\frac{4}{10}\) and 0.25 is 25 hundredths. So, \(\frac{25}{100}\).

Question 21.
Part C
Luke is walking to the skating rink to pick up a practice schedule. Then he is walking to Mark’s house. Will he walk more than a kilometer or less than a kilometer? Explain.
__________

Answer:
Less than a kilometer; \(\frac{4}{10}\) < \(\frac{5}{10}\) or \(\frac{1}{2}\) and \(\frac{25}{100}\) < \(\frac{50}{100}\) or \(\frac{1}{2}\).
\(\frac{4}{10}\) + \(\frac{25}{100}\) < \(\frac{1}{2}\) + \(\frac{1}{2}\). So, \(\frac{1}{2}\) + \(\frac{1}{2}\) = 1.
Therefore, \(\frac{4}{10}\) + \(\frac{25}{100}\) < 1.

Page No. 551

Question 1.
Draw and label \(\overline{A B}\) in the space at the right.
\(\overline{A B}\) is a __________ .
__________

Answer:
grade 4 chapter 9 review test image 1 551
\(\overline{A B}\) is a line segment.

Draw and label an example of the figure.

Question 2.
\(\underset { XY }{ \longleftrightarrow } \)
Type below:
__________

Answer:
grade 4 chapter 9 review test image 2 551
\(\underset { XY }{ \longleftrightarrow } \) is a line

Question 3.
obtuse ∠K
Type below:
__________

Answer:
grade 4 chapter 9 review test image 3 551
Angle K is greater than a right angle and less than a straight angle.

Question 4.
∠CDE
Type below:
__________

Answer:
grade 4 chapter 9 review test image 4 551
angle CDE

Use Figure M for 5 and 6.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 66

Question 5.
Name a line segment.
Type below:
__________

Answer:
line segment TU

Explanation:
TU line is a straight path of points that continues without an end in both directions.

Question 6.
Name a right angle.
Type below:
__________

Answer:
Angle TUW

Explanation:
TUW is a right angle that forms a square corner.

Draw and label an example of the figure.

Question 7.
\(\overrightarrow{P Q}\)
Type below:
__________

Answer:
grade 4 chapter 9 review test image 5 551
\(\overrightarrow{P Q}\) is a ray.

Question 8.
acute ∠RST
Type below:
__________

Answer:
grade 4 chapter 9 review test image 6 551
Angle RST

Question 9.
straight ∠WXZ
Type below:
__________

Answer:
grade 4 chapter 9 review test image 7 551

Use Figure F for 10–15.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 67

Question 10.
Name a ray.
Type below:
__________

Answer:
Ray K

Explanation:
K is a ray that has one endpoint and continues without an end in one direction.

Question 11.
Name an obtuse angle.
Type below:
__________

Answer:
Angle ABK

Explanation:
ABK is an obtuse angle that is greater than a right angle and less than a straight angle.

Question 12.
Name a line.
Type below:
__________

Answer:
Line AC

Explanation:
AC is a line that is a straight path of points that continues without end in
both directions.

Question 13.
Name a line segment.
Type below:
__________

Answer:
Line Segment PQ

Explanation:
PQ is a line segment that is part of a line between two endpoints.

Question 14.
Name a right angle.
Type below:
__________

Answer:
Angle PRC

Explanation:
PRC is a right angle that forms a square corner.

Question 15.
Name an acute angle.
Type below:
__________

Answer:
Angle ABJ

Explanation:
ABJ is an acute angle that is less than a right angle.

Page No. 552

Use the picture of the bridge for 16 and 17.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 68

Question 16.
Classify ∠A.
_____ angle

Answer:
Right Angle

Explanation:
A is the right angle that forms a square corner.

Question 17.
Which angle appears to be obtuse?
∠ _____

Answer:
∠C

Explanation:
C is an obtuse angle that is greater than a right angle and less than a straight angle.

Question 18.
How many different angles are in Figure X?
List them.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 69
Type below:
__________

Answer:
4 Angles;
Right Angle = Angle EBC;
Obtuse angle = Angle DBF;
Acute angle = Angle DBE;
Straight angle = Angle ABC.

Explanation:

Question 19.
Vanessa drew the angle at the right and named it ∠TRS. Explain why Vanessa’s name for the angle is incorrect. Write a correct name for the angle.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 70
Type below:
__________

Answer:
Vanessa’s name for the angle is incorrect. Because She drew ∠TSR. The two rays R and T have the same endpoint at S called the angle. Also, the TSR is an acute angle that is less than a right angle.

Question 20.
Write the word that describes the part of Figure A.
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 71
Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals img 72
\(\overline{B G}\) _________
\(\underset { CD }{ \longleftrightarrow } \) _________
∠FBG _________
\(\overrightarrow{B E}\) _________
∠AGD _________

Answer:
\(\overline{B G}\) Line Segment.
\(\underset { CD }{ \longleftrightarrow } \) Line.
∠FBG Right Angle.
\(\overrightarrow{B E}\) Ray.
∠AGD an acute angle.

Conclusion:

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Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers

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Multiply Fractions by Whole Numbers Go Math Grade 4 Chapter 8 Answer Key Pdf

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Lesson 1: Multiples of Unit Fractions

Lesson 2: Multiples of Fractions

Mid-Chapter Checkpoint

Lesson 3: Multiply a Fraction by a Whole Number Using Models

Lesson 4: Multiply a Fraction or Mixed Number by a Whole Number

Lesson 5: Problem Solving • Comparison Problems with Fractions

Review/Test

Common Core – New – Page No. 459

Multiples of Unit Fractions

Write the fraction as a product of a whole number and a unit fraction.

Question 1.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers Common Core - New img 1

Answer:
5 x 1/6

Explanation:
Given that 5/6 or 5 sixth-size parts.
Each sixth-size part of the given fraction can be shown by the unit fraction 1/6.
You can use unit fractions to show 5/6
5/6 = 5 x 1/6.

Question 2.
\(\frac{7}{8}\) =
Type below:
__________

Answer:
7 x 1/8

Explanation:
Given that 7/8 or 7 eighth-size parts.
Each eighth-size part of the given fraction can be shown by the unit fraction 1/8.
You can use unit fractions to show 7/8
7/8 = 7 x 1/8.

Question 3.
\(\frac{5}{3}\) =
Type below:
__________

Answer:
5 x 1/3

Explanation:
Given that 5/3 or 5 third-size parts.
Each third-size part of the given fraction can be shown by the unit fraction 1/3.
You can use unit fractions to show 5/6
5/3 = 5 x 1/3.

Go Math Grade 4 Chapter 8 Lesson 8.1 Answer Key Question 4.
\(\frac{9}{10}\) =
Type below:
__________

Answer:
9 x 1/10

Explanation:
Given that 9/10 or 9-tenth-size parts.
Each tenth-size part of the given fraction can be shown by the unit fraction 1/10.
You can use unit fractions to show 9/10
9/10 = 9 x 1/10.

Question 5.
\(\frac{3}{4}\) =
Type below:
__________

Answer:
3 x 1/4

Explanation:
Given that 3/4 or 3 fourth-size parts.
Each fourth-size part of the given fraction can be shown by the unit fraction 1/4.
You can use unit fractions to show 5/6
3/4 = 3 x 1/4.

Question 6.
\(\frac{11}{12}\) =
Type below:
__________

Answer:
11 x 1/12

Explanation:
Given that 11/12 or 11 twelve-size parts.
Each twelve-size part of the given fraction can be shown by the unit fraction 1/12.
You can use unit fractions to show 5/6
11/12 = 11 x 1/12.

Question 7.
\(\frac{4}{6}\) =
Type below:
__________

Answer:
4 x 1/6

Explanation:
Given that 4/6 or 4 sixth-size parts.
Each sixth-size part of the given fraction can be shown by the unit fraction 1/6.
You can use unit fractions to show 4/6
4/6 = 4 x 1/6.

Question 8.
\(\frac{8}{20}\) =
Type below:
__________

Answer:
8 x 1/20

Explanation:
Given that 8/20 or 8 twenty-size parts.
Each twenty-size part of the given fraction can be shown by the unit fraction 1/20.
You can use unit fractions to show 8/20
8/20 = 8 x 1/20.

Question 9.
\(\frac{13}{100}\) =
Type below:
__________

Answer:
13 x 1/100

Explanation:
Given that 13/100 or 13 hundred-size parts.
Each hundred-size part of the given fraction can be shown by the unit fraction 1/100.
You can use unit fractions to show 13/100
13/100 = 13 x 1/100.

List the next four multiples of the unit fraction.

Question 10.
\(\frac{1}{5}\) ,
Type below:
__________

Answer:
2/5, 3/5, 4/5, 5/5

Explanation:
Grade 4 Chapter 8 Multiply Fractions Image 2
2/5, 3/5, 4/5, 5/5

Question 11.
\(\frac{1}{8}\) ,
Type below:
__________

Answer:
2/8, 3/8, 4/8, 5/8

Explanation:
Grade 4 Chapter 8 Multiply Fractions Image 3
2/8, 3/8, 4/8, 5/8

Problem Solving

Question 12.
So far, Monica has read \(\frac{5}{6}\) of a book. She has read the same number of pages each day for 5 days. What fraction of the book does Monica read each day?
\(\frac{□}{□}\) of the book

Answer:
1/6 of the book

Explanation:
Monica has read 5/6 of a book. She has read the same number of pages each day for 5 days.
For 1 day, she read one page. In total, she read 5 pages in 5 days. So, Monica read 1/6 of a book each day.

Question 13.
Nicholas buys \(\frac{3}{8}\) pound of cheese. He puts the same amount of cheese on 3 sandwiches. How much cheese does Nicholas put on each sandwich?
\(\frac{□}{□}\) pound of cheese

Answer:
1/8 pound of cheese

Explanation:
Nicholas buys 3/8 pound of cheese. He bought 3 sandwiches. Then, he applied 3/8 pound of cheese on 3 sandwiches. So, 3 x 1/8 cheese he put on 3 sandwiches. So, for one sandwich he put 1/8 pound of cheese.

Common Core – New – Page No. 460

Lesson Check

Question 1.
Selena walks from home to school each morning and back home each afternoon. Altogether, she walks \(\frac{2}{3}\) mile each day. How far does Selena live from school?
Options:
a. \(\frac{1}{3}\) mile
b. \(\frac{2}{3}\) mile
c. 1 \(\frac{1}{3}\) mile
d. 2 miles

Answer:
a. \(\frac{1}{3}\) mile

Explanation:
Selena walks from home to school each morning and back home each afternoon. Altogether, she walks 2/3 miles each day. The distance between home and school will remain the same. So, 2/3 x 1/2 = 1/3 mile far Selena live from the school.

Go Math Lesson 8.1 4th Grade Question 2.
Will uses \(\frac{3}{4}\) cup of olive oil to make 3 batches of salad dressing. How much oil does Will use for one batch of salad dressing?
Options:
a. \(\frac{1}{4}\) cup
b. \(\frac{1}{3}\) cup
c. 2 \(\frac{1}{3}\) cups
d. 3 cups

Answer:
1/8 pound of cheesa. \(\frac{1}{4}\) cup

Explanation:
Will uses 34 cups of olive oil to make 3 batches of salad dressing. To know the one batch of salad dressing, we need to take one part of salad dressing = 1/3. So, 3/4 x 1/3 = 1/4 cup of olive oil will use for one batch of salad dressing.

Spiral Review

Question 3.
Liza bought \(\frac{5}{8}\) pound of trail mix. She gives \(\frac{2}{8}\) pound of trail mix to Michael. How much trail mix does Liza have left?
Options:
a. \(\frac{1}{8}\) pound
b. \(\frac{2}{8}\) pound
c. \(\frac{3}{8}\) pound
d. \(\frac{4}{8}\) pound

Answer:
c. \(\frac{3}{8}\) pound

Explanation:
Liza bought 58 pound of trail mix. She gives 28 pound of trail mix to Michael.
So, Liza have left 5/8 – 2/8 = 3/8 trail mix.

Question 4.
Leigh has a piece of rope that is 6 \(\frac{2}{3}\) feet long. How do you write 6 \(\frac{2}{3}\) as a fraction greater than 1?
Options:
a. \(\frac{11}{3}\)
b. \(\frac{15}{3}\)
c. \(\frac{20}{3}\)
d. \(\frac{62}{3}\)

Answer:
c. \(\frac{20}{3}\)

Explanation:
Multiply the denominator with the whole number. i.e Multiply 3 with 6 in the given example, 6 (2/3).
3 x 6 =18.
Add 18 + 2 =20.
Keep the Denominator the same i.e. 3.
The obtained fraction is 20/3.

Question 5.
Randy’s house number is a composite number. Which of the following could be Randy’s house number?
Options:
a. 29
b. 39
c. 59
d. 79

Answer:
b. 39

Explanation:
The composite numbers can be defined as whole numbers that have more than two factors. Whole numbers that are not prime are composite numbers because they are divisible by more than two numbers. 39 is the composite number. 39 is divided by 13 and 3.

Question 6.
Mindy buys 12 cupcakes. Nine of the cupcakes have chocolate frosting and the rest have vanilla frosting. What fraction of the cupcakes have vanilla frosting?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{1}{3}\)
c. \(\frac{2}{3}\)
d. \(\frac{3}{4}\)

Answer:
a. \(\frac{1}{4}\)

Explanation:
Mindy buys 12 cupcakes.
Nine of the cupcakes have chocolate frosting = 9/12.
The rest have vanilla frosting. So, there are 3 cups remaining = 3/12 = 1/4.
1/4 cupcakes have vanilla frosting.

Page No. 463

Question 1.
Write three multiples of \(\frac{3}{8}\).
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 2
1 × \(\frac{3}{8}\) = \(\frac{■}{8}\)
2 × \(\frac{3}{8}\) = \(\frac{■}{8}\)
3 × \(\frac{3}{8}\) = \(\frac{■}{8}\)
Multiples of \(\frac{3}{8}\) are ____ , ____ , and ____ .
Type below:
__________

Answer:
3/8, 6/8, 9/8, 12/8.

Explanation:
1 x 3/8 = 3/8.
2 x 3/8 = 6/8.
3 x 3/8 = 9/8.
4 x 3/8 = 12/8.
Multiples of 3/8 are 3/8, 6/8, 9/8, 12/8.

List the next four multiples of the fraction.

Question 2.
\(\frac{3}{6}\) ,
Type below:
__________

Answer:
6/6, 9/6, 12/6, 20/6

Explanation:
1 x 3/6 = 3/6.
2 x 3/6 = 6/6.
3 x 3/6 = 9/6.
4 x 3/6 = 12/6.
5 x 4/6 = 20/6.
Next four multiples of 3/6 are 6/6, 9/6, 12/6, 20/6.

Question 3.
\(\frac{2}{10}\) ,
Type below:
__________

Answer:
4/10, 6/10, 8/10, 10/10

Explanation:
1 x 2/10 = 2/10.
2 x 2/10 = 4/10.
3 x 2/10 = 6/10.
4 x 2/10 = 8/10.
5 x 2/10 = 10/10.
The next four multiples of 2/10 are 4/10, 6/10, 8/10, 10/10.

Write the product as the product of a whole number and a unit fraction.

Question 4.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 3
3 × \(\frac{3}{4}\) =
Type below:
__________

Answer:
9/4 = 9 x 1/4

Explanation:
1 group of 3/4 = 3/4
2 groups of 3/4 = 6/4
3 groups of 3/4 = 9/4
3 x 3/4 = 9/4.

Question 5.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 4
2 × \(\frac{4}{6}\) =
Type below:
__________

Answer:
8/6 = 8 x 1/6

Explanation:
1 group of 4/6 = 4/6
2 groups of 4/6 = 8/6
2 x 4/6 = 8/6 = 8 x 1/6.

List the next four multiples of the fraction.

Question 6.
\(\frac{4}{5}\) ,
Type below:
__________

Answer:
8/5, 12/5, 16/5, 20/5

Explanation:
1 x 4/5 = 4/5.
2 x 4/5 = 8/5.
3 x 4/5 = 12/5.
4 x 4/5 = 16/5.
5 x 4/5 = 20/5.
The next four multiples of 4/5 are 8/5, 12/5, 16/5, 20/5.

Question 7.
\(\frac{2}{4}\) ,
Type below:
__________

Answer:
4/4, 6/4, 8/4, 10/4

Explanation:
1 x 2/4 = 2/4.
2 x 2/4 = 4/4.
3 x 2/4 = 6/4.
4 x 2/4 = 8/4.
5 x 2/4 = 10/4.
The next four multiples of 2/4 are 4/4, 6/4, 8/4, 10/4.

Write the product as the product of a whole number and a unit fraction.

Question 8.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 5
4 × \(\frac{2}{8}\) =
Type below:
__________

Answer:
8/8 = 8 x 1/8

Explanation:
1 group of 2/8 = 2/8
2 groups of 2/8 = 4/8
3 groups of 2/8 = 6/8
4 groups of 2/8 = 8/8
4 x 2/8 = 8/8 = 8 x 1/8.

Question 9.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 6
3 × \(\frac{3}{5}\) =
Type below:
__________

Answer:
9/5 = 9 x 1/5

Explanation:
1 group of 3/5 = 3/5
2 groups of 3/5 = 6/5
3 groups of 3/5 = 9/5
3 x 3/5 = 9/5 = 9 x 1/5.

Question 10.
Use Repeated Reasoning Are \(\frac{6}{10}\) and \(\frac{6}{30}\) multiples of \(\frac{3}{10}\)?
Explain.
Type below:
__________

Answer:
3/30

Explanation:
Use Repeated Reasoning Are 6/10 and 6/30 multiples of 3/10 and 3/30.

Question 11.
Which is greater, 4 × \(\frac{2}{7}\) or 3 × \(\frac{3}{7}\)? Explain.
4 × \(\frac{2}{7}\) _____ 3 × \(\frac{3}{7}\)

Answer:
4 × \(\frac{2}{7}\) __<___ 3 × \(\frac{3}{7}\)

Explanation:
8/7 < 9/7
So, 4 x 2/7 < 3 x 3/7

Page No. 464

Question 12.
Josh is watering his plants. He gives each of 2 plants \(\frac{3}{5}\) pint of water. His watering can holds \(\frac{1}{5}\) pint. How many times will he fill his watering can to water both plants?
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 7
a. What do you need to find?
Type below:
__________

Answer:
We need to find how many times Josh needs to fill his watering can to water both plants.

Question 12.
b. What information do you need to use?
Type below:
__________

Answer:
Use the Number of plants = 2.
He gives each plant a 3/5 pint of water.
His watering can hold 1/5 pint.

Question 12.
c. How can drawing a model help you solve the problem?
Type below:
__________

Answer:
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 6

Question 12.
d. Show the steps you use to solve the problem.
Type below:
__________

Answer:
If Josh gives each plant 3/5 pint, then that’s a total of 6/5 pint.
6/5 = 6 x 1/5.

Question 12.
e. Complete the sentence. Josh will fill his watering can ____ times.
____ times

Answer:
Josh will fill his watering can 6 times.

Go Math 4th Grade Pdf Practice and Homework Lesson 8.2 Question 13.
Alma is making 3 batches of tortillas. She adds \(\frac{3}{4}\) cup of water to each batch. The measuring cup holds \(\frac{1}{4}\) cup. How many times must Alma measure \(\frac{1}{4}\) cup of water to have enough for the tortillas? Shade the model to show your answer.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 8
Alma must measure \(\frac{1}{4}\) cup ______ times.
____ times

Answer:
12 times

Explanation:
Alma is making 3 batches of tortillas. She adds a 3/4 cup of water to each batch. The measuring cup holds 1/4 cup.
Alma must measure 1/4 cup 12 times.

Common Core – New – Page No. 465

Multiples of Fractions

List the next four multiples of the fraction.

Question 1.
\(\frac{3}{5}\) ,
Type below:
__________

Answer:
6/5, 9/5, 12/5, 20/5

Explanation:
1 x 3/5 = 3/5.
2 x 3/5 = 6/5.
3 x 3/5 = 9/5.
4 x 3/5 = 12/5.
5 x 4/5 = 20/5.
The next four multiples of 3/5 are 6/5, 9/5, 12/5, 20/5.

Question 2.
\(\frac{2}{6}\) ,
Type below:
__________

Answer:
4/6, 6/6, 8/6, 10/6

Explanation:
1 x 2/6 = 2/6.
2 x 2/6 = 4/6.
3 x 2/6 = 6/6.
4 x 2/6 = 8/6.
5 x 2/6 = 10/6.
The next four multiples of 2/6 are 4/6, 6/6, 8/6, 10/6.

Question 3.
\(\frac{4}{8}\) ,
Type below:
__________

Answer:
8/8, 12/8, 16/8, 20/8

Explanation:
1 x 4/8 = 4/8.
2 x 4/8 = 8/8.
3 x 4/8 = 12/8.
4 x 4/8 = 16/8.
5 x 4/8 = 20/8.
The next four multiples of 4/8 are 8/8, 12/8, 16/8, 20/8.

Question 4.
\(\frac{5}{10}\) ,
Type below:
__________

Answer:
10/10, 15/10, 20/10, 25/10

Explanation:
1 x 5/10 = 5/10.
2 x 5/10 = 10/10.
3 x 5/10 = 15/10.
4 x 5/10 = 20/10.
5 x 5/10 = 25/10.
The next four multiples of 5/10 are 10/10, 15/10, 20/10, 25/10.

Write the product as the product of a whole number and a unit fraction.

Question 5.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers Common Core - New img 9
2 × \(\frac{4}{5}\) =
Type below:
__________

Answer:
8/5 = 8 x 1/5

Explanation:
1 group of 4/5 = 4/5
2 groups of 4/5 = 8/5
2 x 4/5 = 8/5 = 8 x 1/5.

Question 6.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers Common Core - New img 10
5 × \(\frac{2}{3}\) =
Type below:
__________

Answer:
10/3 = 10 x 1/3

Explanation:
1 group of 2/3 = 2/3
2 group of 2/3 = 4/3
3 group of 2/3 = 6/3
4 group of 2/3 = 8/3
5 group of 2/3 = 10/3
5 x 2/3 = 10/3 = 10 x 1/3.

Problem Solving

Question 7.
Jessica is making 2 loaves of banana bread. She needs \(\frac{3}{4}\) cup of sugar for each loaf. Her measuring cup can only hold \(\frac{1}{4}\) cup of sugar. How many times will Jessica need to fill the measuring cup in order to get enough sugar for both loaves of bread?
_____ times

Answer:
6 times

Explanation:
Jessica is making 2 loaves of banana bread. She needs a 3/4 cup of sugar for each loaf.
For 2 loaves, she needs 2 x 3/4 = 6/4 cups of sugar.
Her measuring cup can only hold 1/4 cup of sugar. So, to get the 3/4 cup of sugar, she needs to fill the cup 3 times. 1/4 + 1/4 + 1/4 = 3/4.
So, to fill 2 loaves, she needs to fill cup 3 x 2 = 6 times.

Question 8.
A group of four students is performing an experiment with salt. Each student must add \(\frac{3}{8}\) teaspoon of salt to a solution. The group only has a \(\frac{1}{8}\) teaspoon measuring spoon. How many times will the group need to fill the measuring spoon in order to perform the experiment?
_____ times

Answer:
12 times

Explanation:
A group of four students is performing an experiment with salt. Each student must add a 3/8 teaspoon of salt to a solution. 4 x 3/8 = 12/8 teaspoon of salt required to finish the experiment.
If they have 1/8 teaspoon measuring spoon, 12 x 1/8.
So, the group needs to fill the measuring spoon 12 times in order to perform the experiment.

Common Core – New – Page No. 466

Lesson Check

Question 1.
Eloise made a list of some multiples of \(\frac{5}{8}\). Which of the following lists could be Eloise’s list?
Options:
a. \(\frac{5}{8}, \frac{10}{16}, \frac{15}{24}, \frac{20}{32}, \frac{25}{40}\)
b. \(\frac{5}{8}, \frac{10}{8}, \frac{15}{8}, \frac{20}{8}, \frac{25}{8}\)
c. \(\frac{5}{8}, \frac{6}{8}, \frac{7}{8}, \frac{8}{8}, \frac{9}{8}\)
d. \(\frac{1}{8}, \frac{2}{8}, \frac{3}{8}, \frac{4}{8}, \frac{5}{8}\)

Answer:
b. \(\frac{5}{8}, \frac{10}{8}, \frac{15}{8}, \frac{20}{8}, \frac{25}{8}\)

Explanation:
1 x 5/8 = 5/8.
2 x 5/8 = 10/8.
3 x 5/8 = 15/8.
4 x 5/8 = 20/8.
5 x 5/8 = 25/8.
The next four multiples of 5/8 are 10/8, 15/8, 20/8, 25/8.

Go Math Workbook Grade 4 Pdf Multiples of Fractions Lesson 8.2 Question 2.
David is filling five \(\frac{3}{4}\) quart bottles with a sports drink. His measuring cup only holds \(\frac{1}{4}\) quart. How many times will David need to fill the measuring cup in order to fill the 5 bottles?
Options:
a. 5
b. 10
c. 15
d. 20

Answer:
c. 15

Explanation:
David is filling five 3/4 quart bottles with a sports drink = 5 x 3/4 = 15/4.
His measuring cup only holds 1/4 quart.
So, 15 x 1/4. David needs to fill the measuring cup 15 times in order to fill the 5 bottles.

Spiral Review

Question 3.
Ira has 128 stamps in his stamp album. He has the same number of stamps on each of the 8 pages. How many stamps are on each page?
Options:
a. 12
b. 14
c. 16
d. 18

Answer:
c. 16

Explanation:
Ira has 128 stamps in his stamp album. He has the same number of stamps on each of the 8 pages.
128/8 = 16 stamps on each page.

Question 4.
Ryan is saving up for a bike that costs $198. So far, he has saved $15 per week for the last 12 weeks. How much more money does Ryan need in order to be able to buy the bike?
Options:
a. $ 8
b. $ 18
c. $ 48
d. $ 180

Answer:
b. $ 18

Explanation:
Ryan is saving up for a bike that costs $198.
So far, he has saved $15 per week for the last 12 weeks = $15 x 12 = $180.
$198 – $180 = $18 needed in order to buy the bike.

Question 5.
Tina buys 3 \(\frac{7}{8}\) yards of material at the fabric store. She uses it to make a skirt. Afterward, she has 1 \(\frac{3}{8}\) yards of the fabric left over. How many yards of material did Tina use?
Options:
a. 1 \(\frac{4}{8}\)
b. 2 \(\frac{1}{8}\)
c. 2 \(\frac{4}{8}\)
d. 5 \(\frac{2}{8}\)

Answer:
c. 2 \(\frac{4}{8}\)

Explanation:
Tina buys 3 7/8 yards of material at the fabric store. She uses it to make a skirt. Afterward, she has 1 3/8 yards of the fabric left over.
3 -1 = 2; 7/8 – 3/8 = 4/8. So, the answer is 2 4/8.

Question 6.
Which list shows the fractions in order from least to greatest?
Options:
a. \(\frac{2}{3}, \frac{3}{4}, \frac{7}{12}\)
b. \(\frac{7}{12}, \frac{3}{4}, \frac{2}{3}\)
c. \(\frac{3}{4}, \frac{2}{3}, \frac{7}{12}\)
d. \(\frac{7}{12}, \frac{2}{3}, \frac{3}{4}\)

Answer:
d. \(\frac{7}{12}, \frac{2}{3}, \frac{3}{4}\)

Explanation:
2/3 = 0.666
3/4 = 0.75
7/12 = 0.5833
7/12, 2/3, 3/4

Page No. 467

Choose the best term from the box.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 11

Question 1.
A __________ of a number is the product of the number and a counting number.
__________

Answer:
Multiple

Question 2.
A _________ always has a numerator of 1.
_________

Answer:
Unit Fraction

List the next four multiples of the unit fraction.

Question 3.
\(\frac{1}{2}\) ,
Type below:
_________

Answer:
2/2, 3/2, 4/2, 5/2

Explanation:
1 x 1/2 = 1/2.
2 x 1/2 = 2/2.
3 x 1/2 = 3/2.
4 x 1/2 = 4/2.
5 x 1/2 = 5/2.
The next four multiples of 1/2 are 2/2, 3/2, 4/2, 5/2.

Question 4.
\(\frac{1}{5}\) ,
Type below:
_________

Answer:
2/5, 3/5, 4/5, 5/5

Explanation:
1 x 1/5 = 1/5.
2 x 1/5 = 2/5.
3 x 1/5 = 3/5.
4 x 1/5 = 4/5.
5 x 1/5 = 5/5.
The next four multiples of 1/5 are 2/5, 3/5, 4/5, 5/5.

Write the fraction as a product of a whole number and a unit fraction.

Question 5.
\(\frac{4}{10}\) = _____ × \(\frac{1}{10}\)

Answer:
4

Explanation:
4/10 = 4 x 1/10

Question 6.
\(\frac{8}{12}\) = _____ × \(\frac{1}{12}\)

Answer:
8

Explanation:
8/12 = 8 x 1/12

Question 7.
\(\frac{3}{4}\) = _____ × \(\frac{1}{4}\)

Answer:
3

Explanation:
3/4 = 3 x 1/4

List the next four multiples of the fraction.

Question 8.
\(\frac{2}{5}\) ,
Type below:
_________

Answer:
4/5, 6/5, 8/5, 10/5

Explanation:
1 x 2/5 = 1/5.
2 x 2/5 = 4/5.
3 x 2/5 = 6/5.
4 x 2/5 = 8/5.
5 x 2/5 = 10/5.
The next four multiples of 1/5 are 4/5, 6/5, 8/5, 10/5.

Question 9.
\(\frac{5}{6}\) ,
Type below:
_________

Answer:
10/6, 15/6, 20/6, 25/6

Explanation:
1 x 5/6 = 5/6.
2 x 5/6 = 10/6.
3 x 5/6 = 15/6.
4 x 5/6 = 20/6.
5 x 5/6 = 25/6.
The next four multiples of 5/6 are 10/6, 15/6, 20/6, 25/6.

Write the product as the product of a whole number and a unit fraction.

Question 10.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 12
4 × \(\frac{2}{6}\) =
Type below:
_________

Answer:
8/6 = 8 x 1/6

Explanation:
1 group of 2/6 = 2/6
2 groups of 2/6 = 4/6
3 groups of 2/6 = 6/6
4 groups of 2/6 = 8/6
4 x 2/6 = 8/6 = 8 x 1/6.

Question 11.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 13
3 × \(\frac{3}{8}\) =
Type below:
_________

Answer:
9/8 = 9 x 1/8

Explanation:
1 group of 3/8 = 3/8
2 groups of 3/8 = 6/8
3 groups of 3/8 = 9/8
3 x 3/8 = 9/8 = 9 x 1/8.

Page No. 468

Question 12.
Pedro cut a sheet of poster board into 10 equal parts. His brother used some of the poster board and now \(\frac{8}{10}\) is left. Pedro wants to make a sign from each remaining part of the poster board. How many signs can he make?
______ signs

Answer:
8 signs

Explanation:
Pedro cut a sheet of poster board into 10 equal parts.
His brother uses some of the poster board and now an 8/10 is left.
So, the remaining part of the b\poster board is 8/10 parts.
Pedro can use 8/ 10 parts of the board to make signs.
So, he can make 8 signs.

Question 13.
Ella is making 3 batches of banana milkshakes. She needs \(\frac{3}{4}\) gallon of milk for each batch. Her measuring cup holds \(\frac{1}{4}\) gallon. How many times will she need to fill the measuring cup to make all 3 batches of milkshakes?
______ times

Answer:
9 times

Explanation:
Ella is making 3 batches of banana milkshakes. She needs 3/4 gallon of milk for each batch. So, she needs 3 x 3/4 = 9/4 cups for 3 batches of banana milkshakes. Her measuring cup holds 1/4 gallon.
9/4 = 9 x 1/4.
So, Ella needs to fill the measuring cup 9 times to make all 3 batches of milkshakes.

Question 14.
Darren cut a lemon pie into 8 equal slices. His friends ate some of the pie and now \(\frac{5}{8}\) is left. Darren wants to put each slice of the leftover pie on its own plate. What part of the pie will he put on each plate?
\(\frac{□}{□}\) of the pie on each plate.

Answer:
5/8 of the pie on each plate

Explanation:
Darren cut a lemon pie into 8 equal slices. His friends ate some of the pie and now 5/8 is left. So, 5 pie slices leftover.
Darren can put 5/8 parts of the pie on each plate.

Question 15.
Beth is putting liquid fertilizer on the plants in 4 flowerpots. Her measuring spoon holds \(\frac{1}{8}\) teaspoon. The directions say to put \(\frac{5}{8}\) teaspoon of fertilizer in each pot. How many times will Beth need to fill the measuring spoon to fertilize the plants in the 4 pots?
______ times

Answer:
20 times

Explanation:
Beth is putting liquid fertilizer on the plants in 4 flowerpots. Her measuring spoon holds 1/8 teaspoon.
The directions say to put 5/8 teaspoons of fertilizer in each pot. So, 4 x 5/8 = 20/8.
20/8 = 20 x 1/8. Beth needs to fill the measuring spoon 20 times to fertilize the plants in the 4 pots.

Page No. 471

Question 1.
Find the product of 3 × \(\frac{5}{8}\).
1 group of \(\frac{5}{8}\) = \(\frac{□}{8}\)
2 groups of \(\frac{5}{8}\) = \(\frac{□}{8}\)
3 groups of \(\frac{5}{8}\) = \(\frac{□}{8}\)
3 × \(\frac{5}{8}\) = \(\frac{□}{□}\)

Answer:
15/8

Explanation:
1 group of 5/8 = 2/8
2 groups of 5/8 = 4/8
3 groups of 5/8 = 6/8
3 x 5/8 = 15/8.

Multiply.

Question 2.
2 × \(\frac{4}{5}\) = \(\frac{□}{□}\)

Answer:
8/5

Explanation:
1 group of 4/5 = 4/5
2 groups of 4/5 = 8/5
2 x 4/5 = 8/5.

Question 3.
4 × \(\frac{2}{3}\) = \(\frac{□}{□}\)

Answer:
8/3

Explanation:
1 group of 2/3 = 2/3
2 groups of 2/3 = 4/3
3 groups of 2/3 = 6/3
4 groups of 2/3 = 8/3
4 x 2/3 = 8/3

Question 4.
5 × \(\frac{3}{10}\) = \(\frac{□}{□}\)

Answer:
15/10

Explanation:
1 group of 3/10 = 3/10
2 groups of 3/10 = 6/10
3 groups of 3/10 = 9/10
4 groups of 3/10 = 12/10
5 groups of 3/10 = 15/10
5 x 3/10 = 15/10

Question 5.
4 × \(\frac{5}{6}\) = \(\frac{□}{□}\)

Answer:
20/6

Explanation:
1 group of 5/6 = 5/6
2 groups of 5/6 = 10/6
3 groups of 5/6 = 15/6
4 groups of 5/6 = 20/6
4 x 5/6 = 20/6

Multiply.

Question 6.
2 × \(\frac{7}{12}\) = \(\frac{□}{□}\)

Answer:
7/6

Explanation:
1 group of 7/12 = 7/12
2 groups of 7/12 = 14/12
2 x 7/12 = 14/12 = 7/6

Question 7.
6 × \(\frac{3}{8}\) = \(\frac{□}{□}\)

Answer:
9/4

Explanation:
1 group of 3/8 = 3/8
2 groups of 3/8 = 6/8
3 groups of 3/8 = 9/8
4 groups of 3/8 = 12/8
5 groups of 3/8 = 15/8
6 groups of 3/8 = 18/8
6 x 3/8 = 18/8 = 9/4

Question 8.
5 × \(\frac{2}{4}\) = \(\frac{□}{□}\)

Answer:
5/2

Explanation:
1 group of 2/4 = 2/4
2 groups of 2/4 = 4/4
3 groups of 2/4 = 6/4
4 groups of 2/4 = 8/4
5 groups of 2/4 = 10/4
5 x 2/4 = 10/4 = 5/2

Question 9.
3 × \(\frac{4}{6}\) = \(\frac{□}{□}\)

Answer:
2

Explanation:
1 group of 4/6 = 4/6
2 groups of 4/6 = 8/6
3 groups of 4/6 = 12/6
3 x 4/6 = 12/6 = 2

Question 10.
2 × \(\frac{5}{10}\) = \(\frac{□}{□}\)

Answer:
2

Explanation:
1 group of 5/10 = 5/10
2 groups of 5/10 = 10/10
2 x 10/10 = 2 x 1 = 2

Question 11.
4 × \(\frac{2}{8}\) = \(\frac{□}{□}\)

Answer:
1

Explanation:
1 group of 2/8 = 2/8
2 groups of 2/8 = 4/8
3 groups of 2/8 = 6/8
4 groups of 2/8 = 8/8
4 x 2/8 = 8/8 = 1

Look for a Pattern Algebra Write the unknown number.

Question 12.
□ × \(\frac{2}{3}\) = \(\frac{12}{3}\)
□ = ____

Answer:
6

Explanation:
Let the unknown number is s.
s x 2/3 = 12/3
s = 12/3 x 3/2 = 6.

Question 13.
5 × \(\frac{□}{4}\) = \(\frac{10}{4}\)
□ = ____

Answer:
2

Explanation:
Let the unknown number is s.
5 x s/4 = 10/4
5/4 x s = 10/4
s = 10/4 x 4/5 =2.

Question 14.
2 × \(\frac{7}{□}\) = \(\frac{14}{8}\)
□ = ____

Answer:
8

Explanation:
Let the unknown number is s.
2 x 7/s = 14/8
14/s = 14/8
s x 14/8 = 14
s = 14 x 8/14
s = 8.

Page No. 472

Question 15.
Lisa makes clothes for pets. She needs \(\frac{5}{6}\) yard of fabric to make 1 dog coat. How much fabric does she need to make 3 dog coats?
a. What do you need to find?
Type below:
_________

Answer:
The number of fabric yards required for 3 dog coats

Question 15.
b. What information do you need?
Type below:
_________

Answer:
How much she needs of fabric for 1 dog coat can help to find 3 dog coats.

Question 15.
c. Show the steps you use to solve the problem.
Type below:
_________

Answer:
Lisa makes clothes for pets. She needs a 5/6 yard of fabric to make 1 dog coat.
For 3 dogs = 5/6 x 3 =5/2

Question 15.
d. Complete the sentence.
Lisa needs _____ yards of fabric to make 3 dog coats.
\(\frac{□}{□}\)

Answer:
Lisa needs a 5/2 yard of fabric to make 3 dog coats.

Go Math Grade 4 Chapter 8 Answer Key Pdf Question 16.
Manuel’s small dog eats \(\frac{2}{4}\) bag of dog food in 1 month. His large dog eats \(\frac{3}{4}\) bag of dog food in 1 month. How many bags do both dogs eat in 6 months?
\(\frac{□}{□}\) bags

Answer:
2 bags

Explanation:
Manuel’s small dog eats a 2/4 bag of dog food in 1 month. His large dog eats a 3/4 bag of dog food in 1 month.
In total 2/4 + 3/4 = 5/4 bag of dog food eaten in 1 month.
So, for 6 months = 6 x 5/4 = 30/4 = 15/2.
So, 2 bags are needed for 6 months.

Question 17.
Select the correct product for the equation.
9 × \(\frac{2}{12}\) = □
3 × \(\frac{6}{7}\) = □
6 × \(\frac{4}{7}\) = □
8 × \(\frac{3}{12}\) = □
Type below:
_________

Answer:
8 × \(\frac{3}{12}\) = 2

Explanation:
9 × \(\frac{2}{12}\) = 3/2
3 × \(\frac{6}{7}\) = 18/7
6 × \(\frac{4}{7}\) = 24/7
8 × \(\frac{3}{12}\) = 2

Common Core – New – Page No. 473

Multiply a Fraction by a Whole Number Using Models

Multiply.

Question 1.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers Common Core - New img 14

Answer:
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers Common Core - New img 14

Question 2.
3 × \(\frac{2}{5}\) = \(\frac{□}{□}\)

Answer:
Grade 4 Chapter 8 Image 1 473
3 x 2/5 = 6/5

Question 3.
7 × \(\frac{3}{10}\) = \(\frac{□}{□}\)

Answer:
Grade 4 Chapter 8 Image 2 473
7 x 3/10 = 21/10

Question 4.
3 × \(\frac{5}{12}\) = \(\frac{□}{□}\)

Answer:
Grade 4 Chapter 8 Image 3 473
3 x 5/12 = 15/12

Question 5.
6 × \(\frac{3}{4}\) = \(\frac{□}{□}\)

Answer:
Grade 4 Chapter 8 Image 4 473
6 x 3/4 = 18/4

Question 6.
4 × \(\frac{2}{8}\) = \(\frac{□}{□}\)

Answer:
Grade 4 Chapter 8 Image 5 473
4 x 2/8 = 8/8

Question 7.
5 × \(\frac{2}{3}\) = \(\frac{□}{□}\)

Answer:
Grade 4 Chapter 8 Image 6 473
5 x 2/3 = 10/3

Question 8.
2 × \(\frac{7}{8}\) = \(\frac{□}{□}\)

Answer:
Grade 4 Chapter 8 Image 7 473
2 x 7/8 = 14/8

Question 9.
6 × \(\frac{4}{5}\) = \(\frac{□}{□}\)

Answer:
Grade 4 Chapter 8 Image 8 473
6 x 4/5 = 28/5

Problem Solving

Question 10.
Matthew walks \(\frac{5}{8}\) mile to the bus stop each morning. How far will he walk in 5 days?
\(\frac{□}{□}\)

Answer:
25/8 miles

Explanation:
Matthew walks 5/8 mile to the bus stop each morning.
In 5 days, 5 x 5/8 = 25/8 miles.

Question 11.
Emily uses \(\frac{2}{3}\) cup of milk to make one batch of muffins. How many cups of milk will Emily use if she makes 3 batches of muffins?
\(\frac{□}{□}\)

Answer:
6/3 cups of milk

Explanation:
Emily uses a 2/3 cup of milk to make one batch of muffins.
Emily use 3 x 2/3 = 6/3 cups of milk to make 3 batches of muffins

Common Core – New – Page No. 474

Lesson Check

Question 1.
Aleta’s puppy gained \(\frac{3}{8}\) pound each week for 4 weeks. Altogether, how much weight did the puppy gain during the 4 weeks?
Options:
a. \(\frac{8}{12}\) pound
b. 1 \(\frac{2}{8}\) pounds
c. \(\frac{12}{8}\) pounds
d. 4 \(\frac{3}{8}\) pounds

Answer:
6/3 cups of milk

Explanation:
Aleta’s puppy gained 3/8 pound each week.
It gained 4 x 3/8 = 12/8 pounds in 4 weeks.

Question 2.
Pedro mixes \(\frac{3}{4}\) teaspoon of plant food into each gallon of water. How many teaspoons of plant food should Pedro mix into 5 gallons of water?
Options:
a. \(\frac{3}{20}\) teaspoon
b. \(\frac{4}{15}\) teaspoon
c. \(\frac{8}{4}\) teaspoons
d. \(\frac{15}{4}\) teaspoons

Answer:
d. \(\frac{15}{4}\) teaspoons

Explanation:
If Pedro mixes 3/4 teaspoon of plant food into each gallon of water, then 5 x 3/4 = 15/4 teaspoon of plant food mix into 5 gallons of water.

Spiral Review

Question 3.
Ivana has \(\frac{3}{4}\) pound of hamburger meat. She makes 3 hamburger patties. Each patty weighs the same amount. How much does each hamburger patty weigh?
Options:
a. \(\frac{1}{4}\) pound
b. \(\frac{1}{3}\) pound
c. 2 \(\frac{1}{4}\) pounds
d. 3 pounds

Answer:
a. \(\frac{1}{4}\) pound

Explanation:
Ivana has 3/4 pound of hamburger meat. She makes 3 hamburger patties.
Each patty weighs the same amount. So, each hamburger patty weight 1/4 pound.

Question 4.
Which of the following expressions is NOT equal to \(\frac{7}{10}\)?
Options:
a. \(\frac{5}{10}+\frac{1}{10}+\frac{1}{10}\)
b. \(\frac{2}{10}+\frac{2}{10}+\frac{3}{10}\)
c. \(\frac{3}{10}+\frac{3}{10}+\frac{2}{10}\)
d. \(\frac{4}{10}+\frac{2}{10}+\frac{1}{10}\)

Answer:
c. \(\frac{3}{10}+\frac{3}{10}+\frac{2}{10}\)

Explanation:
a. \(\frac{5}{10}+\frac{1}{10}+\frac{1}{10}\) = 7/10
b. \(\frac{2}{10}+\frac{2}{10}+\frac{3}{10}\) = 7/10
c. \(\frac{3}{10}+\frac{3}{10}+\frac{2}{10}\) = 8/10
d. \(\frac{4}{10}+\frac{2}{10}+\frac{1}{10}\) = 7/10

Question 5.
Lance wants to find the total length of 3 boards. He uses the expression 3 \(\frac{1}{2}\) + (2 + 4 \(\frac{1}{2}\)). How can Lance rewrite the expression using both the Associative and Commutative Properties of Addition?
Options:
a. 5 + 4 \(\frac{1}{2}\)
b. (3 \(\frac{1}{2}\) + 2) + 4 \(\frac{1}{2}\)
c. 2 + (3 \(\frac{1}{2}\) + 4 \(\frac{1}{2}\))
d. 3 \(\frac{1}{2}\) + (4 \(\frac{1}{2}\) + 2)

Answer:
She can write as (3 \(\frac{1}{2}\) + 2) + 4 \(\frac{1}{2}\)

Question 6.
Which of the following statements is true?
Options:
a. \(\frac{5}{8}>\frac{9}{10}\)
b. \(\frac{5}{12}>\frac{1}{3}\)
c. \(\frac{3}{6}>\frac{4}{5}\)
d. \(\frac{1}{2}>\frac{3}{4}\)

Answer:
6/3 cups of milk

Explanation:
0.625 > 0.9
0.416 > 0.333
0.5 > 0.8
0.5 > 0.75

Page No. 477

Question 1.
2 × 3 \(\frac{2}{3}\) = □
_____ \(\frac{□}{□}\)

Answer:
7\(\frac{1}{3}\)

Explanation:
3 \(\frac{2}{3}\) = 11/3
2 x 11/3 = 22/3
22/3 = 7 and remainder 1. So, 22/3 = 7 (1/3)

Multiply. Write the product as a mixed number.

Question 2.
6 × \(\frac{2}{5}\) = _____ \(\frac{□}{□}\)

Answer:
2\(\frac{2}{5}\)

Explanation:
6 × \(\frac{2}{5}\) = 12/5. 12/5 = 2 and remainder. So, 12/5 = 2 2/5

Question 3.
3 × 2 \(\frac{3}{4}\) = _____ \(\frac{□}{□}\)

Answer:
8\(\frac{1}{4}\)

Explanation:
2 \(\frac{3}{4}\) = 11/4
3 x 11/4 = 33/4. 33/4 = 8 and the remainder 1. So, 33/4 = 8 1/4

Go Math 4th Grade Lesson 8.4 Homework Answer Key Question 4.
4 × 1 \(\frac{5}{6}\) = _____ \(\frac{□}{□}\)

Answer:
7 \(\frac{2}{6}\)

Explanation:
1 \(\frac{5}{6}\) = 11/6
4 x 11/6 = 44/6. 44/6 = 7 and the remainder 2. So, 44/6 = 7 2/6

Question 5.
4 × \(\frac{5}{8}\) = _____ \(\frac{□}{□}\)

Answer:
2\(\frac{1}{2}\)

Explanation:
4 × \(\frac{5}{8}\) = 5/2. 5/2 = 2 and remainder 1. So, 5/2 = 2 1/2

Question 6.
6 × \(\frac{5}{12}\) = _____ \(\frac{□}{□}\)

Answer:
2\(\frac{1}{2}\)

Explanation:
6 × \(\frac{5}{12}\) = 5/2. 5/2 = 2 and remainder 1. So, 5/2 = 2 1/2

Question 7.
3 × 3 \(\frac{1}{2}\) = _____ \(\frac{□}{□}\)

Answer:
10 \(\frac{1}{2}\)

Explanation:
3 \(\frac{1}{2}\) = 7/2
3 x 7/2 = 21/2. 21/2 = 10 and remainder 1. So, 21/2 = 10 1/2

Question 8.
2 × 2 \(\frac{2}{3}\) = _____ \(\frac{□}{□}\)

Answer:
5\(\frac{1}{3}\)

Explanation:
2 \(\frac{2}{3}\) = 8/3
2 x 8/3 = 16/3. 16/3 = 5 and remainder 1. So, 16/3 = 5 1/3

Question 9.
5 × 1 \(\frac{2}{4}\) = _____ \(\frac{□}{□}\)

Answer:
7 \(\frac{1}{2}\)

Explanation:
1 \(\frac{2}{4}\) = 6/4
5 x 6/4 = 30/4 = 15/2. 15/2 = 7 and remainder 1. So, 15/2 = 7 1/2

Question 10.
4 × 2 \(\frac{2}{5}\) = _____ \(\frac{□}{□}\)

Answer:
9\(\frac{3}{5}\)

Explanation:
2 \(\frac{2}{5}\) = 12/5
4 x 12/5 = 48/5. 48/5 = 9 and remainder 3. So, 48/5 = 9 3/5

Look for a Pattern Algebra Write the unknown number.

Question 11.
□ × 2 \(\frac{1}{3}\) = 9 \(\frac{1}{3}\)
□ = ______

Answer:
4

Explanation:
2 \(\frac{1}{3}\) = 7/3
9 \(\frac{1}{3}\) = 28/3
Let the unknown numer s.
s x 7/3 = 28/3
s = 4

Question 12.
3 × 2 \(\frac{2}{□}\) = 7 \(\frac{2}{4}\)
□ = ______

Answer:
4

Explanation:
7 \(\frac{2}{4}\) = 30/4
Let the unknown number s. If s is 4, 3 × 2 \(\frac{2}{4}\) = 3 x 10/4 = 30/4.
So, the unknown number is 4.

Question 13.
3 × □ \(\frac{3}{8}\) = 4 \(\frac{1}{8}\)
□ = ______

Answer:
1

Explanation:
4 \(\frac{1}{8}\) = 33/8
Let the unknown number is s. If s is 1, 3 × 1 \(\frac{3}{8}\) = 3 x 11/8 = 33/8.

Question 14.
Describe two different ways to write \(\frac{7}{3}\) as a mixed number.
Type below:
_________

Answer:
One is 2\(\frac{1}{3}\)
Another one is 2 + 1/3

Explanation:
7/3 = 2 and the remainder is 1. So, 2 1/3 is one mixed fraction.
Seond method is 3/3 + 3/3 + 1/3 = 2 + 1/3.

Page No. 478

Use the recipe for 15–18.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 15

Question 15.
Otis plans to make 3 batches of sidewalk chalk. How much plaster of Paris does he need?
______ \(\frac{□}{□}\) cups plaster of Paris

Answer:
4\(\frac{1}{2}\) cups plaster of Paris

Explanation:
1\(\frac{1}{2}\) = 3/2 + 3/2 + 3/2 = 9/2
9/2 = 4, the remainder is 1. So, 4 1/2 cups plaster of Paris need for 3 batches of sidewalk chalk.

Question 16.
What’s the Question? The answer is \(\frac{32}{3}\).
Type below:
_________

Answer:
How many tablespoons of powdered paint are needed for 4 batches of chalk?

Question 17.
Patty has 2 cups of warm water. Is that enough water to make 4 batches of sidewalk chalk? Explain how you know without finding the exact product.
______

Answer:
No. 4 x 1/2 = 2 and also 3/4 is greater than 1/2. So, 4 x 3/4 is greater than 2.

Go Math Lesson 8.4 4th Grade Question 18.
Rita makes sidewalk chalk 2 days a week. Each of those days, she spends 1 \(\frac{1}{4}\) hours making the chalk. How much time does Rita spend making sidewalk chalk in 3 weeks?
______ \(\frac{□}{□}\) hours

Answer:
7\(\frac{1}{2}\) hours

Explanation:
Rita makes sidewalk chalk 2 days a week. Each of those days, she spends 1 1/4 hours making the chalk.
1 week = 2 x 5/4 = 10/4 = 5/2.
3 weeks = 3 x 5/2 = 15/2 = 7 1/2.

Question 19.
Oliver has music lessons Monday, Wednesday, and Friday. Each lesson is \(\frac{3}{4}\) of an hour. Oliver says he will have lessons for 3 \(\frac{1}{2}\) hours this week. Without multiplying, explain how you know Oliver is incorrect.
Type below:
__________

Answer:
3/4 is less than 1, and 1 × 3 = 3. So 3/4 × 3 will also be less than 3.
Oliver’s answer, 3 1/2 is greater than 3, so it is incorrect.

Common Core – New – Page No. 479

Multiply a Fraction or Mixed Number by a Whole Number.

Multiply. Write the product as a mixed number.

Question 1.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers Common Core - New img 16

Answer:
1\(\frac{5}{10}\)

Explanation:
5 x 3/10 = 15/10 = 1 and remainder is 5. So, the mixed fraction is 1 5/10

Question 2.
3 × \(\frac{3}{5}\) =
______ \(\frac{□}{□}\)

Answer:
1\(\frac{4}{5}\)

Explanation:
3 x 3/5 = 9/5 = 1 and remainder is 4. So, the mixed fraction is 1 4/5

Question 3.
5 × \(\frac{3}{4}\) =
______ \(\frac{□}{□}\)

Answer:
3\(\frac{3}{4}\)

Explanation:
15/4 = 3 and remainder is 3. So, the mixed fraction is 3 3/4

Question 4.
4 × 1 \(\frac{1}{5}\) =
______ \(\frac{□}{□}\)

Answer:
4\(\frac{4}{5}\)

Explanation:
1 \(\frac{1}{5}\) = 6/5.
4 x 6/5 = 24/5 = 4 and the remainder is 4. So, the mixed fraction is 4 4/5

Question 5.
2 × 2 \(\frac{1}{3}\) =
______ \(\frac{□}{□}\)

Answer:
4\(\frac{2}{3}\)

Explanation:
2 \(\frac{1}{3}\) = 7/3.
2 x 7/3 = 14/3.
14/3 = 4 and the remainder is 2. So, the mixed fraction is 4 2/3

Question 6.
5 × 1 \(\frac{1}{6}\) =
______ \(\frac{□}{□}\)

Answer:
5\(\frac{5}{6}\)

Explanation:
1 \(\frac{1}{6}\) = 7/6
5 x 7/6 = 35/6.
35/6 = 5 and the remainder is 5. So, the mixed fraction is 5 5/6

Question 7.
2 × 2 \(\frac{7}{8}\) =
______ \(\frac{□}{□}\)

Answer:
6\(\frac{1}{1}\)

Explanation:
2 \(\frac{7}{8}\) = 23/8
2 x 23/8 = 46/8 = 6 1/1

Question 8.
7 × 1 \(\frac{3}{4}\) =
______ \(\frac{□}{□}\)

Answer:
9\(\frac{3}{4}\)

Explanation:
1 \(\frac{3}{4}\) = 7/4
7 x 7/4 = 39/4
39/4 = 9 and the remainder is 3. So, the mixed fraction is 9 3/4

Question 9.
8 × 1 \(\frac{3}{5}\) =
______ \(\frac{□}{□}\)

Answer:
12\(\frac{4}{5}\)

Explanation:
1 \(\frac{3}{5}\) = 8/5
8 x 8/5 = 64/5
64/5 = 12 and the remainder is 4. So, the mixed fraction is 12 4/5

Problem Solving

Question 10.
Brielle exercises for \(\frac{3}{4}\) hour each day for 6 days in a row. Altogether, how many hours does she exercise during the 6 days?
______ \(\frac{□}{□}\)

Answer:
4\(\frac{2}{4}\)

Explanation:
6 x 3/4 = 18/4 = 4 and the remainder is 2. So, the mixed fraction is 4 2/4.

Question 11.
A recipe for quinoa calls for 2 \(\frac{2}{3}\) cups of milk. Conner wants to make 4 batches of quinoa. How much milk does he need?
______ \(\frac{□}{□}\)

Answer:
10\(\frac{2}{3}\)

Explanation:
quinoa calls for 8/3 cups of milk. Conner wants to make 4 batches of quinoa.
So, 4 x 8/3 = 32/3 = 10 and the remainder is 2. So, the mixed fraction is 10 2/3

Common Core – New – Page No. 480

Lesson Check

Question 1.
A mother is 1 \(\frac{3}{4}\) times as tall as her son. Her son is 3 feet tall. How tall is the mother?
Options:
a. 4 \(\frac{3}{4}\) feet
b. 5 \(\frac{1}{4}\) feet
c. 5 \(\frac{1}{2}\) feet
d. 5 \(\frac{3}{4}\) feet

Answer:
b. 5 \(\frac{1}{4}\) feet

Explanation:
A mother is 1 3/4 times as tall as her son. Her son is 3 feet tall.
So, 3 x 7/4 = 21/4 = 5 and the remainder is 1. The mixed fraction is 5 1/4 feet.

Question 2.
The cheerleaders are making a banner that is 8 feet wide. The length of the banner is 1 \(\frac{1}{3}\) times the width of the banner. How long is the banner?
Options:
a. 8 \(\frac{1}{3}\) feet
b. 8 \(\frac{3}{8}\) feet
c. 10 \(\frac{1}{3}\) feet
d. 10 \(\frac{2}{3}\) feet

Answer:
d. 10 \(\frac{2}{3}\) feet

Explanation:
The cheerleaders are making a banner that is 8 feet wide. he length of the banner is 1 1/3 times the width of the banner.
So, 8 x 4/3 = 32/3 =10 and the remainder is 2. The mixed fraction is 10 2/3 feet.

Spiral Review

Question 3.
Karleigh walks \(\frac{5}{8}\) mile to school every day. How far does she walk to school in 5 days?
Options:
a. \(\frac{5}{40}\) mile
b. \(\frac{25}{40}\) mile
c. \(\frac{10}{8}\) miles
d. \(\frac{25}{8}\) miles

Answer:
d. \(\frac{25}{8}\) miles

Explanation:
5 x 5/8 = 25/8.

Question 4.
Which number is a multiple of \(\frac{4}{5}\)?
Options:
a. \(\frac{8}{10}\)
b. \(\frac{12}{15}\)
c. \(\frac{16}{20}\)
d. \(\frac{12}{5}\)

Answer:
d. \(\frac{12}{5}\)

Explanation:
The multiple of \(\frac{4}{5}\) has the denominator 5. So, \(\frac{12}{5}\) is the correct answer.

Go Math Chapter 8 Grade 4 Answer Key Question 5.
Jo cut a key lime pie into 8 equal-size slices. The next day, \(\frac{7}{8}\) of the pie is left. Jo puts each slice on its own plate. How many plates does she need?
Options:
a. 5
b. 6
c. 7
d. 8

Answer:
c. 7

Explanation:
Jo cut a key lime pie into 8 equal-size slices. The next day, \(\frac{7}{8}\) of the pie is left. Jo puts each slice on its own plate. She needs 7 plates.

Question 6.
Over the weekend, Ed spent 1 \(\frac{1}{4}\) hours doing his math homework and 1 \(\frac{3}{4}\) hours doing his science project. Altogether, how much time did Ed spend doing homework over the weekend?
Options:
a. 3 hours
b. 2 \(\frac{3}{4}\) hours
c. 2 \(\frac{1}{2}\) hours
d. 2 hours

Answer:
a. 3 hours

Explanation:
5/4 + 7/4 = 12/4 = 3 hours

Page No. 483

Question 1.
Komodo dragons are the heaviest lizards on Earth. A baby Komodo dragon is 1 \(\frac{1}{4}\) feet long when it hatches. Its mother is 6 times as long. How long is the mother?
First, draw a bar model to show the problem.
Type below:
_________

Answer:
Grade 4 Chapter 8 Image 1 483

Question 1.
Then, write the equation you need to solve.
Type below:
_________

Answer:
A baby Komodo dragon is 5/4 feet.
Her mother is 6 x 5/4 = 30/4 feet long.

Question 1.
Finally, find the length of the mother Komodo dragon.
The mother Komodo dragon is _____ feet long.
______ \(\frac{□}{□}\)

Answer:
7\(\frac{2}{4}\)

Explanation:
30/4 = 7 and the remainder is 2. The mixed fraction is 7 2/4 feet.

Question 2.
What if a male Komodo dragon is 7 times as long as the baby Komodo dragon? How long is the male? How much longer is the male than the mother?
______ \(\frac{□}{□}\) feet long
______ \(\frac{□}{□}\) feet longer

Answer:
35/4 feet long
5/4 feet longer

Explanation:
If a male Komodo dragon is 7 times as long as the baby Komodo dragon, then 7 x 5/4 = 35/4.
35/4 – 30/4 = 5/4 feet male Komodo dragon is grater than female Komodo dragon.

Question 3.
The smallest hummingbird is the Bee hummingbird. It has a mass of about 1 \(\frac{1}{2}\) grams. A Rufous hummingbird’s mass is 3 times the mass of the Bee hummingbird. What is the mass of a Rufous hummingbird?
______ \(\frac{□}{□}\) grams

Answer:
9/2 grams

Explanation:

The smallest hummingbird is the Bee hummingbird. It has a mass of about 1 \(\frac{1}{2}\) grams. A Rufous hummingbird’s mass is 3 times the mass of the Bee hummingbird.
3 x 3/2 = 9/2 grams.

Question 4.
Sloane needs \(\frac{3}{4}\) hour to drive to her grandmother’s house. It takes her 5 times as long to drive to her cousin’s house. How long does it take to drive to her cousin’s house?
______ \(\frac{□}{□}\) hours

Answer:
\(\frac{15}{4}\) hours

Explanation:
5 x 3/4 = 15/4
To drive to her cousin’s house, it takes 15/4 hours.

Page No. 484

Use the table for 5 and 6.

Payton has a variety of flowers in her garden. The table shows the average heights of the flowers.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 17

tulip = 5/4 = 1.25
daisy = 5/2 = 2.5
tiger lily = 10/3 = 3.33
sunflower = 31/4 = 7.75

Question 5.
Make Sense of Problems What is the difference between the height of the tallest flower and the height of the shortest flower in Payton’s garden?
______ \(\frac{□}{□}\) feet

Answer:
6\(\frac{2}{4}\) feet

Explanation:
tallest flower = sunflower
shortest flower = tulip
The difference between the tallest flower and shortest flower = 31/4 – 5/4 = 26/4 =6 and the remainder is 2. So, the mixed fraction is 6 2/4 feet.

Question 6.
Payton says her average sunflower is 7 times the height of her average tulip. Do you agree or disagree with her statement? Explain your reasoning.
Type below:
_________

Answer:
I will disagree with her statement. Tulip = 5/4. 7 x 5/4 = 35/4. 31/4 is smaller than 35/4. So the statement is not correct.

Question 7.
Miguel ran 1 \(\frac{3}{10}\) miles on Monday. On Friday, Miguel ran 3 times as far as he did on Monday. How much farther did Miguel run on Friday than he did on Monday?
______ \(\frac{□}{□}\) miles

Answer:
3\(\frac{9}{10}\) miles

Explanation:
Miguel ran 13/10 miles on Monday.
On Friday, 3 x 13/10 = 39/10 miles = 3 and the remainder is 9. the mixed fraction is 3 9/10 miles

Question 8.
The table shows the lengths of different types of turtles at a zoo.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 18
For numbers 8a–8d, select True or False for each statement.
a. Daisy is 4 times as long as Tuck.
i. True
ii. False

Answer:
ii. False

Explanation:
Tuck = 7/6
Lolly = 35/6
Daisy = 7/2
7/6 x 4 = 28/6.
So, the statement is false.

Question 8.
b. Lolly is 5 times as long as Tuck.
i. True
ii. False

Answer:
i. True

Explanation:
5 x 7/6 = 35/6.
So, the statement is true.

Question 8.
c. Daisy is 3 times as long as Tuck.
i. True
ii. False

Answer:
i. True

Explanation:
3 x 7/6 = 21/6 = 7/2
So, the statement is true.

Question 8.
d. Lolly is 2 times as long as Daisy.
i. True
ii. False

Answer:
ii. False

Explanation:
2 x 7/2 = 7.
So, the statement is false.

Common Core – New – Page No. 485

Problem Solving Comparison

Problems with Fractions

Read each problem and solve.

Question 1.
A shrub is 1 \(\frac{2}{3}\) feet tall. A small tree is 3 times as tall as the shrub. How tall is the tree?
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers Common Core - New img 19

Answer:
5 feet

Explanation:
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers Common Core - New img 19

Question 2.
You run 1 \(\frac{3}{4}\) miles each day. Your friend runs 4 times as far as you do. How far does your friend run each day?
__________ miles

Answer:
7 miles

Explanation:
4 x 7/4 = 7 miles each day

Question 3.
At the grocery store, Ayla buys 1 \(\frac{1}{3}\) pounds of ground turkey. Tasha buys 2 times as much ground turkey as Ayla. How much ground turkey does Tasha buy?
______ \(\frac{□}{□}\) pounds

Answer:
2\(\frac{2}{3}\) pounds

Explanation:
2 x 4/3 = 8/3 = 2 and the remainder is 2. The mixed fraction is 2 2/3 pounds

Go Math Grade 4 Chapter 8 Review Test Answers Question 4.
When Nathan’s mother drives him to school, it takes \(\frac{1}{5}\) hour. When Nathan walks to school, it takes him 4 times as long to get to school. How long does it take Nathan to walk to school?
\(\frac{□}{□}\) hours

Answer:
\(\frac{4}{5}\) hours

Explanation:
4 x 1/5 = 4/5 hour

Common Core – New – Page No. 486

Lesson Check

Question 1.
A Wilson’s Storm Petrel is a small bird with a wingspan of 1 \(\frac{1}{3}\) feet. A California Condor is a larger bird with a wingspan almost 7 times as wide as the wingspan of the petrel. About how wide is the wingspan of the California Condor?
Options:
a. \(\frac{4}{21}\) foot
b. 2 \(\frac{1}{3}\) feet
c. 7 \(\frac{1}{3}\) feet
d. 9 \(\frac{1}{3}\) feet

Answer:
d. 9 \(\frac{1}{3}\) feet

Explanation:
1 1/3 = 4/3.
7 x 4/3 = 28/3 feet = 9 and the remainder is 1. The mixed fraction is 9 1/3

Question 2.
The walking distance from the Empire State Building in New York City to Times Square is about \(\frac{9}{10}\) mile. The walking distance from the Empire State Building to Sue’s hotel is about 8 times as far. About how far is Sue’s hotel from the Empire State Building?
Options:
a. \(\frac{9}{80}\) mile
b. \(\frac{72}{80}\) mile
c. 1 \(\frac{7}{10}\) miles
d. 7 \(\frac{2}{10}\) miles

Answer:
d. 7 \(\frac{2}{10}\) miles

Explanation:
8 x 9/10 mile = 72/10 mile = 7 and the remainder is 2. The mixed fraction is 7 2/10 miles.

Spiral Review

Question 3.
Which of the following expressions is NOT equal to 3 × 2 \(\frac{1}{4}\)?
Options:
a. 3 × \(\frac{9}{4}\)
b. (3 × 2) + (3 × \(\frac{1}{4}\))
c. 6 \(\frac{3}{4}\)
d. 3 × 2 + \(\frac{1}{4}\)

Answer:
d. 3 × 2 + \(\frac{1}{4}\)

Explanation:
3 × 2 \(\frac{1}{4}\) = 3 x 9/4 = 27/4
a. 3 × \(\frac{9}{4}\) = 27/4
b. (3 × 2) + (3 × \(\frac{1}{4}\)) = 6 + 3/4 = 27/4
c. 6 \(\frac{3}{4}\) = 27/4
d. 3 × 2 + \(\frac{1}{4}\) = 6 + 1/4 = 25/4

Question 4.
At a bake sale, Ron sells \(\frac{7}{8}\) of an apple pie and \(\frac{5}{8}\) of a cherry pie. Altogether, how much pie does he sell at the bake sale?
Options:
a. \(\frac{2}{8}\)
b. \(\frac{12}{16}\)
c. \(\frac{12}{8}\)
d. \(\frac{35}{8}\)

Answer:
c. \(\frac{12}{8}\)

Explanation:
7/8 + 5/8 = 12/8
The bake sale 12/8 pie.

Question 5.
On a ruler, which measurement is between \(\frac{3}{16}\) inch and \(\frac{7}{8}\) inch?
Options:
a. \(\frac{1}{16}\) inch
b. \(\frac{1}{8}\) inch
c. \(\frac{11}{16}\) inch
d. \(\frac{15}{16}\) inch

Answer:
c. \(\frac{11}{16}\) inch

Question 6.
Which of the following numbers is composite?
Options:
a. 4
b. 3
c. 2
d. 1

Answer:
a. 4

Explanation:
4 has more than 2 factors.

Page No. 487

Question 1.
What are the next four multiples of \(\frac{1}{8}\)?
Type below:
_________

Answer:
2/8, 3/8, 4/8, 5/8

Explanation:
1 x 1/8 = 1/8.
2 x 1/8 = 2/8.
3 x 1/8 = 3/8.
4 x 1/8 = 4/8.
5 x 1/8 = 5/8.
Next four multiples of 1/8 are 2/8, 3/8, 4/8, 5/8.

Question 2.
Marta is making 3 servings of fruit salad. She adds \(\frac{3}{8}\) cup blueberries for each serving. Her measuring cup holds \(\frac{1}{8}\) cup. How many times must Marta measure \(\frac{1}{8}\) cup of blueberries to have enough for the fruit salad? Shade the models to show your answer.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 20
Marta must measure \(\frac{1}{8}\) _________ cup times.
_________

Answer:
Grade 4 Chapter 8 Image 1 487

Marta must measure \(\frac{1}{8}\) 9 cup times.

Question 3.
Mickey exercises \(\frac{3}{4}\) hour every day. How many hours does he exercise in 8 days?
_____ hours

Answer:
6 hours

Explanation:
8 x 3/4 = 24/4 = 6

Page No. 488

Question 4.
Molly is baking for the Moms and Muffins event at her school. She will bake 4 batches of banana muffins. She needs 1 \(\frac{3}{4}\) cups of bananas for each batch of muffins.
Part A
Molly completed the multiplication below and said she needed 8 cups of bananas for 4 batches of muffins. What is Molly’s error?
\(4 \times 1 \frac{3}{4}=4 \times \frac{8}{4}=\times \frac{32}{4}=8\)
Type below:
_________

Answer:
4 x 1 3/4 = 4 x 8/4 = 8
Molly did not write the mixed number, 1 3/4 as a fraction correctly. 1 3/4 is not equal to 8/4.

Question 4.
Part B
What is the correct number of cups Molly needs for 4 batches of muffins? Explain how you found your answer.
_____ cups

Answer:
7 cups

Explanation:
She will bake 4 batches of banana muffins. She needs 7/4 cups of bananas for each batch of muffins.
So, if she prepares 4 batches of muffins = 4 x 7/4 = 7 cups of banana.

Question 5.
Which fraction is a multiple of \(\frac{1}{9}\)? Mark all that apply.
Options:
a. \(\frac{3}{9}\)
b. \(\frac{9}{12}\)
c. \(\frac{2}{9}\)
d. \(\frac{4}{9}\)
e. \(\frac{9}{10}\)
f. \(\frac{9}{9}\)

Answer:
a. \(\frac{3}{9}\)
c. \(\frac{2}{9}\)
d. \(\frac{4}{9}\)
f. \(\frac{9}{9}\)

Explanation:
The multiples of \(\frac{1}{9}\) have the denominator of 9.

Question 6.
Mimi recorded a soccer game that lasted 1 \(\frac{2}{3}\) hours. She watched it 3 times over the weekend to study the plays. How many hours did Mimi spend watching the soccer game? Show your work.
_____ hours

Answer:
5 hours

Explanation:
3 x 1 2/3 = 3 x 5/3 = 5 hours.

Question 7.
Theo is comparing shark lengths. He learned that a horn shark is 2 \(\frac{3}{4}\) feet long. A blue shark is 4 times as long. Complete the model. Then find the length of a blue shark.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 21
A blue shark is ____ feet long.
_____

Answer:
Grade 4 Chapter 8 Image 2 487
4 x 11/4 = 11.
A blue shark is 11 feet long.

Page No. 489

Question 8.
Joel made a number line showing the multiples of \(\frac{3}{5}\).
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 22
The product 2 × \(\frac{3}{5}\) is shown by the fraction _________ on the number line.
\(\frac{□}{□}\)

Answer:
The product 2 × \(\frac{3}{5}\) is shown by the fraction \(\frac{6}{5}\) on the number line.

Question 9.
Bobby has baseball practice Monday, Wednesday, and Friday. Each practice is 2 \(\frac{1}{2}\) hours. Bobby says he will have practice for 4 hours this week.
Part A
Without multiplying, explain how you know Bobby is incorrect.
Type below:
_________

Answer:
Bobby needs to find 3 × 2 1/2. If he estimates 3 × 2 hours, then he finds the practice is at least 6 hours. 6 is greater than 4, so Bobby’s answer is incorrect.

Question 9.
Part B
How long will Bobby have baseball practice this week? Write your answer as a mixed number. Show your work.
______ \(\frac{□}{□}\) hours

Answer:
7\(\frac{1}{2}\) hours

Explanation:
3 x 2 1/2 = 3 x 5/2 = 15/2 = 7 1/2

Question 10.
Look at the number line. Write the missing fractions.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 23
Type below:
_________

Answer:
9/6, 10/6, 11/6, 12/6

Go Math Grade 4 Pdf Chapter 8 Review/Test Answer Key Question 11.
Ana’s dachshund weighed 5 \(\frac{5}{8}\) pounds when it was born. By age 4, the dog weighed 6 times as much. Fill each box with a number or symbol from the list to show how to find the weight of Ana’s dog at age 4. Not all numbers and symbols may be used.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 24
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 25
Type below:
_________

Answer:
Grade 4 Chapter 8 Image 1 489

Page No. 490

Question 12.
Asta made a fraction number line to help her find 3 × \(\frac{4}{5}\).
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 26
Select a way to write 3 × \(\frac{4}{5}\) as the product of a whole number and a unit fraction.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 27
Type below:
_________

Answer:
Grade 4 Chapter 8 Image 1 490
12 × \(\frac{1}{5}\)

Explanation:
3 x 4/5 = 12/5 = 12 x 1/5.

Question 13.
Yusif wanted to give \(\frac{1}{3}\) of his total toy car collection to 2 of his friends. How many of his toy cars will he give away?
\(\frac{□}{□}\)

Answer:
\(\frac{2}{3}\)

Explanation:
Yusif wanted to give \(\frac{1}{3}\) of his total toy car collection to 2 of his friends. He has three toy cars in total. He has given 2 cars out of 3 cars. So, the answer is \(\frac{2}{3}\).

Question 14.
Select the correct product for the equation.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 28
4 × \(\frac{5}{8}\) = □ 4 × \(\frac{4}{8}\) = □
Type below:
_________

Answer:
4 × \(\frac{5}{8}\) = \(\frac{20}{8}\)
4 × \(\frac{4}{8}\) = \(\frac{16}{8}\)

Page No. 491

Question 15.
The lengths of different types of snakes at a zoo are shown in the table.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 29
For numbers 15a–15d, select True or False for the statement.
a. Bobby is 4 times as long as Kenny.
i. True
ii. False

Answer:
ii. False

Explanation:
Kenny = 3/2
Bobby = 9/2
Puck = 15/2
4 x 3/2 =6
So, the statement is false.

Question 15.
b. Bobby is 3 times as long as Kenny.
i. True
ii. False

Answer:
i. True

Explanation:
3 x 3/2 = 9/2
So, the statement is true.

Question 15.
c. Puck is 5 times as long as Kenny.
i. True
ii. False

Answer:
i. True

Explanation:
5 x 3/2 = 15/2
So, the statement is true.

Question 15.
d. Puck is 2 times as long as Bobby.
i. True
ii. False

Answer:
ii. False

Explanation:
2 x 9/2 = 9
So, the statement is false.

Question 16.
Hank used 3 \(\frac{1}{2}\) bags of seed to plant grass in his front yard. He used 3 times as much seed to plant grass in his back yard. How much seed did Hank need for the backyard?
_____ \(\frac{□}{□}\)

Answer:
10\(\frac{1}{2}\)

Explanation:
3 x 7/2 = 21/2 = 10 and the remainder is 1. The answer is 10 1/2.

Question 17.
Jess made a big kettle of rice and beans. He used 1 \(\frac{1}{2}\) cups of beans. He used 4 times as much rice.
Part A
Draw a model to show the problem.
Type below:
_________

Answer:
Grade 4 Chapter 8 Image 1 491

Question 17.
Part B
Use your model to write an equation. Then solve the equation to find the amount of rice Jess needs.
Type below:
_________

Answer:
6 cups

Explanation:
Rice = 4 x 3/2 = 12/2 = 6.
Jess needs 6 cups of rice.

Page No. 492

Question 18.
Mrs. Burnham is making modeling clay for her class. She needs \(\frac{2}{3}\) cup of warm water for each batch.
Part A
Mrs. Burnham has a 1-cup measure that has no other markings. Can she make 6 batches of modeling clay using only the 1-cup measure? Describe two ways you can find the answer.
Type below:
_________

Answer:
Yes. She needs 6 x 2/3 cups of water. 6 x 2/3 = 12/3 = 4 cups.
So, she can use the 1-cup measure 4 times to make 6 batches.

Question 18.
Part B
The modeling clay recipe also calls for \(\frac{1}{2}\) cup of cornstarch. Nikki says Mrs. Burnham will also need 4 cups of cornstarch. Do you agree or disagree? Explain.
Type below:
_________

Answer:
Disagree; 6 x 1/2 = 3 cups of cornstrach.
She doesn’t need 4 cups of cornstarch.

Question 19.
Donna buys some fabric to make place mats. She needs \(\frac{1}{5}\) yard of each type of fabric. She has 9 different types of fabrics to make her design. Use the following equation. Write the number in the box to make the statement true.
\(\frac{9}{5}\) = ______ × \(\frac{1}{5}\)

Answer:
9

Question 20.
Mr. Tuyen uses \(\frac{5}{8}\) of a tank of gas each week to drive to and from his job. How many tanks of gas does Mr. Tuyen use in 5 weeks? Write your answer two different ways.
Mr. Tuyen uses __________ or _________ tanks of gas.
Type below:
_________

Answer:
Mr. Tuyen uses 25/8 or 3\(\frac{1}{8}\) tanks of gas

Explanation:
5 x 5/8 = 25/8 = 3 and the remainder is 1. So, the mixed fraction is 3 1/8.

Question 21.
Rico is making 4 batches of salsa. Each batch needs \(\frac{2}{3}\) cup of corn. He only has a \(\frac{1}{3}\)– cup measure. How many times must Rico measure \(\frac{1}{3}\) cup of corn to have enough for all of the salsa?
______ times

Answer:
8 times

Explanation:
Rico is making 4 batches of salsa. Each batch needs \(\frac{2}{3}\) cup of corn. He only has a \(\frac{1}{3}\)– cup measure.
So, he needs 2x 1/3 cups for one batch. For 4 batches of salsa, 4 x 2 = 8 cups of corn required.

Page No. 497

Question 1.
Write five tenths as a fraction and as a decimal.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 30
Fraction: __________ Decimal: __________
Type below:
_________

Answer:
Grade 4 Chapter 8 Image 1 497
5/10 = 0.5

Write the fraction or mixed number and the decimal shown by the model.

Question 2.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 31
Type below:
_________

Answer:
3\(\frac{2}{10}\)
three and two-tenths

Question 3.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 32
Type below:
_________

Answer:
\(\frac{8}{10}\)
Grade 4 Chapter 8 Image 2 497

Write the fraction or mixed number and the decimal shown by the model.

Question 4.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 33
Type below:
_________

Answer:
4/10 = 0.4

Explanation:
4 boxes are shaded out of 10 boxes. So, the fraction is 4/10.

Question 5.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 34
Type below:
_________

Answer:
1\(\frac{2}{10}\)

Question 6.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 35
Type below:
_________

Answer:
2\(\frac{9}{10}\)

Question 7.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 36
Type below:
_________
Answer:
3\(\frac{4}{10}\)

Practice: Copy and Solve Write the fraction or mixed number as a decimal.

Question 8.
5 \(\frac{9}{10}\) = _____

Answer:
\(\frac{59}{10}\)

Explanation:
Multiply 10 x 5 = 50.
Add 50 + 9 = 59.
The fraction is 59/10

Question 9.
\(\frac{1}{10}\) = _____

Answer:
0.1

Question 10.
\(\frac{7}{10}\) = _____

Answer:
0.7

Question 11.
8 \(\frac{9}{10}\) = _____

Answer:
\(\frac{89}{10}\)

Explanation:
Multiply 10 x 8 = 80.
Add 80 + 9 = 89.
The fraction is 89/10

Question 12.
\(\frac{6}{10}\) = _____

Answer:
0.6

Question 13.
6 \(\frac{3}{10}\) = _____

Answer:
\(\frac{63}{10}\)

Explanation:
Multiply 10 x 6 = 60.
Add 60 + 3 = 63.
The fraction is 63/10

Question 14.
\(\frac{5}{10}\) = _____

Answer:
0.5

Question 15.
9 \(\frac{7}{10}\) = _____

Answer:
\(\frac{97}{10}\)

Explanation:
Multiply 10 x 9 = 90.
Add 90 +7 = 97.
The fraction is 97/10

Page No. 498

Use the table for 16−19.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 37
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 38

Question 16.
What part of the rocks listed in the table are igneous? Write your answer as a decimal.
_____

Answer:
0.5

Question 17.
Sedimentary rocks make up what part of Ramon’s collection? Write your answer as a fraction and in word form.
Type below:
_________

Answer:
3/10 and three-tenths

Question 18.
What part of the rocks listed in the table are metamorphic? Write your answer as a fraction and as a decimal.
Type below:
_________

Answer:
2/10 or 0.2

Question 19.
Communicate Niki wrote the following sentence in her report: “Metamorphic rocks make up 2.0 of Ramon’s rock collection.” Describe her error.
Type below:
_________

Answer:
Metamorphic rocks make up 2.0 of Ramon’s rock collection. But from the given table, it is clearly mentioned that the answer is 0.2. So, she made a mistake to make up Ramon’s rock collection.

Question 20.
Josh paid for three books with two $20 bills. He received $1 in change. Each book was the same price. How much did each book cost?
$ _____ each book

Answer:
$19/3 for each book.

Explanation:
Josh paid for three books with two $20 bills. He received $1 in change. So, he paid $19 for three books. As the each book has same price, the answer is $19/3 for each book.

Question 21.
Select a number shown by the model. Mark all that apply.
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers img 39
Type below:
_________

Answer:
1\(\frac{7}{10}\)
1.7

Conclusion:

Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers PDF with solved problems are provided here. Review every problem and way of answering. Refer Grade 4 Chapter 8 Answer Key to get success in exams. Get your estimated grade with easy learning. It is possible when you use Go Math Grade 4 Chapter 8 Multiply Fractions by Whole Numbers Solution Key.

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Go Math Grade 4 Chapter 6 Answer Key Pdf Fraction Equivalence and Comparison

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Fraction Equivalence and Comparison Go Math Grade 4 Chapter 6 Answer Key Pdf

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Lesson 1: Investigate • Equivalent Fractions

Lesson 2: Generate Equivalent Fractions

Lesson 3: Simplest Form

Lesson 4: Common Denominators

Lesson 5: Problem Solving • Find Equivalent Fractions

Mid-Chapter Checkpoint

Lesson 6: Compare Fractions Using Benchmarks

Lesson 7: Compare Fractions

Lesson 8: Compare and Order Fractions

Review/Test

Common Core – Equivalent Fractions – Page No. 331

Equivalent Fractions
Use the model to write an equivalent fraction.

Question 1.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Equivalent Fractions img 1
\(\frac{4}{6}=\frac{2}{3}\)

Answer:
\(\frac{4}{6}=\frac{2}{3}\)

Explanation:
The first image has 4 parts shaded our of 6 parts. Divide \(\frac{8}{10}\) with 2. You will get \(\frac{2}{3}\). That means 2 parts are shaded out of 3 parts.

Question 2.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Equivalent Fractions img 2
\(\frac{3}{4}\) = \(\frac{□}{□}\)

Answer:
\(\frac{3}{4}\) = \(\frac{6}{8}\)

Explanation:
The first image has 3 parts shaded our of 4 parts. Multiply \(\frac{8}{10}\) with 2. You will get \(\frac{6}{8}\). That means 6 parts are shaded out of 8 parts.

Tell whether the fractions are equivalent. Write = or ≠.

Question 3.
\(\frac{8}{10}\) _______ \(\frac{4}{5}\)

Answer:
\(\frac{8}{10}\) = \(\frac{4}{5}\)

Explanation:
Multiply the numerator and denominator of 4 / 5 with 2
8 / 10 = (2 / 2 ) x (4 / 5 )
= 8 / 10
So, 8 / 10 = 4 / 5.

Question 4.
\(\frac{1}{2}\) _______ \(\frac{7}{12}\)

Answer:
\(\frac{1}{2}\) ≠ \(\frac{7}{12}\)

Explanation:
Multiply the numerator and denominator of 1 / 2 with 6
1 / 2 = (6 / 6) x (1 / 2)
= (6 / 12)
So, 1/2 ≠ 7 / 12

My Homework Lesson 6 Answer Key 4th Grade Question 5.
\(\frac{3}{4}\) _______ \(\frac{8}{12}\)

Answer:
\(\frac{3}{4}\) ≠ \(\frac{8}{12}\)

Explanation:
Multiply the numerator and denominator of 3 / 4 with 3
3 / 4 = (3 / 3) x (3 / 4)
= (9 / 12)
So, 3 / 4 ≠ 8 / 12

Question 6.
\(\frac{2}{3}\) _______ \(\frac{4}{6}\)

Answer:
\(\frac{2}{3}\) = \(\frac{4}{6}\)

Explanation:
Multiply the numerator and denominator of 2 / 3 with 2
2 / 3 = (2 / 2) x ( 2 / 3 )
= 4 / 6
So, 2 / 3 = 4 / 6.

Question 7.
\(\frac{5}{8}\) _______ \(\frac{4}{10}\)

Answer:
\(\frac{5}{8}\) ≠ \(\frac{4}{10}\)

Explanation:
Multiply the numerator and denominator of 5 / 8 with 2
5 / 8 =(2 / 2) x (5 / 8)
= (10 / 16)
So, 5 / 8 ≠ 4 / 10

Question 8.
\(\frac{2}{6}\) _______ \(\frac{4}{12}\)

Answer:
\(\frac{2}{6}\) = \(\frac{4}{12}\)

Explanation:
Multiply the numerator and denominator of 2 / 6 with 2
2 / 6 = (2 / 2) x (2 / 6)
= (4 / 12)
So, 2 / 6 = 4 / 12.

Question 9.
\(\frac{20}{100}\) _______ \(\frac{1}{5}\)

Answer:
\(\frac{20}{100}\) = \(\frac{1}{5}\)

Explanation:
Cross Multiply the 20 / 100 with 20 / 20
20 / 100 = (20 / 20) x (20 / 100)
= (1 / 5)
So, 20 / 100 = 1 / 5.

Question 10.
\(\frac{5}{8}\) _______ \(\frac{9}{10}\)

Answer:
\(\frac{5}{8}\) ≠ \(\frac{9}{10}\)

Explanation:
Multiply the numerator and denominator of 5 / 8 with 2
5 / 8 = (2 / 2) x (5 / 8)
= 10 / 16
So, 5 / 8 ≠ 9 / 10

Question 11.
Jamal finished \(\frac{5}{6}\) of his homework. Margaret finished \(\frac{3}{4}\) of her homework, and Steve finished \(\frac{10}{12}\) of his homework. Which two students finished the same amount of homework?
_______

Answer:
Jamal and Steve

Explanation:
As per the given data,
Jamal finished work = 5 /6 of his homework
Margaret finished work = 3 / 4th of her homework
Steve finished work = 10 / 12 of his homework
Multiply the numerator and denominator of 5/ 6 with 2
Then, (2 / 2) x (5 / 6) = 10 / 12
Then, Jamal and Steve finished the same amount of homework.

Go Math Grade 4 Chapter 6 Review/Test Answer Key Question 12.
Sophia’s vegetable garden is divided into 12 equal sections. She plants carrots in 8 of the sections. Write two fractions that are equivalent to the part of Sophia’s garden that is planted with carrots.
Type below:
___________

Answer:
\(\frac{2}{3}\) and \(\frac{4}{6}\)

Explanation:
As per the given data,
Sophia’s vegetable garden is divided into 12 equal sections
She plants carrots in 8 of the sections out of 12 sections = 8 / 12
By simplifying the 8 / 12, we will get 4 / 6
Again simplify the 4 /6 by dividing method, you will get 2 /3
2 / 3 = (2 / 2) x (2 / 3)
= 4 / 6
Then, the equivalent fractions are 2 / 3, 4 /6

Common Core – Equivalent Fractions – Page No. 332

Question 1.
A rectangle is divided into 8 equal parts. Two parts are shaded. Which fraction is equivalent to the shaded area of the rectangle?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{1}{3}\)
c. \(\frac{2}{6}\)
d. \(\frac{3}{4}\)

Answer:
a. \(\frac{1}{4}\)

Explanation:
As per the given data,
A rectangle is divided into 8 equal parts
Two parts are shaded
Then, the shaded area of the rectangle = 2 / 8
By simplifying the 2/ 8, you will get 1/ 4
So, the shaded area of the rectangle = 1 / 4

Question 2.
Jeff uses 3 fifth-size strips to model \(\frac{3}{5}\). He wants to use tenth-size strips to model an equivalent fraction. How many tenth-size strips will he need?
Options:
a. 10
b. 6
c. 5
d. 3

Answer:
b. 6

Explanation:
From the given data,
Jeff uses 3 fifth–size strips to model = 3 / 5 size strips
If he wants to use tenth–size strips to an equivalent fraction = 1 / 10 size strips
The number of strips = x
(1 / 10) x = 3 / 5
x = 30/5
Then, the required number of tenth-size trips = 6

Go Math Grade 4 Chapter 6 Answer Key Pdf Question 3.
Cassidy places 40 stamps on each of the 8 album pages. How many stamps does she place in all?
Options:
a. 300
b. 320
c. 360
d. 380

Answer:
b. 320

Explanation:
As per the given data,
Cassidy places 40 stamps on each of 8 album pages = 8 x 40
= 320
So, the total placed stamps on album pages by Cassidy = 320 stamps

Question 4.
Maria and 3 friends have 1,200 soccer cards. If they share the soccer cards equally, how many will each person receive?
Options:
a. 30
b. 40
c. 300
d. 400

Answer:
c. 300

Explanation:
As per the given data,
Maria and 3 friends have 1200 soccer cards
If soccer cards shared equally by four members = 1200/4
= 300
Then, each person received soccer cards = 300

Question 5.
Six groups of students sell 162 balloons at the school carnival. There are 3 students in each group. If each student sells the same number of balloons, how many balloons does each student sell?
Options:
a. 9
b. 18
c. 27
d. 54

Answer:
a. 9

Explanation:
As per the given, data,
Six groups of students sell 162 balloons at the school carnival
There are 3 students in each group
Then, total number of students in 6 groups = 6 x 3 = 18
If each student sells the same number of balloons = 162 / 18
= 9
Number of balloons sells by each student = 9

Question 6.
Four students each made a list of prime numbers.
Eric: 5, 7, 17, 23
Maya: 3, 5, 13, 17
Bella: 2, 3, 17, 19
Jordan: 7, 11, 13, 21
Who made an error and included a composite number?
Options:
a. Eric
b. Maya
c. Bella
d. Jordan

Answer:
d. Jordan

Explanation:
As per the given data,
Four students each made a list of prime numbers.
Eric: 5, 7, 17, 23
Maya: 3, 5, 13, 17
Bella: 2, 3, 17, 19
Jordan: 7, 11, 13, 21
21 is not a prime number
So, An error made by Jordan

Page No. 335

Question 1.
Complete the table below.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 3
Type below:
___________

Answer:
chapter 6 - Common Core - Image 3. jpg

Write two equivalent fractions.

Question 2.
\(\frac{4}{5}\)
\(\frac{4}{5}\) = \(\frac { 4×□ }{ 5×□ } \) = \(\frac{□}{□}\)
\(\frac{4}{5}\) = \(\frac { 4×□ }{ 5×□ } \) = \(\frac{□}{□}\)
\(\frac{4}{5}\) = \(\frac{□}{□}\) = \(\frac{□}{□}\)
Type below:
___________

Answer:
\(\frac{4}{5}\) = \(\frac{8}{10}\) = \(\frac{80}{100}\)

Explanation:
Two equivalent fractions of 4/5,
(4/5) x (2/2) = 8/10
And
(4/5) x (20/20) = 80/100
8/10 = (8/10) (10/10)
= (80/100)
So, the equivalent fractions of 4/5 = 8/10, 80/100

Question 3.
\(\frac{2}{4}\)
\(\frac{2}{4}\) = \(\frac { 2×□ }{ 4×□ } \) = \(\frac{□}{□}\)
\(\frac{2}{4}\) = \(\frac { 2×□ }{ 4×□ } \) = \(\frac{□}{□}\)
\(\frac{2}{4}\) = \(\frac{□}{□}\) = \(\frac{□}{□}\)
Type below:
___________

Answer:
\(\frac{2}{4}\) = \(\frac{4}{8}\) = \(\frac{8}{16}\)

Explanation:
Two equivalent fractions of 2/4,
(2/4) x (2/2) = 4/8
And
(2/4) x (4/4) = 8/16
4/8 = (4/8) (2/2)
= (8/16)
So, the equivalent fractions of 2/4 = 4/8, 8/16

Write two equivalent fractions.

Question 4.
\(\frac{3}{6}\)
\(\frac{3}{6}\) = \(\frac{□}{□}\) = \(\frac{□}{□}\)
Type below:
___________

Answer:
\(\frac{3}{6}\) = \(\frac{6}{12}\) = \(\frac{12}{24}\)

Explanation:
Two equivalent fractions of 3/6,
(3/ 6) x (2/2) = 6/12
And
(3/6) x (4/ 4) = 12/24
6/12 = (6/12) (2/2)
= (12/24)
So, the equivalent fractions of 3/6 = 6/12, 12/24

Question 5.
\(\frac{3}{10}\)
\(\frac{3}{10}\) = \(\frac{□}{□}\) = \(\frac{□}{□}\)
Type below:
___________

Answer:
\(\frac{3}{10}\) = \(\frac{6}{20}\) = \(\frac{12}{40}\)

Explanation:
Two equivalent fractions of 3/10,
(3/ 10) x (2/2) = 6/20
And
(3/10) x (4/ 4) = 12/40
6/20 = (6/20) (2/2)
= (12/40)
So, the equivalent fractions of 3/10 = 6/20, 12/40

Question 6.
\(\frac{2}{5}\)
\(\frac{2}{5}\) = \(\frac{□}{□}\) = \(\frac{□}{□}\)
Type below:
___________

Answer:
\(\frac{2}{5}\) = \(\frac{4}{10}\) = \(\frac{8}{20}\)

Explanation:
Two equivalent fractions of 2/5,
(2/ 5) x (2/2) = 4/10
And
(2/5) x (4/ 4) = 8/20
4/10 = (4/10) (2/2)
= (8/20)
So, the equivalent fractions of 2/5 = 4/10, 8/20

Tell whether the fractions are equivalent. Write = or ≠.

Question 7.
\(\frac{5}{6}\) ______ \(\frac{10}{18}\)

Answer:
\(\frac{5}{6}\) ≠ \(\frac{10}{18}\)

Explanation:
Multiply the numerator and denominator of 5/6 with 2
5/6 =(2/2) x (5/6)
= (10/12)
So, 5/6 ≠ 10/ 18

Go Math Grade 4 Answer Key Chapter 6 Question 8.
\(\frac{4}{5}\) ______ \(\frac{8}{10}\)

Answer:
\(\frac{4}{5}\) = \(\frac{8}{10}\)

Explanation:
Multiply the numerator and denominator of 4/5 with 2
4/5 =(2/2) x (4/5)
= (8/10)
So, 4/5 = 8/10

Question 9.
\(\frac{1}{5}\) ______ \(\frac{4}{10}\)

Answer:
\(\frac{1}{5}\) ≠ \(\frac{4}{10}\)

Explanation:
Multiply the numerator and denominator of 1/5 with 4
1/5 =(4/4) x (1/5)
= (4/20)
So, 1/5 ≠ 4/10

Question 10.
\(\frac{1}{4}\) ______ \(\frac{2}{8}\)

Answer:
\(\frac{1}{4}\) = \(\frac{2}{8}\)

Explanation:
Multiply the numerator and denominator of 1/4 with 2
1/4 =(2/2) x (1/4)
= (2/8)
So, 1/4 = 2/8

Page No. 336

Use the recipe for 11–12.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 4

Question 11.
Kim says the amount of flour in the recipe can be expressed as a fraction. Is she correct? Explain.
______

Answer:
As per the given data, Kim says the amount of flour in the recipe can be expressed as a fraction. But in the recipe, 1 tablespoon flour is added. So, Kim says wrong.

Question 12.
How could you use a \(\frac{1}{8}\) – cup measuring cup to measure the light corn syrup?
Type below:
_________

Answer:
As per the given data,
By using the 1/8 cup measure the 9/12 cup light corn syrup
(9/12)/(1/8) = (9 x 8)/12
= (3 x 8)/4
= (3 x 2)
= 6
So, required 6 cups of 1/8 to measure the light corn syrup of 9/12.

Question 13.
Communicate Explain using words how you know a fraction is equivalent to another fraction.
Type below:
_________

Answer:
If you multiply the numerator and denominator of the first fraction by the same number and the products are the numerator and denominator of the second fraction, then the fractions are equivalent

Question 14.
Kyle drank \(\frac{2}{3}\) cup of apple juice. Fill in each box with a number from the list to generate equivalent fractions for \(\frac{2}{3}\). Not all numbers will be used.
Type below:
_________

Answer:
\(\frac{4}{6}\) and \(\frac{12}{18}\)

Explanation:
As per the given data,
Kyle drank 2/3 cup of apple juice
(2/3) x (2/2) = 4/6
(4/6) x (3/3) = 12/18
Equivalent fractions of 2/3 are 4/6 and 12/18

Common Core – Equivalent Fractions – Page No. 337

Write two equivalent fractions for each.

Question 1.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Equivalent Fractions img 5

Answer:
\(\frac{2}{6}\) and \(\frac{4}{12}\)

Explanation:
1/3
(1/3) x (2/2) = 2/6
(1/3) x (4/4) = 4/12
So, the equivalent fractions of 1/3 are 2/6 and 4/12

Question 2.
\(\frac{2}{3}\)
Type below:
_________

Answer:
\(\frac{4}{6}\) and \(\frac{8}{12}\)

Explanation:
2/3
(2/3) x (2/2) = 4/6
(2/3) x (4/4) = 8/12
Then, the equivalent fractions of 2/3 = 4/6 and 8/12

Go Math Grade 4 Lesson 6.2 Answer Key Question 3.
\(\frac{1}{2}\)
Type below:
_________

Answer:
\(\frac{2}{4}\) and \(\frac{4}{8}\)

Explanation:
1/2
(1/2) x (2/2) = 2/4
(1/2) x (4/4) = 4/8
Then, the equivalent fractions of 1/2 = 2/4, 4/8

Question 4.
\(\frac{4}{5}\)
Type below:
_________

Answer:
\(\frac{8}{10}\) and \(\frac{80}{100}\)

Explanation:
4/5
(4/5) x (2/2) = 8/10
(4/5) x (20/20) = 80/100
Then, the equivalent fractions of 4/5 = 8/10 and 80/100

Tell whether the fractions are equivalent. Write # or ≠.

Question 5.
\(\frac{1}{4}\) ______ \(\frac{3}{12}\)

Answer:
\(\frac{1}{4}\) = \(\frac{3}{12}\)

Explanation:
1/4
Multiply the numerator and denominator of 1/4 with 3
Then, (1/4) x (3/3) = 3/12
So, 1/4 = 3/12

Question 6.
\(\frac{4}{5}\) ______ \(\frac{5}{10}\)

Answer:
\(\frac{4}{5}\) ≠ \(\frac{5}{10}\)

Explanation:
4/5
Multiply numerator and denominator of 4/5 with 2
(4/5) x (2/2) = 8/10
Then 4/5 ≠ 5/10

Question 7.
\(\frac{3}{8}\) ______ \(\frac{2}{6}\)

Answer:
\(\frac{3}{8}\) ≠ \(\frac{2}{6}\)

Explanation:
3/8 ≠ 2/6

Question 8.
\(\frac{3}{4}\) ______ \(\frac{6}{8}\)

Answer:
\(\frac{3}{4}\) = \(\frac{6}{8}\)

Explanation:
3/4
Multiply the numerator and denominator of 3/4 with 2
Then, (3/4) x (2/2) = 6/8
So, 3/4 = 6/8

Question 9.
\(\frac{5}{6}\) ______ \(\frac{10}{12}\)

Answer:
\(\frac{5}{6}\) = \(\frac{10}{12}\)

Explanation:
5/6
Multiply the numerator and denominator with 2
(5/6) x (2/2) = 10/12
So, 5/6 = 10/12

Question 10.
\(\frac{6}{12}\) ______ \(\frac{5}{8}\)

Answer:
\(\frac{6}{12}\) ≠ \(\frac{5}{8}\)

Explanation:
6/12 ≠ 5/8

Question 11.
\(\frac{2}{5}\) ______ \(\frac{4}{10}\)

Answer:
\(\frac{2}{5}\) = \(\frac{4}{10}\)

Explanation:
2/5
Multiply the numerator and denominator of 2/5 with 2
(2/5) x (2/2) = 4/10
So, 2/5 = 4/10

Question 12.
\(\frac{2}{4}\) ______ \(\frac{3}{12}\)

Answer:
\(\frac{2}{4}\) ≠ \(\frac{3}{12}\)

Explanation:
2/4
Multiply the numerator and denominator of 2/4 with 3
(2/4) x (3/3) = 6/12
So, 2/4 ≠ 3/ 12

Question 13.
Jan has a 12-ounce milkshake. Four ounces in the milkshake are vanilla, and the rest is chocolate. What are two equivalent fractions that represent the fraction of the milkshake that is vanilla?
Type below:
_________

Answer:
\(\frac{1}{3}\) and \(\frac{2}{6}\)

Explanation:
As per the given data,
Jan has a 12-ounce milkshake
Four ounces in the milkshake are vanilla = 4/12 = 1/3
Then, 8-ounces in milkshake are chocolate = 8/12 = 2/3
4/12 = 1/3
By multiplying 1/3 with 2
(1/3) x (2/2) = 2/6
So, the equivalent fractions of vanilla milkshake are 1/3 and 2/6

Question 14.
Kareem lives \(\frac{4}{10}\) of a mile from the mall. Write two equivalent fractions that show what fraction of a mile Kareem lives from the mall.
Type below:
_________

Answer:
\(\frac{2}{5}\) and \(\frac{8}{20}\)

Explanation:
As per the given data,
Kareem lives 4/10 of a mile from the mall
To find the equivalent fractions of 4/10
Simplify the 4/10 = 2/5
Multiply the numerator and denominator of 2/5 with 4
(2/5) x (4/4) = 8/20
Then, the equivalent fraction of a mile Kareem lives from the mall = 2/5 and 8/20

Common Core – Equivalent Fractions – Page No. 338

Question 1.
Jessie colored a poster. She colored \(\frac{2}{5}\) of the poster red. Which fraction is equivalent to \(\frac{2}{5}\)?
Options:
a. \(\frac{4}{10}\)
b. \(\frac{7}{10}\)
c. \(\frac{4}{5}\)
d. \(\frac{2}{2}\)

Answer:
a. \(\frac{4}{10}\)

Explanation:
As per the given data,
Jessie colored a poster
She colored 2/5th of the poster red
Multiply the numerator and denominator of 2/5 with 2
Then, (2/5) x (2/2) = 4 /10
So, the equivalent fraction of 2/5 is 4/10

Question 2.
Marcus makes a punch that is \(\frac{1}{4}\) cranberry juice. Which two fractions are equivalent to \(\frac{1}{4}\)?
Options:
a. \(\frac{2}{5}, \frac{3}{12}\)
b. \(\frac{2}{8}, \frac{4}{12}\)
c. \(\frac{3}{4}, \frac{6}{8}\)
d. \(\frac{2}{8}, \frac{3}{12}\)

Answer:
d. \(\frac{2}{8}, \frac{3}{12}\)

Explanation:
As per the given data,
Marcus makes a punch that is 1/4th of cranberry juice
Multiply the numerator and denominator of 1/4 with 2
Then, (1/4) x (2/2) = 2/8
Multiply the numerator and denominator of 1/4 with 3
Then, (1/4) x (3/3) = 3/12
Equivalent fractions of 1/4 are 2/8 and 3/12

Question 3.
An electronics store sells a large flat-screen television for $1,699. Last month, the store sold 8 of these television sets. About how much money did the store make on the television sets?
Options:
a. $160,000
b. $16,000
c. $8,000
d. $1,600

Answer:
b. $16,000

Explanation:
As per the given data,
An electronics store sells a large flat-screen television for $1,699
Last month, the store sold 8 of these television sets = 8 x $1,699 = $13,952. The money is about to $16,000.

Question 4.
Matthew has 18 sets of baseball cards. Each set has 12 cards. About how many baseball cards does Matthew have in all?
Options:
a. 300
b. 200
c. 150
d. 100

Answer:
b. 200

Explanation:
From the given data,
Matthew has 18 sets of basketball cards
Each set has 12 cards = 12 x 18
= 216
Total number of basketball cards with Matthew = 216. So, it is near to 200.

Question 5.
Diana had 41 stickers. She put them in 7 equal groups. She put as many as possible in each group. She gave the leftover stickers to her sister. How many stickers did Diana give to her sister?
Options:
a. 3
b. 4
c. 5
d. 6

Answer:
d. 6

Explanation:
As per the given data,
Diana has 41 stickers
She put them in 7 equal groups = 41/7
= 5 (remaining 6)
She gave the leftover stickers to her sister
The number of stickers Diana gives to her sister = 6

Question 6.
Christopher wrote the number pattern below. The first term is 8.
8, 6, 9, 7, 10, …
Which is a rule for the pattern?
Options:
a. Add 2, add 3.
b. Add 6, subtract 3.
c. Subtract 6, add 3.
d. Subtract 2, add 3

Answer:
d. Subtract 2, add 3

Explanation:
From the given data,
Christopher wrote the number pattern = 8, 6, 9, 7, 10, …..
The first number in the pattern = 8
8 – 2 = 6 + 3 = 9 – 2 = 7 +3 = 10 ….
So, the rule for the above pattern is to subtract 2, add 3

Page No. 341

Question 1.
Write \(\frac{8}{10}\) in simplest form.
\(\frac{8}{10}\) = \(\frac { 8÷□ }{ 10÷□ } \) = \(\frac{□}{□}\)
\(\frac{□}{□}\)

Answer:
\(\frac{4}{5}\)

Explanation:
8/10 in simplest form
Divide the 8/10 with 2
(8/2)/(10/2) = 4/5
So, the simplest form of 8/10 is 4/5

Write the fraction in simplest form.

Question 2.
\(\frac{6}{12}\)
\(\frac{□}{□}\)

Answer:
\(\frac{1}{2}\)

Explanation:
6/12 in simplest form
Divide the 6/12 with 6
(6/6)/(12/6) = 1/2
So, the simplest form of 6/12 is 1/2

Question 3.
\(\frac{2}{10}\)
\(\frac{□}{□}\)

Answer:
\(\frac{1}{5}\)

Explanation:
2/10 in simplest form
Divide the 2/10 with 2
(2/2)/(10/2) = 1/5
So, the simplest form of 2/10 is 1/5

Question 4.
\(\frac{6}{8}\)
\(\frac{□}{□}\)

Answer:
\(\frac{3}{4}\)

Explanation:
6/8 in simplest form
Divide the 6/8 with 2
(6/2)/(8/2) = 3/4
So, the simplest form of 6/8 is 3/4

Question 5.
\(\frac{4}{6}\)
\(\frac{□}{□}\)

Answer:
\(\frac{2}{3}\)

Explanation:
4/6 in simplest form
Divide the 4/6 with 2
(4/2)/(6/2) = 2/3
So, the simplest form of 4/6 is 2/3

Write the fraction in simplest form.

Question 6.
\(\frac{9}{12}\)
\(\frac{□}{□}\)

Answer:
\(\frac{3}{4}\)

Explanation:
9/12in simplest form
Divide the 9/12 with 3
(9/3)/(12/3) = 3/4
So, the simplest form of 9/12 is 3/4

Lesson 6.3 Answer Key 4th Grade Question 7.
\(\frac{4}{8}\)
\(\frac{□}{□}\)

Answer:
\(\frac{1}{2}\)

Explanation:
4/8in simplest form
Divide the 4/8 with 4
(4/4)/(8/4) = 1/2
So, the simplest form of 4/8 is 1/2

Question 8.
\(\frac{10}{12}\)
\(\frac{□}{□}\)

Answer:
\(\frac{5}{6}\)

Explanation:
10/12 in simplest form
Divide the 10/12 with 2
(10/2)/(12/2) = 5/6
So, the simplest form of 10/12 is 5/6

Question 9.
\(\frac{20}{100}\)
\(\frac{□}{□}\)

Answer:
\(\frac{1}{5}\)

Explanation:
20 /100 in simplest form
Divide the 20/100 with 20
(20/20)/(100/20) = 1/5
So, the simplest form of 20/100 is 1/5

Tell whether the fraction is in simplest form. Write yes or no.

Question 10.
\(\frac{2}{8}\)
______

Answer:
No

Explanation:
2/8 in simplest form
Divide the 2/8 with 2
(2/2)/(8/2) = 1/4
The simplest form of 2/8 is 1/4
So, 2/8 is not the simplest form

Question 11.
\(\frac{9}{12}\)
______

Answer:
No

Explanation:
9/12 in simplest form
Divide the 9/12 with 3
(9/3)/(12/3) = 3/4
The simplest form of 9/12 is 3/4
So, 9/12 is not the simplest form

Question 12.
\(\frac{5}{6}\)
______

Answer:
Yes

Explanation:
5/6 is not divided by any number
Yes, 5/6 is the simplest form

Question 13.
\(\frac{4}{10}\)
______

Answer:
No

Explanation:
4/10 in simplest form
Divide the 4/10 with 2
(4/2)/(10/2) = 2/5
So, 4/10 is not the simplest form

Question 14.
There are 18 students in Jacob’s homeroom. Six students bring their lunch to school. The rest eat lunch in the cafeteria. In the simplest form, what fraction of students eat lunch in the cafeteria?
\(\frac{□}{□}\) of students

Answer:
\(\frac{2}{3}\) of students

Explanation:
As per the given data,
There are 18 students in Jacob’s homeroom
6 students bring their lunch to school = 6/18 = 1/3
The rest eat lunch in the cafeteria = 18 – 6 = 12/18
Divide the numerator and denominator of 12/18 with 6
(12/6) x (18/6) = 2/3
So, 2/3 of students eat lunch in the cafeteria

Page No. 342

Use the map for 15−16.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 6

Question 15.
Identify Relationships What fraction of the states in the southwest region share a border with Mexico? Is this fraction in simplest form?
\(\frac{□}{□}\)

Answer:
Yes, \(\frac{3}{4}\)

Explanation:
As per the given data,
Southwest region states = 4
Number of states in the southwest region shares a border with Mexico out of total southwest region states = 3/4
Yes, 3/4 is the simplest form

Question 16.
What’s the Question? \(\frac{1}{3}\) of the states in this region are on the Gulf of Mexico.
Type below:
_________

Answer:
In the simplest form, what fraction of the states in the southeast area on the Gulf of Mexico?

Common Denominators Lesson 6.4 Question 17.
Pete says that to write \(\frac{4}{6}\) as \(\frac{2}{3}\), you combine pieces, but to write \(\frac{4}{6}\) as \(\frac{8}{12}\), you break apart pieces. Does this make sense? Explain.
______

Answer:
As per the given data,
Yes, it makes sense,
To write 4/6 as 2/3 combine sixth-size pieces into equal groups of 2
Then (4/2)/(6/2) = 2/3
To write 4/6 as 8/12, break each sixth piece into 2 pieces
Then, 4/6 = (4 x 2)/(6 x 2) = 8/12

Question 18.
In Michelle’s homeroom, \(\frac{9}{15}\) of the students ride the bus to school, \(\frac{4}{12}\) get a car ride, and \(\frac{2}{30}\) walk to school.
For numbers 18a–18c, select True or False for each statement.
a. In simplest form, \(\frac{3}{5}\) of the students ride the bus to school.
i. True
ii. False

Answer:
i. True

Explanation:
9/15 of the students ride the bus to school
By dividing the numerator and denominator of 9/15 with 3
(9/3)/(15/3) =3/5
So, 3/5 of the students ride the bus to school
True

Question 18.
b. In simplest form, \(\frac{1}{4}\) of the students get a car ride to school.
i. True
ii. False

Answer:
ii. False

Explanation:
a. 4/12 of the students get a car ride
The simplest form of 4/12 = 1/3
So, 1/4 of the students get a car ride to school is a False statement

Question 18.
c. In simplest form, \(\frac{1}{15}\) of the students walk to school.
i. True
ii. False

Answer:
i. True

Explanation:
a. 2/30 of the students walk to school
By dividing the 2/30 with 2
(2/2)/(30/2) = 1/15
So, 1/15 of the students walk to school is a true statement

Common Core – Simplest Form – Page No. 343

Write the fraction in simplest form.

Question 1.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Simplest Form img 7

Answer:
\(\frac{3}{5}\)

Explanation:
To write the 6/10 in the simplest form
Divide the numerator and denominator of 6/10 with 2
(6 ÷2)/(10 ÷2) = 3/5
So, the simplest form of 6/10 = 3/5

Question 2.
\(\frac{6}{8}\) = \(\frac{□}{□}\)

Answer:
\(\frac{3}{4}\)

Explanation:
To write the 6/8in a simplest form
Divide the numerator and denominator of 6/8 with 2
(6 ÷2)/(8 ÷2) = 3/4
So, the simplest form of 6/8 = 3/4

Question 3.
\(\frac{5}{5}\) = \(\frac{□}{□}\)

Answer:
\(\frac{1}{1}\) = 1

Explanation:
To write the 5/5in a simplest form
Divide the numerator and denominator of 5/5 with 5
(5 ÷5)/(5 ÷5) = 1/1
So, the simplest form of 5/5 = 1

Question 4.
\(\frac{8}{12}\) = \(\frac{□}{□}\)

Answer:
\(\frac{2}{3}\)

Explanation:
To write the 8/12in a simplest form
Divide the numerator and denominator of 8/12 with 4
(8 ÷4)/(12 ÷4) = 2/3
So, the simplest form of 8/12 = 2/3

Question 5.
\(\frac{100}{100}\) = \(\frac{□}{□}\)

Answer:
\(\frac{1}{1}\) = 1

Explanation:
The simplest form of 100/100 = 1

Question 6.
\(\frac{2}{6}\) = \(\frac{□}{□}\)

Answer:
\(\frac{1}{3}\)

Explanation:
To write the 2/6in a simplest form
Divide the numerator and denominator of 2/6 with 2
(2 ÷2)/(6 ÷2) = 1/3
So, the simplest form of 2/6 = 1/3

Question 7.
\(\frac{2}{8}\) = \(\frac{□}{□}\)

Answer:
\(\frac{1}{4}\)

Explanation:
To write the 2/8in a simplest form
Divide the numerator and denominator of 2/8 with 2
(2 ÷2)/(8 ÷2) = 1/4
So, the simplest form of 2/8 = 1/4

Question 8.
\(\frac{4}{10}\) = \(\frac{□}{□}\)

Answer:
\(\frac{2}{5}\)

Explanation:
To write the 4/10 in a simplest form
Divide the numerator and denominator of 4 /10 with 2
(4 ÷2)/(10 ÷2) = 2/5
So, the simplest form of 4/10 = 2/5

Tell whether the fractions are equivalent. Write = or ≠. (if you do not have ≠on your keyboard, copy and paste this one: ≠ )

Question 9.
\(\frac{6}{12}\) _______ \(\frac{1}{12}\)

Answer:
\(\frac{6}{12}\) ≠ \(\frac{1}{12}\)

Explanation:
6/12 ≠ 1/12

Question 10.
\(\frac{3}{4}\) _______ \(\frac{5}{6}\)

Answer:
\(\frac{3}{4}\) ≠ \(\frac{5}{6}\)

Explanation:
3/4 ≠ 5/6

Question 11.
\(\frac{6}{10}\) _______ \(\frac{3}{5}\)

Answer:
\(\frac{6}{10}\) = \(\frac{3}{5}\)

Explanation:
6/10
Divide the numerator and denominator of 6/10 with 2
(6 ÷ 2)/( 10 ÷ 2) = 3/5
So, 6/10 = 3/5

Question 12.
\(\frac{3}{12}\) _______ \(\frac{1}{3}\)

Answer:
\(\frac{3}{12}\) ≠ \(\frac{1}{3}\)

Explanation:
3/12 ≠ 1/3

Question 13.
\(\frac{6}{10}\) _______ \(\frac{60}{100}\)

Answer:
\(\frac{6}{10}\) = \(\frac{60}{100}\)

Explanation:
6/10
Multiply the numerator and denominator of 6/10 with 10
(6 x 10)/(10 x 10) = 60/100
So, 6/10 = 60/100

Lesson 6.4 Go Math 4th Grade Question 14.
\(\frac{11}{12}\) _______ \(\frac{9}{10}\)

Answer:
\(\frac{11}{12}\) ≠ \(\frac{9}{10}\)

Explanation:
11/12 ≠ 9/10

Question 15.
\(\frac{2}{5}\) _______ \(\frac{8}{20}\)

Answer:
\(\frac{2}{5}\) = \(\frac{8}{20}\)

Explanation:
2/5
Multiply the numerator and denominator of 2/5 with 4
(2 x 4)/(5 x 4) = 8/20
So, 2/5 = 8/20

Question 16.
\(\frac{4}{8}\) _______ \(\frac{1}{2}\)

Answer:
\(\frac{4}{8}\) = \(\frac{1}{2}\)

Explanation:
4/8
Divide the numerator and denominator of 4/8 with 4
(4 x 4)/(8 x 4) = 1/2
So, 4/8 = 1/2

Question 17.
At Memorial Hospital, 9 of the 12 babies born on Tuesday were boys. In the simplest form, what fraction of the babies born on Tuesday were boys?
_______

Answer:
\(\frac{3}{4}\)

Explanation:
As per the given data,
At Memorial Hospital, 9 of the 12 babies born on Tuesday were boys = 9/12
Divide the numerator and denominator of 9/12 with 3
(9 ÷ 3)/(12 ÷ 3) = 3/4
So, in the simplest form
3/4 of the babies born on Tuesday were boys

Question 18.
Cristina uses a ruler to measure the length of her math textbook. She says that the book is \(\frac{4}{10}\) meter long. Is her measurement in simplest form? If not, what is the length of the book in simplest form?
\(\frac{□}{□}\)

Answer:
\(\frac{2}{5}\)

Explanation:
As per the given data,
Cristiana uses a ruler to measure the length of her math textbook
She says that the book is 4/10meter long
It is not in the simplest form
Divide the numerator and denominator of 4/10 with 2
(4÷ 2)/( 10 ÷ 2) = 2/5
The length of the book in the simplest form = 2/5

Common Core – Simplest Form – Page No. 344

Question 1.
Six out of the 12 members of the school choir are boys. In the simplest form, what fraction of the choir is boys?
Options:
a. \(\frac{1}{6}\)
b. \(\frac{6}{12}\)
c. \(\frac{1}{2}\)
d. \(\frac{12}{6}\)

Answer:
c. \(\frac{1}{2}\)

Explanation:
As per the given data,
Six out of the 12 members of the school choir are boys = 6/12
To write the simplest form of 6/12, divide the numerator and denominator with 6
Then, (6 ÷ 6)/(12 ÷ 6) = 1/2
In the simplest form, 1/2 of the choir is boys

Question 2.
Which of the following fractions is in simplest form?
Options:
a. \(\frac{5}{6}\)
b. \(\frac{6}{8}\)
c. \(\frac{8}{10}\)
d. \(\frac{2}{12}\)

Answer:
a. \(\frac{5}{6}\)

Explanation:
5/6 is in the simplest form
6/8 simplest form = 3/4
8/10 simplest form = 4/5
2/12 simplest form = 1/6

Question 3.
Each of the 23 students in Ms. Evans’ class raised $45 for the school by selling coupon books. How much money did the class raise in all?
Options:
a. $207
b. $225
c. $1,025
d. $1,035

Answer:
d. $1,035

Explanation:
As per the given data,
Each of the 23 students in Ms. Evan’s class raised $45 for the school by selling coupon books
= 23 x $45
= $1,035

Question 4.
Which pair of numbers below have 4 and 6 as common factors?
Options:
a. 12, 18
b. 20, 24
c. 28, 30
d. 36, 48

Answer:
d. 36, 48

Explanation:
36, 48
Here, 36 = 4 x 9
= 2 x 2 x 3 x 3
48 = 6 x 8
= 2 x 3 x 4 x 2

Question 5.
Bart uses \(\frac{3}{12}\) cup milk to make muffins. Which fraction is equivalent to \(\frac{3}{12}\)?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{1}{3}\)
c. \(\frac{1}{2}\)
d. \(\frac{2}{3}\)

Answer:
a. \(\frac{1}{4}\)

Explanation:
As per the given data,
Bart uses 3/12 cup of milk to make muffins
Divide the fraction with 3
(3 ÷ 3)/(12 ÷ 3) = 1/4
So, the equivalent fraction for 3/12 = 1/4

Go Math Lesson 6.4 Answer Key Homework 4th Grade Question 6.
Ashley bought 4 packages of juice boxes. There are 6 juice boxes in each package. She gave 2 juice boxes to each of 3 friends. How many juice boxes does Ashley have left?
Options:
a. 24
b. 22
c. 18
d. 12

Answer:
c. 18

Explanation:
As per the given data,
Ashley bought 4 packages of juice boxes
There are 6 juice boxes in each package = 6 x 4 = 24
She gave 2 juice boxes to each of 3 friends = 2 x 3 = 6 juice boxes
So, 24 – 6 = 18
Total number of juice boxes left with Ashley = 18

Page No. 347

Question 1.
Find a common denominator for \(\frac{1}{3}\) and \(\frac{1}{12}\) by dividing each whole into the same number of equal parts. Use the models to help.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 8
common denominator:

Answer:
common denominator: 12

Explanation:
List the multiples of 3 = 3, 6, 9, 12, 15, 18, 21, ….
List the multiples of 12 = 12, 24, 36, 48, ….
So, the common denominators of 1/3 and 1/ 12 are 12

Write the pair of fractions as a pair of fractions with a common denominator.

Question 2.
\(\frac{1}{2}\) and \(\frac{1}{4}\)
Type below:
_________

Answer:
\(\frac{4}{8}\) and \(\frac{2}{8}\)

Explanation:
Common denominator of 1/2 and 1/4
List the multiples of 2 = 2, 4, 6, 8, 10, …
List the multiples of 4 = 4, 8, 12, 16, 20, 24, . . .
Then, the common denominator of 1/2 and 1/4 is 4
For the Common pair of fractions, multiply the common denominator with fractions
That is, (1 x 4) ÷( 2 x 4) and ( 1 x 4 ) ÷ ( 4 x 4)
So, the common pair of fractions = 4/8 and 2/8

Question 3.
\(\frac{3}{4}\) and \(\frac{5}{8}\)
Type below:
_________

Answer:
\(\frac{6}{8}\) and \(\frac{5}{8}\)

Explanation:
Common denominator of 3/4 and 5/8
List the multiples of 4 = 4, 8, 12, 16, 20, 24, . . .
List the multiples of 8 = 8, 16, 24, 32, . . . .
Then, the common denominator of 3/4 and 5/8 is 8
For the Common pair of fractions, multiply the common denominator with fractions
That is, (3 x 8) ÷( 4 x 8) and ( 5 x 8 ) ÷ ( 8 x 8)
So, the common pair of fractions = 6/8 and 5/8

Question 4.
\(\frac{1}{3}\) and \(\frac{1}{4}\)
Type below:
_________

Answer:
\(\frac{4}{12}\) and \(\frac{3}{12}\)

Explanation:
The common denominator of 1/3 and 1/4
List the multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, ….
List the multiples of 4 = 4, 8, 12, 16, 20, 24, . . .
Then, the common denominator of 1 /3 and 1/4 is 12
For the Common pair of fractions, multiply the common denominator with fractions
That is, (1 x 12) ÷( 3 x 12) and ( 1 x 12 ) ÷ ( 4 x 12)
So, the common pair of fractions = 4/12 and 3/12

Question 5.
\(\frac{4}{12}\) and \(\frac{5}{8}\)
Type below:
_________

Answer:
\(\frac{8}{24}\) and \(\frac{15}{24}\)

Explanation:
Common denominator of 4/12 and 5/8
List the multiples of 12 = 12, 24, 36, 48, 60, …..
List the multiples of 8 = 8, 16, 24, 32, 40, 48, …
Then, the common denominator of 4/12 and 5/8 is 24
For the Common pair of fractions, multiply the common denominator with fractions
That is, (4 x 24) ÷( 12 x 24) and ( 5 x 24 ) ÷ ( 8 x 24)
So, the common pair of fractions = 8/24 and 15/24

Write the pair of fractions as a pair of fractions with a common denominator.

Question 6.
\(\frac{1}{4}\) and \(\frac{5}{6}\)
Type below:
_________

Answer:
\(\frac{3}{12}\) and \(\frac{10}{12}\)

Explanation:
The common denominator of 1/4 and 5/6
List the multiples of 4 = 4, 8, 12, 16, 20, 24, . . .
List the multiples of 6 = 6, 12, 18, 24, 30, 36, ….
Then, the common denominator of 1/4 and 5/6 is 12
For the Common pair of fractions, multiply the common denominator with fractions
That is, (1 x 12) ÷( 4 x 12) and ( 5 x 12 ) ÷ ( 6 x 12)
So, common pair of fractions = 3/12 and 10/12

Lesson 6.4 Common Denominators Answer Key Question 7.
\(\frac{3}{5}\) and \(\frac{4}{10}\)
Type below:
_________

Answer:
\(\frac{6}{10}\) and \(\frac{4}{10}\)

Explanation:
The common denominator of 3/5 and 4/10
List the multiples of 5 = 5, 10, 15, 20, 25, 30, …..
List the multiples of 10 = 10, 20, 30, 40, 50 ….
Then, the common denominator of 3/5 and 4/10 is 10
For the Common pair of fractions, multiply the common denominator with fractions
That is, (3 x 10) ÷( 5 x 10) and ( 4 x 10 ) ÷ ( 10 x 10)
So, the common pair of fractions = 6/10 and 4/10

Tell whether the fractions are equivalent. Write = or ≠.

Question 8.
\(\frac{3}{4}\) ______ \(\frac{1}{2}\)

Answer:
\(\frac{3}{4}\) ≠ \(\frac{1}{2}\)

Explanation:
3/4 ≠ 1/2

Question 9.
\(\frac{3}{4}\) ______ \(\frac{6}{8}\)

Answer:
\(\frac{3}{4}\) = \(\frac{6}{8}\)

Explanation:
3/4
Multiply the numerator and denominator of 3/4 with 2
(3 x 2) ÷ ( 4 x 2 ) = 6/8
So, 3/4 = 6/8

Question 10.
\(\frac{1}{2}\) ______ \(\frac{4}{8}\)

Answer:
\(\frac{1}{2}\) = \(\frac{4}{8}\)

Explanation:
1/2
Multiply the numerator and denominator of 1/2 with 4
(1 x 4) ÷ ( 2 x 4 ) = 4/8
So, 1/2 = 4/8

Question 11.
\(\frac{6}{8}\) ______ \(\frac{4}{8}\)

Answer:
\(\frac{6}{8}\) ≠ \(\frac{4}{8}\)

Explanation:
6/8 ≠ 4/8

Question 12.
Jerry has two same-size circles divided into the same number of equal parts. One circle has \(\frac{3}{4}\) of the parts shaded, and the other has \(\frac{2}{3}\) of the parts shaded. His sister says the least number of pieces each circle could be divided into is 7. Is his sister correct? Explain.
______

Answer:
As per the given data,
Jerry has two same size circles divided into the same number of equal parts
One circle has 3/4 of the parts shaded
So, non-shaded parts of one circle = 1 – 3/4 = 1/4
Another circle has 2/3 of the parts shaded
Non – shaded parts = 1 – 2/3 = 1/3
We can’t draw a conclusion about how many parts or pieces a circle can be divided
So, his sister is incorrect

Page No. 348

Question 13.
Carrie has a red streamer that is \(\frac{3}{4}\) yard long and a blue streamer that is \(\frac{5}{6}\) yard long. She says the streamers are the same length. Does this make sense? Explain.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 9
______

Answer:
Carrie has a red streamer that is 3/4 yard long
The blue streamer that is 5/6 yard long
3/4 ≠ 5/6
She says the streamers are the same length, it doesn’t make any sense.

Question 14.
Leah has two same-size rectangles divided into the same number of equal parts. One rectangle has \(\frac{1}{3}\) of the parts shaded, and the other has \(\frac{2}{5}\) of the parts shaded. What is the least number of parts into which both rectangles could be divided?
______ parts

Answer:
15 parts

Explanation:
As per the given data,
Leah has two same size rectangles divided into the same number of equal parts
One rectangle has 1/3 of the parts shaded
Other rectangle has 2/5 of the parts shaded
15 parts

Question 15.
Julian says a common denominator for \(\frac{3}{4}\) and \(\frac{2}{5}\) is 9. What is Julian’s error? Explain.
Type below:
___________

Answer:
As per the given data,
Julian says a common denominator for 3/4 and 2/5 is 9
To find the common denominator for 3/4 and 2/5
List the multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, …..
List the multiples of 5 = 5, 10, 15, 20, 25, 30, ….
So, the common denominator for 3/4 and 2/5 is 20
Julian says 9 in place of 20 and it is wrong.

Go Math 4th Grade Chapter 6 Answer Key Question 16.
Miguel has two same-size rectangles divided into the same number of equal parts. One rectangle has \(\frac{3}{4}\) of the parts shaded, and the other has \(\frac{5}{8}\) of the parts shaded.
Into how many parts could each rectangle be divided? Show your work by sketching the rectangles.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 10
______ parts

Answer:
chapter 6 - simplest form - image 1. jpg
8 parts

Explanation:
As per the given data,
Miguel has two same–size rectangles divided into the same number of equal parts.
One rectangle has 3/4 of the parts shaded.
Another has 5/8 of the parts shaded.
The possible parts are 8.

Common Core – Common Denominators – Page No. 349

Write the pair of fractions as a pair of fractions with a common denominator.

Question 1.
\(\frac{2}{3} \text { and } \frac{3}{4}\)
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Common Denominators img 11

Answer:
\(\frac{8}{12} \text { and } \frac{9}{12}\)

Explanation:
2/3 and 3/4
List the multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, …
List the multiples of 4 = 4, 8, 12, 16, 20, …
Common multiple of 3 and 4 is 12
For the Common pair of fractions, multiply the common denominator with fractions
That is, (2 x 12) ÷( 3 x 12) and ( 3 x 12 ) ÷ ( 4 x 12)
So, common pair of fractions = 8/12 and 9/12

Question 2.
\(\frac{1}{4} \text { and } \frac{2}{3}\)
Type below:
_________

Answer:
\(\frac{3}{12} \text { and } \frac{8}{12}\)

Explanation:
1/4 and 2/3
List the multiples of 4 = 4, 8, 12, 16, 20, …
List the multiples of 3 = 3, 6, 9, 12, 15, 18, …
Common multiple of 4 and 3 is 12
For the Common pair of fractions, multiply the common denominator with fractions
That is, (1 x 12) ÷( 4 x 12) and ( 2 x 12 ) ÷ ( 3 x 12)
So, common pair of fractions = 3/12 and 8/12

Question 3.
\(\frac{3}{10} \text { and } \frac{1}{2}\)
Type below:
_________

Answer:
\(\frac{3}{10} \text { and } \frac{5}{10}\)

Explanation:
3/10 and 1/2
List the multiples of 10 = 10, 20, 30, 40, 50, ….
List the multiples of 2 = 2, 4, 6, 8, 10, 12, 14, ….
Common multiple of 10 and 2 is 10
For the Common pair of fractions, multiply the common denominator with fractions
That is, (3 x 10) ÷( 10 x 10) and ( 1 x 10 ) ÷ ( 2 x 10)
So, common pair of fractions = 3/10 and 5/10

Question 4.
\(\frac{3}{5} \text { and } \frac{3}{4}\)
Type below:
_________

Answer:
\(\frac{12}{20} \text { and } \frac{15}{20}\)

Explanation:
3/5 and 3/4
List the multiples of 5 = 5, 10, 15, 20, 25, 30, ….
List the multiples of 4 = 4, 8, 12, 16, 20, 24, …
Common multiple of 5 and 4 is 20
For the Common pair of fractions, multiply the common denominator with fractions
That is, (3 x 20) ÷( 5 x 20) and ( 3 x 20 ) ÷ ( 4 x 20)
So, common pair of fractions = 12/20 and 15/20

Question 5.
\(\frac{2}{4} \text { and } \frac{7}{8}\)
Type below:
_________

Answer:
\(\frac{4}{8} \text { and } \frac{7}{8}\)

Explanation:
2/4 and 7/8
List the multiples of 4 = 4, 8, 12, 16, 20, 24, …
List the multiples of 8 = 8, 16, 24, 32, 40, ….
Common multiple of 4 and 8 is 8
For the Common pair of fractions, multiply the common denominator with fractions
That is, (2 x 8) ÷( 4 x 8) and ( 7 x 8 ) ÷ ( 8 x 8)
So, common pair of fractions = 4/8 and 7/8

Question 6.
\(\frac{2}{3} \text { and } \frac{5}{12}\)
Type below:
_________

Answer:
\(\frac{8}{12} \text { and } \frac{5}{12}\)

Explanation:
2/3 and 5/12
List the multiples of 3 = 3, 6, 9, 12, 15, 18, …
List the multiples of 12 = 12, 24, 36, 48, 60, …
Common multiple of 3 and 12 is 12
For the Common pair of fractions, multiply the common denominator with fractions
That is, (2 x 12) ÷( 3 x 12) and ( 5 x 12 ) ÷ ( 12 x 12)
So, common pair of fractions = 8/12 and 5/12

Question 7.
\(\frac{1}{4} \text { and } \frac{1}{6}\)
Type below:
_________

Answer:
\(\frac{3}{12} \text { and } \frac{2}{12}\)

Explanation:
1/4 and 1/6
List the multiples of 4 = 4, 8, 12, 16, 20, 24, …
List the multiples of 6 = 6, 12, 18, 24, 30, …
Common multiple of 4 and 6 is 12
For the Common pair of fractions, multiply the common denominator with fractions
That is, (1 x 12) ÷( 4 x 12) and ( 1 x 12 ) ÷ ( 6 x 12)
So, common pair of fractions = 3/12 and 2/12

Tell whether the fractions are equivalent. Write = or ≠.

Question 8.
\(\frac{1}{2}\) ______ \(\frac{2}{5}\)

Answer:
\(\frac{1}{2}\) ≠ \(\frac{2}{5}\)

Explanation:
Multiply the numerator and denominator of 1/2 with 2
(1 x 2) ÷ (2 x 2) = 2/4
So, 1/2 ≠ 2/5

Question 9.
\(\frac{1}{2}\) ______ \(\frac{3}{6}\)

Answer:
\(\frac{1}{2}\) = \(\frac{3}{6}\)

Explanation:
1/2
Multiply the numerator and denominator of 1/2 with 3
(1 x 3) ÷ (2 x 3) = 3/6
So, 1/2 = 3/6

Question 10.
\(\frac{3}{4}\) ______ \(\frac{5}{6}\)

Answer:
\(\frac{3}{4}\) ≠ \(\frac{5}{6}\)

Explanation:
3/4 ≠ 5/6

Question 11.
\(\frac{6}{10}\) ______ \(\frac{3}{5}\)

Answer:
\(\frac{6}{10}\) = \(\frac{3}{5}\)

Explanation:
6/10
Divide the numerator and denominator of 6/10 with 2
(6 ÷ 2)/(10 ÷2) = 3/5
So, 6/10 = 3/5

Question 12.
\(\frac{6}{8}\) ______ \(\frac{3}{4}\)

Answer:
\(\frac{6}{8}\) = \(\frac{3}{4}\)

Explanation:
6/8
Divide the numerator and denominator of 6/8 with 2
(6 ÷2)/(8 ÷2) = 3/4
So, 6/8 = 3/4

Question 13.
\(\frac{3}{4}\) ______ \(\frac{2}{3}\)

Answer:
\(\frac{3}{4}\) ≠ \(\frac{2}{3}\)

Explanation:
3/4 ≠ 2/3

Question 14.
\(\frac{2}{10}\) ______ \(\frac{4}{5}\)

Answer:
\(\frac{2}{10}\) ≠ \(\frac{4}{5}\)

Explanation:
2/10
Divide the numerator and denominator of 2/10 with 2
(2 ÷ 2)/(10 ÷ 2) = 1/5
So, 2/10 ≠ 1/5

Question 15.
\(\frac{1}{4}\) ______ \(\frac{3}{12}\)

Answer:
\(\frac{1}{4}\) = \(\frac{3}{12}\)

Explanation:
1/4
Multiply the numerator and denominator of 1/4 with 3
(1 x 3)/(4 x 3) = 3/12
So, 1/4 = 3/12

Go Math Grade 4 Chapter 6 Review Test Answer Key Question 16.
Adam drew two same-sized rectangles and divided them into the same number of equal parts. He shaded \(\frac{1}{3}\) of one rectangle and \(\frac{1}{4}\) of other rectangle. What is the least number of parts into which both rectangles could be divided?
_________

Answer:
12 parts

Explanation:
As per the given data,
Adam drew two same size rectangles and divided them into the same number of equal parts
He shaded 1/3 of one rectangle
1/4 of another rectangle
List the multiples of 3 = 3, 6, 9, 12, 15, 18, …
List the multiples of 4 = 4, 8, 12, 16, 20, …
A common multiple of 3 and 4 is 12
So, the least number of parts which rectangles could be divided = 12 parts

Question 17.
Mera painted equal sections of her bedroom wall to make a pattern. She painted \(\frac{2}{5}\) of the wall white and \(\frac{1}{2}\) of the wall lavender. Write an equivalent fraction for each using a common denominator.
Type below:
_________

Answer:
1/2 are 4/10 and 5/10

Explanation:
As per the given data,
Mera painted equal sections of her bedroom wall to make a pattern
She painted 2/5 of the wall white and 1/2 of the wall lavender
List the multiples of 5 = 5, 10, 15, 20, 25, 30, …
List the multiples of 2 = 2 ,4, 6, 8, 10, 12, 14, …
The common denominator of 2/5 and 1/2 = 10
Multiply the 2/5 and 1/2 with 10
(2 x 10)/(5 x 10) and (1 x 10)/(2 x 10)
4/10 and 5/10
So, common fractions of 2/5 and 1/2 are 4/10 and 5/10

Common Core – Common Denominators – Page No. 350

Question 1.
Which of the following is a common denominator of \(\frac{1}{4}\) and \(\frac{5}{6}\)?
Options:
a. 8
b. 9
c. 12
d. 15

Answer:
c. 12

Explanation:
The common denominator of 1/4 and 5/6
List the multiples of 4 = 4, 8, 12, 16, 20, 24, …
List the multiples of 6 = 6, 12, 18, 24, 30, ….
So, the common denominator of 1/4 and 5/6 is 12

Question 2.
Two fractions have a common denominator of 8. Which of the following could be the two fractions?
Options:
a. \(\frac{1}{2} \text { and } \frac{2}{3}\)
b. \(\frac{1}{4} \text { and } \frac{1}{2}\)
c. \(\frac{3}{4} \text { and } \frac{1}{6}\)
d. \(\frac{1}{2} \text { and } \frac{4}{5}\)

Answer:
b. \(\frac{1}{4} \text { and } \frac{1}{2}\)

Explanation:
As per the given data,
Two fractions have a common denominator of 8
a. 1/2 and 2/3
List the multiples of 2 = 2, 4, 6, 8,10, ….
List the multiples of 3 = 3, 6, 9, 12, …
There is no common denominator of 8 for 1/2 and 2/3
b. 1/4 and 1 /2
List the multiples of 2 = 2, 4, 6, 8,10, ….
List the multiples of 4 = 4, 8, 12, 16, …
Here, the common denominator of 1 /4 and 1 /2 is 8
So, the answer is 1/4 and 1/2

Question 3.
Which number is 100,000 more than seven hundred two thousand, eighty-three?
Options:
a. 703,083
b. 712,083
c. 730,083
d. 802,083

Answer:
d. 802,083

Explanation:
802,083

Question 4.
Aiden baked 8 dozen muffins. How many total muffins did he bake?
Options:
a. 64
b. 80
c. 96
d. 104

Answer:
c. 96

Explanation:
As per the given data,
Aiden baked 8 dozen muffins
1 dozen = 12
then, 8 dozens = 12 x 8 = 96
So, Aiden baked total 96 muffins

Question 5.
On a bulletin board, the principal, Ms. Gomez, put 115 photos of the fourth grade students in her school. She put the photos in 5 equal rows. How many photos did she put in each row?
Options:
a. 21
b. 23
c. 25
d. 32

Answer:
b. 23

Explanation:
As per the given data,
On a bulletin board, the principal, Ms. Gomez, put 115 photos of the fourth-grade students in her school
She put the photos in 5 equal rows
Then, number of photos in each row = 115/5 = 23
So, Ms. Gomez put photos in each row = 23

Question 6.
Judy uses 12 tiles to make a mosaic. Eight of the tiles are blue. What fraction, in simplest form, represents the tiles that are blue?
Options:
a. \(\frac{2}{3}\)
b. \(\frac{2}{5}\)
c. \(\frac{3}{4}\)
d. \(\frac{12}{18}\)

Answer:
a. \(\frac{2}{3}\)

Explanation:
As per the given data,
Judy uses 12 tiles to make a mosaic
Eight of the tiles are blue = 8/12
Divide the numerator and denominator of 8/12 with 4
(8 ÷ 4)/(12 ÷ 4) = 2/3
The simplest form of 8/12 is 2/3

Page No. 353

Question 1.
Keisha is helping plan a race route for a 10-kilometer charity run. The committee wants to set up the following things along the course.
Viewing areas: At the end of each half of the course
Water stations: At the end of each fifth of the course
Distance markers: At the end of each tenth of the course
Which locations have more than one thing located there?
First, make a table to organize the information.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 12
Next, identify a relationship. Use a common denominator, and find equivalent fractions.
Finally, identify the locations at which more than one thing will be set up. Circle the locations.
Type below:
___________

Answer:
Keisha is helping plan a race route for a 10-kilometer charity run.

Question 2.
What if distance markers will also be placed at the end of every fourth of the course? Will any of those markers be set up at the same location as another distance marker, a water station, or a viewing area? Explain.
Type below:
___________

Answer:
It really depends on where you place the other markers.

Question 3.
Fifty-six students signed up to volunteer for the race. There were 4 equal groups of students, and each group had a different task.
How many students were in each group?
_____ students

Answer:
14 students

Explanation:
As per the given data,
Fifty-six students signed up to volunteer for the race
There are four groups of students
Number of students in each group = 56/4 = 14
Total number of students in each group = 14

Page No. 354

Question 4.
A baker cut a pie in half. He cut each half into 3 equal pieces and each piece into 2 equal slices. He sold 6 slices. What fraction of the pie did the baker sell?
\(\frac{□}{□}\)

Answer:
\(\frac{1}{2}\)

Explanation:
A baker cut a pie in half. He cut each half into 3 equal pieces and each piece into 2 equal slices. He sold 6 slices. So, the remaining part is 1/2 of the pie.

Question 5.
Andy cut a tuna sandwich and a chicken sandwich into a total of 15 same-size pieces. He cut the tuna sandwich into 9 more pieces than the chicken sandwich. Andy ate 8 pieces of the tuna sandwich. What fraction of the tuna sandwich did he eat?
\(\frac{□}{□}\)

Answer:
\(\frac{2}{3}\)

Explanation:
Let x be the number of pieces of the chicken sandwich so that x + 9 is the number of pieces of a tuna sandwich.
There is a total of 15 same-size pieces. So, we can write as
x + (x + 9) = 15
2x + 9 = 15
2x = 6
x = 3.
This means that there ate 3 + 9 = 12 pieces of a tuna sandwich. Since Andy ate 8, then this corresponds to a fraction of 8/12 = 2/3.

Question 6.
Luke threw balls into these buckets at a carnival. The number on the bucket gives the number of points for each throw. What is the least number of throws needed to score exactly 100 points? Explain.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 13
_____ throws

Answer:
13 throws

Explanation:
Take the maximum number to get the minimum throws = 9 X 10 = 90.
6 X 1 = 6; 2 X 2 = 4.
Add 90 + 6 + 4 = 100;
So, the least number of throws needed to score exactly 100 points = 10 + 1 + 2 = 13.

Question 7.
Victoria arranges flowers in vases at her restaurant. In each arrangement, \(\frac{2}{3}\) of the flowers are yellow. What other fractions can represent the part of the flowers that are yellow? Shade the models to show your work.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 14
\(\frac{□}{□}\)

Answer:
chapter 6
\(\frac{2}{3}\), \(\frac{8}{12}\), \(\frac{40}{60}\)

Explanation:
Basically, any fraction obtained by multiplying both the numerator and denominator by the same value would be an equivalent fraction:
2/3 = 2/3 * 4/4 = 8/12
8/12 = 8/12 * 5/5 = 40/60
etc.

Common Core – Find Equivalent Fractions – Page No. 355

Question 1.
Miranda is braiding her hair. Then she will attach beads to the braid. She wants \(\frac{1}{3}\) of the beads to be red. If the greatest number of beads that will fit on the braid is 12, what other fractions could represent the part of the beads that are red?
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Find Equivalent Fractions img 15

Answer:
\(\frac{2}{6}\), \(\frac{3}{9}\), \(\frac{4}{12}\)

Explanation:
Miranda is braiding her hair. Then she will attach beads to the braid. She wants \(\frac{1}{3}\) of the beads to be red. If the greatest number of beads that will fit on the braid is 12.
\(\frac{1}{3}\) X \(\frac{2}{2}\) = \(\frac{2}{6}\)
\(\frac{1}{3}\) X \(\frac{3}{3}\) = \(\frac{3}{9}\)
\(\frac{1}{3}\) X \(\frac{4}{4}\) = \(\frac{4}{12}\)

Question 2.
Ms. Groves has trays of paints for students in her art class. Each tray has 5 colors. One of the colors is purple. What fraction of the colors in 20 trays is purple?
\(\frac{□}{□}\)

Answer:
\(\frac{20}{100}\) or \(\frac{1}{5}\)

Explanation:
If you have 20 trays that are 100 colors with 20 being purple. 20/ 100 is 1/5

Question 3.
Miguel is making an obstacle course for field day. At the end of every sixth of the course, there is a tire. At the end of every third of the course, there is a cone. At the end of every half of the course, there is a hurdle. At which locations of the course will people need to go through more than one obstacle?
Type below:
_________

Answer:
\(\frac{1}{3}\), \(\frac{1}{2}\), \(\frac{2}{3}\) and final locations

Explanation:
We have three fractions with different denominators: sixths, thirds, and halves.
The first step is to make all the denominators equal for 1/6, 1/3, 1/2.
In this case, we want sixths since LCM(2, 3, 6) = 6
since 1/3 = 2/6, and 1/2 = 3/6. Now we can start solving.
1. There are six tires at the following: 1/6, 2/6, 3/6, 4/6, 5/6, and 6/6.
2. There are three cones at the following (G.C.F.): 2/6 (or 1/3), 4/6 (or 2/3), and 6/6 (or 3/3).
3. There are two hurdles at the following (G.C.F.): 3/6 (or 1/2) and 6/6 (or 2/2).
We look for common numbers.
1. On 2/6, there are two obstacles: a tire and a cone.
2. On 3/6, there are two obstacles: a tire and a hurdle.
3. On 4/6, there are two obstacles: a tire and a cone.
4. At 6/6, there are three obstacles: a tire, cone, and a hurdle.
2/6 = 1/3
3/6 = 1/2
4/6 = 2/3
6/6 = 1
The answers are 1/3, 1/2, 2/3, and 1.

Question 4.
Preston works in a bakery where he puts muffins in boxes. He makes the following table to remind himself how many blueberry muffins should go in each box.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Find Equivalent Fractions img 16
How many blueberry muffins should Preston put in a box with 36 muffins?
_________

Answer:
12 blueberry muffins

Explanation:
Preston works in a bakery where he puts muffins in boxes. He makes the following table to remind himself how many blueberry muffins should go in each box.
So, he had 2 blueberry muffins out of 6 muffins.
2/6 X 2/2 = 4/12. 4 blueberry muffins out of 12 muffins.
2/6 X 4/4 = 8/24. 8 blueberry muffins out of 24 muffins.
2/6 X 6/6 = 12/36. 12 blueberry muffins out of 36 muffins.

Common Core – Find Equivalent Fractions – Page No. 356

Question 1.
A used bookstore will trade 2 of its books for 3 of yours. If Val brings in 18 books to trade, how many books can she get from the store?
Options:
a. 9
b. 12
c. 18
d. 27

Answer:
b. 12

Explanation:
A used bookstore will trade 2 of its books for 3 of yours. If Val brings in 18 books to trade 2/3 X 6/6 = 12/18, she get 12 books

Question 2.
Every \(\frac{1}{2}\) hour Naomi stretches her neck; every \(\frac{1}{3}\) hour she stretches her legs; and every \(\frac{1}{6}\) hour she stretches her arms. Which parts of her body will Naomi stretch when \(\frac{2}{3}\) of an hour has passed?
Options:
a. neck and legs
b. neck and arms
c. legs and arms
d. none

Answer:
c. legs and arms

Explanation:
Summing \(\frac{1}{2}\)‘s only gives integer values giving 1, 2, 3, 4…or
integer values +\(\frac{1}{2}\) and 0 + \(\frac{1}{2}\) = \(\frac{1}{2}\), 1 \(\frac{1}{2}\), 2 \(\frac{1}{2}\)…
So neck is excluded
Every \(\frac{1}{3}\): \(\frac{1}{3}\) + \(\frac{1}{2}\) = \(\frac{2}{3}\)
Legs will be stretched at \(\frac{2}{3}\) hour
Every \(\frac{1}{6}\): \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) = \(\frac{4}{6}\)
Divide top and bottom by 2 giving:
(4 ÷ 2)/(6 ÷ 2) = \(\frac{2}{3}\)
Arms will be stretched at latex]\frac{2}{3}[/latex] hour

Question 3.
At the beginning of the year, the Wong family car had been driven 14,539 miles. At the end of the year, their car had been driven 21,844 miles. How many miles did the Wong family drive their car during that year?
Options:
a. 6,315 miles
b. 7,295 miles
c. 7,305 miles
d. 36,383 miles

Answer:
c. 7,305 miles

Explanation:
If at the beginning of the year, the Wong family’s car had driven 14539 miles and at the end of the year, it had driven 21844 miles, then subtract 14539 from 21844 to determine the difference between the two values, which will tell you how many miles the Wong family drove their car for during the year.
21844 – 14539 = 7305 miles

Question 4.
Widget Company made 3,600 widgets in 4 hours. They made the same number of widgets each hour. How many widgets did the company make in one hour?
Options:
a. 80
b. 90
c. 800
d. 900

Answer:
d. 900

Explanation:

3,600 widgets in 4 hours therefore 3,600 / 4 for one hour = 900 widgets 900 widgets in one hour.

Question 5.
Tyler is thinking of a number that is divisible by 2 and by 3. By which of the following numbers must Tyler’s number also be divisible?
Options:
a. 6
b. 8
c. 9
d. 12

Answer:
a. 6

Explanation:
The number 6 is divisible by 2 and by 3.

Question 6.
Jessica drew a circle divided into 8 equal parts. She shaded 6 of the parts. Which fraction is equivalent to the part of the circle that is shaded?
Options:
a. \(\frac{2}{3}\)
b. \(\frac{3}{4}\)
c. \(\frac{10}{16}\)
d. \(\frac{12}{18}\)

Answer:
b. \(\frac{3}{4}\)

Explanation:
Jessica drew a circle divided into 8 equal parts. She shaded 6 of the parts.
6/8 = 3/4

Page No. 357

Choose the best term from the box.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 17

Question 1.
________ name the same amount.
________

Answer:
Equivalent Fractions

Question 2.
A _________ is a common multiple of two or more denominators
________

Answer:
Common Denominator

Write two equivalent fractions.

Question 3.
\(\frac{2}{5}\)
Type below:
________

Answer:
\(\frac{4}{10}\) and \(\frac{6}{15}\)

Explanation:
Two equivalent fractions of 2/5
Multiply the 2/5 with 2
(2 x 2)/(5 x 2) = 4/10
Multiply the 2/5 with 3
(2 x 3)/(5 x 3) = 6/15
So, the equivalent fractions of 2/5 are 4/10 and 6/15

Question 4.
\(\frac{1}{3}\)
Type below:
________

Answer:
\(\frac{2}{6}\) and \(\frac{3}{9}\)

Explanation:
Two equivalent fractions of 1/3
Multiply the 1/3 with 2
(1 x 2)/(3 x 2) = 2/6
Multiply the 1/3 with 3
(1 x 3)/(3 x 3) = 3/9
So, the equivalent fractions of 1/3 are 2/6 and 3/9

Question 5.
\(\frac{3}{4}\)
Type below:
________

Answer:
\(\frac{6}{8}\) and \(\frac{9}{12}\)

Explanation:
Two equivalent fractions of 3/4
Multiply the 3/4 with 2
(3 x 2)/(4 x 2) = 6/8
Multiply the 3/4 with 3
(3 x 3)/(4 x 3) = 9/12
So, the equivalent fractions of 3/4 are 6/8 and 9/12

Tell whether the fractions are equivalent. Write = or ≠.

Question 6.
\(\frac{2}{3}\) ______ \(\frac{4}{12}\)

Answer:
\(\frac{2}{3}\) ≠ \(\frac{4}{12}\)

Explanation:
2/ 3
Multiply the numerator and denominator of 2/3 with 2
(2 x 2)/(3 x 2) = 4/6
So, 2/3 ≠ 4/12

Question 7.
\(\frac{5}{6}\) ______ \(\frac{10}{12}\)

Answer:
\(\frac{5}{6}\) =_ \(\frac{10}{12}\)

Explanation:
5/6
Multiply the 5/6 with 2
(5 x 2)/(6 x 2) = 10/12
So, 5/6 = 10/12

Question 8.
\(\frac{1}{4}\) ______ \(\frac{4}{8}\)

Answer:
\(\frac{1}{4}\) ≠ \(\frac{4}{8}\)

Explanation:
1/4
Multiply the numerator and denominator of 1/4 with 4
(1 x 4)/(4 x 4) = 4/16
So, 1/4 ≠ 4/8

Write the fraction in simplest form.

Question 9.
\(\frac{6}{8}\)
\(\frac{□}{□}\)

Answer:
\(\frac{3}{4}\)

Explanation:
6/8
Divide the numerator and denominator of 6/8 with 2
(6 ÷ 2)/( 8 ÷ 2) = 3/4
The simplest form of 6/8 is 3/4

Question 10.
\(\frac{25}{100}\)
\(\frac{□}{□}\)

Answer:
\(\frac{1}{4}\)

Explanation:
25/100
Divide the numerator and denominator of 25/100 with 25
(25 ÷ 25)/( 100 ÷ 25) = 1/4
The simplest form of 25/100 is 1/4

Question 11.
\(\frac{8}{10}\)
\(\frac{□}{□}\)

Answer:
\(\frac{4}{5}\)

Explanation:
8/10
Divide the numerator and denominator of 8/10 with 2
(8 ÷ 2)/( 10 ÷ 2) = 4/5
The simplest form of 8/10 is 4/5

Write the pair of fractions as a pair of fractions with a common denominator.

Question 12.
\(\frac{3}{10} \text { and } \frac{2}{5}\)
Type below:
_________

Answer:
\(\frac{3}{10} \text { and } \frac{4}{10}\)

Explanation:
3/ 10 and 2/5
List the multiples of 10 = 10, 20, 30, 40, 50, …
List the multiples of 5 = 5, 10, 15, 20, 25, 30, …
Common denominator of 3/10 and 2/5 = 10
Multiply the 3/10 and 2/5 with 10
(3 x 10)/(10 x 10) and (2 x 10)/(5 x 10)
3/ 10 and 4/10
Pair of fractions of 3/10 and 2/5 are 3/10 and 4/10

My Homework Lesson 6 Compare and Order Fractions Answer Key Question 13.
\(\frac{1}{3} \text { and } \frac{3}{4}\)
Type below:
_________

Answer:
\(\frac{3}{12} \text { and } \frac{9}{12}\)

Explanation:
1/3 and 3/4
List the multiples of 3 = 3, 6, 9, 12, 15, 18, …
List the multiples of 4 = 4, 8, 12, 16, 20, ….
The common denominator of 1/3 and 3/4 are 12
Multiply the 1/3 and 3/4 with 12
(1 x 12)/(3 x 12) and (3 x 12)/(4 x 12)
3/ 12 and 9/12.
Pair of fractions of 1/3 and 3/4 are 3/12 and 9/12

Page No. 358

Question 14.
Sam needs \(\frac{5}{6}\) cup mashed bananas and \(\frac{3}{4}\) cup mashed strawberries for a recipe. He wants to find out whether he needs more bananas or more strawberries. How can he write \(\frac{5}{6}\) and \(\frac{3}{4}\) as a pair of fractions with a common denominator?
Type below:
_________

Answer:
\(\frac{10}{12}\) and \(\frac{9}{12}\)

Explanation:
Sam needs 5/6 cup mashed bananas and 3/4 cup mashed strawberries for a recipe
He wants to find out whether he needs more bananas or strawberries
List the multiples of 6 = 6, 12, 18, 24, 30, 36, 42,…..
List the multiples of 4 = 4, 8, 12, 16, 20, 24, ….
The common denominator of 6 and 4 is 12
Multiply the numerator and denominator of 5/6 and 3/4 with 12
(5 x 12)/(6 x 12) and (3 x 12)/(4 x 12)
10/12 and 9/12
Pair of fractions with a common denominator for 5/6 and 3/4 are 10/12 and 9/12

Question 15.
Karen will divide her garden into equal parts. She will plant corn in \(\frac{8}{12}\) of the garden. What is the fewest number of parts she can divide her garden into?
______ parts

Answer:
\(\frac{2}{3}\) parts

Explanation:
As per the given data,
Keren will divide her garden into equal parts
She will plant corn in 8/12 of the garden
To get the least number of parts she can divide her garden, simplify the 8/12
Divide the numerator and denominator of 8/12 with 4
(8 ÷ 4)/(12 ÷ 4) = 2/3
So, Karen can divide her garden into 2/3 of parts

Question 16.
Olivia is making scarves. Each scarf will have 5 rectangles, and \(\frac{2}{5}\) of the rectangles will be purple. How many purple rectangles does she need for 3 scarves?
______ purple rectangles

Answer:
6 purple rectangles

Explanation:
As per the given data,
Olivia is making scarves
Each scarf will have 5 rectangles and 2/5 of the rectangles will be purple = 5 x 2/5 = 2
That means each scarf will have 2 purple rectangles
For 3 scarves = 3 x 2 = 6
So, she needs 6 purple rectangles.

Question 17.
Paul needs to buy \(\frac{5}{8}\) pound of peanuts. The scale at the store measures parts of a pound in sixteenths. What measure is equivalent to \(\frac{5}{8}\) pound?
\(\frac{□}{□}\) pound of peanuts

Answer:
\(\frac{10}{16}\) pound of peanuts

Explanation:
As per the given data,
Paul needs to buy 5/8 pounds of peanuts
The scale at the store measures parts of a pound in sixteenths = 16 x 5/8 = 10
To find an Equivalent fraction of 5/8
Multiply the numerator and denominator of 5/8 with 2
(5 x 2)/( 8 x 2) = 10/16
So, the equivalent fraction of 5/8 is 10/16

Page No. 361

Question 1.
Compare \(\frac{2}{5}\) and \(\frac{1}{8}\). Write < or >.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 18
\(\frac{2}{5}\) _____ \(\frac{1}{8}\)

Answer:
\(\frac{2}{5}\) > \(\frac{1}{8}\)

Explanation:
Least common denominator of 5 and 8 = 40
Multiply the numerator and denominator of 2/5 and 1/8 with 40
2/ 5 = (2 x 8)/(5 x 8) = 16/40
1/8 = (1 x 5)/(8 x 5) = 5/40
The denominators are the same now
So, compare the numerator to find the greater number
16/40 > 5/40
So, 2/5 > 1/8

Compare. Write < or >.

Question 2.
\(\frac{1}{2}\) _____ \(\frac{4}{6}\)

Answer:
\(\frac{1}{2}\) < \(\frac{4}{6}\)

Explanation:
1/2 and 4/6
Least common denominator of 2 and 6 = 6
Multiply the numerator and denominator of 1/2 and 4/6 with 6
1/ 2 = (1 x 6)/(2 x 6) = 6/12
4/ 6 = (4x 2)/(6 x 2) = 8/12
The denominators are the same now
So, compare the numerator to find the greater number.
6/12 < 8/12
So, 1/2 < 4/6

Question 3.
\(\frac{3}{10}\) _____ \(\frac{1}{2}\)

Answer:
\(\frac{3}{10}\) > \(\frac{1}{2}\)

Explanation:
1 / 10 and 1/2
The least common denominator of 10 and 2 = 10
Multiply the numerator and denominator of 3/10 and 1/2 by 10
3/ 10 = (3 x 2)/(10 x 2) = 6/20
1/2 = (1 x 10)/(2 x 10) = 10/20
The denominators are the same now
So, compare the numerator to find the greater number.
6/20 < 10/20
So, 3/10 > 1/2

Question 4.
\(\frac{11}{12}\) _____ \(\frac{4}{8}\)

Answer:
\(\frac{11}{12}\) > \(\frac{4}{8}\)

Explanation:
11/12 and 4/8
Least common denominator of 12 and 8 = 24
Multiply the numerator and denominator of 11/12 and 4/8 with 24
11/ 12 = (11 x 8)/(12 x 8) = 88/96
4/8 = (4 x 12)/(8 x 12) = 48/96
The denominators are the same now
So, compare the numerator to find the greater number
88/96 > 48/96
So, 11/12 > 4/8

Practice and Homework Lesson 6.6 Answer Key Question 5.
\(\frac{5}{8}\) _____ \(\frac{2}{5}\)

Answer:
\(\frac{5}{8}\) > \(\frac{2}{5}\)

Explanation:
5/ 8 and 2/5
Least common denominator of 5 and 8 = 40
Multiply the numerator and denominator of 5/8 and 2/8 with 40
5/ 8 = (5 x 5)/(8 x 5) = 25/40
2/5 = (2 x 8)/(5 x 8) = 16/40
The denominators are same now
So, compare the numerator to find the greater number
25/ 40 > 16/40
So, 5/8 > 2/5

Question 6.
\(\frac{8}{10}\) _____ \(\frac{3}{8}\)

Answer:
\(\frac{8}{10}\) > \(\frac{3}{8}\)

Explanation:
8/10 and 3/8
Least common denominator of 10 and 8 = 40
Multiply the numerator and denominator of 8/10 and 3/8 with 40
8/ 10 = (8 x 8)/(10 x 8) = 64/80
3/8 = (3 x 10)/(8 x 10) = 30/80
The denominators are same now
So, compare the numerator to find the greater number
64/80 > 30/80
So, 8/10 > 3/8

Question 7.
\(\frac{1}{3}\) _____ \(\frac{7}{12}\)

Answer:
\(\frac{1}{3}\) < \(\frac{7}{12}\)

Explanation:
1/3 and 7/12
Least common denominator of 3 and 12 = 12
Multiply the numerator and denominator of 1/3 and 7/12 with 40.
1/ 3 = (1 x 12)/(3 x 12) = 12/36
7/12 = (7 x 3)/(12 x 3) = 21/36
The denominators are same now
So, compare the numerator to find the greater number
12/36 < 21/36
So, 1/3 < 7/12

Question 8.
\(\frac{2}{6}\) _____ \(\frac{7}{8}\)

Answer:
\(\frac{2}{6}\) < \(\frac{7}{8}\)

Explanation:
2/6 and 7/8
Least common denominator of 6 and 8 = 24
Multiply the numerator and denominator of 2/6 and 7/8 with 40
2/ 6 = (2 x 8)/(6 x 8) = 16/48
7/8 = (7 x 6)/(8 x 6) = 42/48
The denominators are same now
So, compare the numerator to find the greater number
16/48<42/48
So, 2/6 < 7/8

Question 9.
\(\frac{4}{8}\) _____ \(\frac{2}{10}\)

Answer:
\(\frac{4}{8}\) > \(\frac{2}{10}\)

Explanation:
4/8 and 2/10
Least common denominator of 8 and 10 = 40
Multiply the numerator and denominator of 4/8 and 2/10 with 40
4/ 8 = (4 x 10)/(8 x 10) = 40/80
2/10 = (2 x 8)/(10 x 8) = 16/80
The denominators are same now
So, compare the numerator to find the greater number
40/80 > 16/80
So, 4/8 > 2/10

Reason Quantitatively Algebra Find a numerator that makes the statement true.

Question 10.
\(\frac{2}{4}<\frac { □ }{ 6 } \)
□ = _____

Answer:
4

Explanation:
2/4 < x/6
Least common denominator of 4 and 6 = 12
Multiply the numerator and denominator of 2/4 < x/6 with 40
2/4 = (2 x 6)/(4 x 6) = 12/24
x/6 = (x x 4)/(6 x 4) = 4 x/24
The denominators are same now
So, compare the numerator to find the greater number
12/24 < 4 X 4/24

Question 11.
\(\frac{8}{10}>\frac { □ }{ 8 } \)
□ = _____

Answer:
1

Explanation:
8/10 < x/8
Least common denominator of 10 and 8 = 40
8/10 = (8 x 4)/(10 x 4) = 32/40
x/8 = (x X 5)/(8 x 5) = 5x/40
The denominators are same now
So, compare the numerator to find the greater number
8/10 < 5x/40. X will be 1

Question 12.
\(\frac{10}{12}>\frac { □ }{ 4 } \)
□ = _____

Answer:
1

Explanation:
10/12 < x/4
Least common denominator of 12 and 4 = 12
10/12 = (10 x 1)/(12 x 1) = 10/12
x/4 = (x X 3)/(4 x 3) = 3x/12
The denominators are same now
So, compare the numerator to find the greater number
10/12 < 3/12. X will be 1.

Question 13.
\(\frac{2}{5}<\frac { □ }{ 10 } \)
□ = _____

Answer:
5

Explanation:
2/5 < x/10
Least common denominator of 5 and 10 = 10
2/5 = (2x 2)/(5 x 2) = 4/10
x/10 = (x X 1)/(10 x 1) = x/10
The denominators are same now
So, compare the numerator to find the greater number
2/5 < 5/10. X will be 5.

Question 14.
When two fractions are between 0 and \(\frac{1}{2}\), how do you know which fraction is greater? Explain.
Type below:
_______

Answer:
When two fractions are between 0 and \(\frac{1}{2}\). \(\frac{1}{2}\) is greater. As the tenths place of 5 is greater than 0. \(\frac{1}{2}\) is greater.

Question 15.
If you know that \(\frac{2}{6}<\frac{1}{2}\) and \(\frac{3}{4}<\frac{1}{2}\), what do you know about \(\frac{2}{6} \text { and } \frac{3}{4}\)?
Type below:
_______

Answer:

Explanation:
As per the given data,
2/6 < 1/2 and 3/4 < 1/2
Then, 2/6 and 3/4 is
The least common denominator of 6 and 4 is 12
(2 x 4)/(6 x 4) and (3 x 6)/(4 x 6)
8/24 and 18/24
Now, the denominators are same, then compare the numerators
8/24 > 18/24
So, 2/6 > 3/4

Question 16.
Sandra has ribbons that are \(\frac{3}{4}\) yard, \(\frac{2}{6}\) yard, \(\frac{1}{5}\) yard, and \(\frac{4}{7}\) yard long. She needs to use the ribbon longer than \(\frac{2}{3}\) yard to make a bow. Which length of ribbon could she use for the bow?
\(\frac{□}{□}\) yard

Answer:

Explanation:

Page No. 362

Question 17.
Saundra ran \(\frac{7}{12}\) of a mile. Lamar ran \(\frac{3}{4}\) of a mile. Who ran farther? Explain.
_______

Answer:
As per the given data,
Saundra ran 7/12 of a mile
Lamar ran 3/4 of a mile
The least common denominator of 7/12 and 3/4 is 12
(7x 1)/( 12 x 1) and ( 3 x 3 )/( 4 x 3)
7/12 and 9/12
So, 7/12 < 9/12
So, 7/12 < 3/4
Lamar ran greater distance than Saundra

Question 18.
What’s the Question? Selena ran farther than Manny.
Type below:
_______

Answer:
Who ran farther? Selena or Manny

Go Math Grade 4 Practice Book Pdf Lesson 6.6 Question 19.
Chloe made a small pan of ziti and a small pan of lasagna. She cut the ziti into 8 equal parts and the lasagna into 9 equal parts. Her family ate \(\frac{2}{3}\) of the lasagna. If her family ate more lasagna than ziti, what fraction of the ziti could have been eaten?
Type below:
_______

Answer:
\(\frac{1}{4}\)

Explanation:
As per the given data,
Chloe made a small pan of ziti and a small pan of lasagna
She cut the ziti into 8 equal parts and the lasagna into 9 equal parts
Her family ate 2/3 of the lasagna = (2/3) x 9 = 6 parts
If her family ate more lasagna than ziti, then that is less than 6 parts
So, 1/4 of the ziti = (1/4) x 8 = 2 parts
So, 1/4 of the ziti eaten by Chloe’s family

Question 20.
James, Ella, and Ryan biked around Eagle Lake. James biked \(\frac{2}{10}\) of the distance in an hour. Ella biked \(\frac{4}{8}\) of the distance in an hour. Ryan biked \(\frac{2}{5}\) of the distance in an hour. Compare the distances biked by each person by matching the statements to the correct symbol. Each symbol may be used more than once or not at all.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 19
Type below:
_______

Answer:
2/10 < 4/8
1 / 8 > 2/5
2/10 < 2/5

Explanation:
As per the given data,
James, Ella, and Ryan biked around eagle lake
James biked 2/10 of the distance in an hour
Ella biked 4/8 of the distance in an hour
Ryan biked 2/5 of the distance in an hour
Least common denominator of 2 /10, 4/8, and 2/5 is 40
(2x 4)/(10 x 4), (4 x 5)/(8 x 5), and (2 x 8)/(5 x 8)
8/40, 20/ 40, and 16/ 40
8/40 < 16/40 < 20/40
2/10 < 2/5 < 4/8
So, 2/10 < 4/8
1 / 8 > 2/5
2/10 < 2/5

Common Core – Compare Fractions Using Benchmarks – Page No. 363

Compare. Write < or > .

Question 1.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Compare Fractions Using Benchmarks img 20

Answer:
\(\frac{1}{8}\) < \(\frac{6}{10}\)

Explanation:
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Compare Fractions Using Benchmarks img 20

Question 2.
\(\frac{4}{12}\) _______ \(\frac{4}{6}\)

Answer:
\(\frac{4}{12}\) < \(\frac{4}{6}\)

Explanation:
4/12 and 4/6
4/12 is less than 1/2
4/6 is greater than 1/2
So, 4/12 < 4/6

Question 3.
\(\frac{2}{8}\) _______ \(\frac{1}{2}\)

Answer:
\(\frac{2}{8}\) < \(\frac{1}{2}\)

Explanation:
2/8 and 1/2
2/8 is less than 1/2
1/2 is equal to 1/2
So, 2/8 < 1/2

Question 4.
\(\frac{3}{5}\) _______ \(\frac{3}{3}\)

Answer:
\(\frac{3}{5}\) < \(\frac{3}{3}\)

Explanation:
3/5 and 3/3
3/5 is greater than 1/2
3/3 is equal to 1
So, 3/5 < 3/3

Question 5.
\(\frac{7}{8}\) _______ \(\frac{5}{10}\)

Answer:
\(\frac{7}{8}\) > \(\frac{5}{10}\)

Explanation:
7/8 and 5/10
7/8 is greater than 1/2
5/10 is equal to 1/2
So, 5/10 < 7/8

Question 6.
\(\frac{9}{12}\) _______ \(\frac{1}{3}\)

Answer:
\(\frac{9}{12}\) > \(\frac{1}{3}\)

Explanation:
9/12 and 1/3
9/ 12 is greater than 1/2
1/3 is less than 1/2
1/3 < 9/12

Question 7.
\(\frac{4}{6}\) _______ \(\frac{7}{8}\)

Answer:
\(\frac{4}{6}\) < \(\frac{7}{8}\)

Explanation:
4/6 and 7/8
4/6 is greater than 1/2
7/8 is closer to 1
So, 4/6 < 7/8

Question 8.
\(\frac{2}{4}\) _______ \(\frac{2}{3}\)

Answer:
\(\frac{2}{4}\) < \(\frac{2}{3}\)

Explanation:
2/4 and 2/3
2/4 is equal to 1/2
2/3 is greater than 1/2
So, 2/4 < 2/3

Question 9.
\(\frac{3}{5}\) _______ \(\frac{1}{4}\)

Answer:
\(\frac{3}{5}\) > \(\frac{1}{4}\)

Explanation:
3/5 and 1/4
3/5 is greater than 1/2
1/4 is less than 1/2
So, 1/4 < 3/5

Question 10.
\(\frac{6}{10}\) _______ \(\frac{2}{5}\)

Answer:
\(\frac{6}{10}\) > \(\frac{2}{5}\)

Explanation:
6/10 and 2/5
6/10 is greater than 1/2
2/5 is less than 1/2
So, 2/5 < 6/10

Question 11.
\(\frac{1}{8}\) _______ \(\frac{2}{10}\)

Answer:
\(\frac{1}{8}\) < \(\frac{2}{10}\)

Explanation:
1/8 and 2/10
1/8 is less than 1/2
2/10 is less than 1/2 but greater than 1/8
So, 1/8 < 2/10

Question 12.
\(\frac{2}{3}\) _______ \(\frac{5}{12}\)

Answer:
\(\frac{2}{3}\) > \(\frac{5}{12}\)

Explanation:
2/3 and 5/12
2/3 is greater than 1/2
5/12 is less than 1/2
So, 5/12 < 2/3

Question 13.
\(\frac{4}{5}\) _______ \(\frac{5}{6}\)

Answer:
\(\frac{4}{5}\)< \(\frac{5}{6}\)

Explanation:
4/5 and 5/6
4/5 is greater than 1/2
5/6 is greater than 1/2
Common denominator is 30
(4×6)/(5×6) and (5×5)/(6×5)
24/30 and 25/30
24/30 < 25/30
So, 4/5 < 5/6

Question 14.
\(\frac{3}{5}\) _______ \(\frac{5}{8}\)

Answer:
\(\frac{3}{5}\) < \(\frac{5}{8}\)

Explanation:
3/5 and 5/8
3/5 is greater than 1/2
5/8 is greater than 1/2
Common denominator is 40
(3×8)/(5×8) and (5×5)/(8×5)
24/40 and 25/ 40
24/40 < 25/40
3/5 < 5/8

Question 15.
\(\frac{8}{8}\) _______ \(\frac{3}{4}\)

Answer:
\(\frac{8}{8}\) > \(\frac{3}{4}\)

Explanation:
8/8 and 3/4
8/8 is equal to 1
3/4 is less than 1
3/4 < 8/8

Question 16.
Erika ran \(\frac{3}{8}\) mile. Maria ran \(\frac{3}{4}\) mile. Who ran farther?
_________

Answer:
Maria

Explanation:
As per the data,
Erika ran 3/8 mile
Maria ran 3/4 mile
Multiply the numerator and denominator of 3/4 with 2
(3×2)/(4×2) = 6/8
3/8 < 6/8
So, 3/8 < 3/4
So, Maria ran faster than Erika

Lesson 6.8 Compare and Order Fractions Question 17.
Carlos finished \(\frac{1}{3}\) of his art project on Monday. Tyler finished \(\frac{1}{2}\) of his art project on Monday. Who finished more of his art project on Monday?
_________

Answer:
Tyler

Explanation:
From the given data,
Carlos finished 1/3 of his art project on Monday
Tyler finished ½ of his art project on Monday
1/3 is less than 1/2
1/2 is equal to 1/2
So, 1/3 < 1/2
Then, Tyler finished more of his work on Monday

Common Core – Compare Fractions Using Benchmarks – Page No. 364

Question 1.
Which symbol makes the statement true?
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Compare Fractions Using Benchmarks img 21
Options:
a. >
b.<
c. =
d. none

Answer:
a. >

Explanation:
4/6 ? 3/8
By comparing 4/6 with 1/2, 4/6 > 1/2
By comparing 3/8 with 1/2, 3/8 < 1/2
So, 4/6 > 3/8

Question 2.
Which of the following fractions is greater than \(\frac{3}{4}\)?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{5}{6}\)
c. \(\frac{3}{8}\)
d. \(\frac{2}{3}\)

Answer:
b. \(\frac{5}{6}\)

Explanation:
From the given data,
By comparing the 3/4 with 1/2, 3/4 > 1/2
Same as above, compare the options with ½
a. 1/4 < 1/2
b. 5/6 > 1/2
c. 3/8 < 1/2
d. 2/3 > 1/2
5/6 and 2/3 are greater than the 1/2
So, compare the 5/6 with 2/3
Then, 5/6 > 2/3
So, 5/6 > 3/4

Question 3.
Abigail is putting tiles on a tabletop. She needs 48 tiles for each of the 8 rows. Each row will have 6 white tiles. The rest of the tiles will be purple. How many purple tiles will she need?
Options:
a. 432
b. 384
c. 336
d. 48

Answer:
c. 336

Explanation:
As per the given data
Abigail is putting tiles on a tabletop
Number of rows = 8
She needs 48 tiles for each row = 48×8 = 384
Number of white tiles per row = 6×8 = 48
Rest of the tiles will be purple = 384 – 48 =336
So, the total number of purple color tiles = 336

Question 4.
Each school bus going on the field trip holds 36 students and 4 adults. There are 6 filled buses on the field trip. How many people are going on the field trip?
Options:
a. 216
b. 240
c. 256
d. 360

Answer:
b. 240

Explanation:
From the given data,
Each school bus going on the field trip holds 36 students and 4 adults
There are 6 filled buses on the field trip
6 x (36 + 4) = 6 x 40 = 240
So, the total number of people on the field trip = 240

Question 5.
Noah wants to display his 72 collector’s flags. He is going to put 6 flags in each row. How many rows of flags will he have in his display?
Options:
a. 12
b. 15
c. 18
d. 21

Answer:
a. 12

Explanation:
As mentioned in the data,
Noah wants to display his 72 collector’s flag
He is going to put 6 flags in each row = 6x = 72
X = 12
So, a total 12 number of rows of flags will have on his display

Question 6.
Julian wrote this number pattern on the board:
3, 10, 17, 24, 31, 38.
Which of the numbers in Julian’s pattern are composite numbers?
Options:
a. 3, 17, 31
b. 10, 24, 38
c. 10, 17, 38
d. 17, 24, 38

Answer:
b. 10, 24, 38

Explanation:
As per the given information
Julian wrote his number pattern on the board =3, 10, 17, 24, 31, 38
Factors of 3 = 1,3
Factors of 10 = 1,2,5,10
Factors of 17 = 1, 17
Factors of 24 = 1, 2, 3, 4, 6
Factors of 31 = 1, 31
Factors of 38 = 1, 2, 19, 38
So, the composite number is 10, 24, and 38, which numbers have more than 2 factors

Page No. 367

Question 1.
Compare \(\frac{2}{5}\) and \(\frac{1}{10}\).
Think: Use ______ as a common denominator.
\(\frac{2}{5}=\frac { □×□ }{ □×□ } \) = \(\frac{□}{□}\)
\(\frac{1}{10}\)
Think: 4 tenth-size parts Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 22 1 tenth-size part.
\(\frac{2}{5}\) _____ \(\frac{1}{10}\)

Answer:
\(\frac{2}{5}\) > \(\frac{1}{10}\)

Explanation:
Compare 2/5 and 1/10
Think: 10 as common denominator
Multiply the numerator and denominator of 2/5 with 2
Then, (2×2) ÷ (5×2) = 4/10
Now, compare the 4/10 with 1/10
4/10 > 1/10
So, 2/5 > 1/10

Question 2.
Compare \(\frac{6}{10}\) and \(\frac{3}{4}\).
Think: Use ______ as a common denominator.
\(\frac{6}{10}\)
\(\frac{3}{4}=\frac { □×□ }{ □×□ } \) = \(\frac{□}{□}\)
Think: A tenth-size part Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 23 an eighth-size part.
\(\frac{6}{10}\) _____ \(\frac{3}{4}\)

Answer:
\(\frac{6}{10}\) < \(\frac{3}{4}\)

Explanation:
Compare 6/10 and 3/4
Think: Use 40 as a common denominator
So, multiply the denominator and numerator of 3/4 with 10
That is, (3×10) ÷ (4×10) = 30/40
Multiply the numerator and denominator of 6/10 with 4
That is, (6×4) ÷ (10×4) = 24/40
Denominators are same, compare the numerator values of 24/40 and 30/40
So, 24/40 < 30/40
Then, 6/10 < 3/4

Compare. Write <, >, or =.

Question 3.
\(\frac{7}{8}\) _____ \(\frac{2}{8}\)

Answer:
\(\frac{7}{8}\) > \(\frac{2}{8}\)

Explanation:
Compare 7/8 and 2/8
Denominator values are same but numerator values are different
Now, compare the numerator values of 7/8 and 2/8
Then, 7/8 > 2/8

Question 4.
\(\frac{5}{12}\) _____ \(\frac{3}{6}\)

Answer:
\(\frac{5}{12}\) < \(\frac{3}{6}\)

Explanation:
Compare 5/12 and 3/6
Multiply the numerator and denominator of 3/6 with 2
(3×2) ÷ (6×2) = 6/12
So, 5/12 < 6/12

Question 5.
\(\frac{4}{10}\) _____ \(\frac{4}{6}\)

Answer:
\(\frac{4}{10}\) < \(\frac{4}{6}\)

Explanation:
Compare 4/10 and 4/6
Multiply the numerator and denominator of 4/6 with 10
(4×10) ÷ (6×10) = 40/60
Multiply the numerator and denominator of 4/10 with 6
(4×6) ÷ (10×6) = 24/60
So, 24/60 < 40/60
Then, 4/10 < 4/6

Question 6.
\(\frac{6}{12}\) _____ \(\frac{2}{4}\)

Answer:
\(\frac{6}{12}\) = \(\frac{2}{4}\)

Explanation:
Compare 6/12 and 2/4
Multiply the numerator and denominator of 2/4 with 3
(2×3) ÷ (4×3) = 6/12
So, 6/12 = 6/12
Then, 6/12 = 2/4

Question 7.
\(\frac{1}{3}\) _____ \(\frac{1}{4}\)

Answer:
\(\frac{1}{3}\) < \(\frac{1}{4}\)

Explanation:
Compare 1/3 and 1/4
Multiply the numerator and denominator of 1/3 with 4
(1×4) ÷ (3×4) = 4/12
Multiply the numerator and denominator of 1/4 with 3
(1×3) ÷ (4×3) = 3/12
So, 4/12 < 3/12
Then, 1/3 < 1/4

Question 8.
\(\frac{4}{5}\) _____ \(\frac{8}{10}\)

Answer:
\(\frac{4}{5}\) = \(\frac{8}{10}\)

Explanation:
Compare 4/5 and 8/10
Multiply the numerator and denominator of 4/5 with 2
(4×2) ÷ (5×2) = 8/10
So, 8/10 = 8/10
Then, 4/5 = 8/10

Question 9.
\(\frac{3}{4}\) _____ \(\frac{2}{6}\)

Answer:
\(\frac{3}{4}\) < \(\frac{2}{6}\)

Explanation:
Compare 3/4 and 2/6
Multiply the numerator and denominator of 3/4 with 6
(3×6) ÷ (4×6) = 18/24
Multiply the numerator and denominator of 2/6 with 4
(2×4) ÷ (6×4) = 8/24
So, 18/24 < 8/24
Then, 3/4 < 2/6

Question 10.
\(\frac{1}{2}\) _____ \(\frac{5}{8}\)

Answer:
\(\frac{1}{2}\) < \(\frac{5}{8}\)

Explanation:
Compare 1/2 and 5/8
Multiply the numerator and denominator of 1/2 with 4
(1×4) ÷ (2×4) = 4/8
So, 4/8 < 5/8
Then, 1/2 < 5/8

Reason Quantitatively Algebra Find a number that makes the statement true.

Question 11.
\(\frac{1}{2}>\frac { □ }{ 3 } \)
□ = ______

Answer:
1

Explanation:
1/2 > x/3
Multiply the numerator and denominator of 1/2 with 3
(1×3) ÷ (2×3) = 3/6
Multiply the numerator and denominator of x/3 with 2
(Xx2) ÷ (3×2) = 2x/6
3/6 > 2x/6
So, x= 1
Then, 3/6 > 2/6
1/2 > 1/3

Question 12.
\(\frac{3}{10}>\frac { □ }{ 5 } \)
□ = ______

Answer:
1

Explanation:
3/10 > x/5
Multiply the numerator and denominator of x/5 with 2
(Xx2) ÷ (5×2) =2x/10
3/10 > 2x/10
So, x=1
3/10 > 2/10
3/10 > 1/5

Question 13.
\(\frac{5}{12}>\frac { □ }{ 3 } \)
□ = ______

Answer:
1

Explanation:
5/12 > x/3
Multiply numerator and denominator of x/3 with 4
(Xx4) ÷(3×4) = 4x/12
5/12 > 4x/12
So, x = 1
Then, 5/12 > 4/12
5/12 > 1/3

Question 14.
\(\frac{2}{3}>\frac { 4 }{ □ } \)
□ = ______

Answer:

Explanation:

Question 15.
Students cut a pepperoni pizza into 12 equal slices and ate 5 slices. They cut a veggie pizza into 6 equal slices and ate 4 slices. Use fractions to compare the amounts of each pizza that were eaten.
Type below:
_________

Answer:
\(\frac{5}{12}\) < \(\frac{4}{6}\)

Explanation:
As per the given data,
Students cut a pepperoni pizza into 12 equal slices and ate 5 slices
=5/12
They cut veggie pizza into 6 equal slices and ate 4 slices = 4/6
Compare 5/12 and 4/6
Multiply the numerator and denominator of 4/6 with 2
(4×2) ÷ (6×2) = 8/12
So, 5/12 < 8/12
Then, 5/12 < 4/6

Page No. 368

Question 16.
Jerry is making a strawberry smoothie. Which measure is greatest, the amount of milk, cottage cheese, or strawberries?
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 24
a. What do you need to find?
Type below:
_________

Answer:
I need to find the greatest measure from milk, cottage cheese, or strawberries

Question 16.
b. How will you find the answer?
Type below:
_________

Answer:
Equal the denominators of 3/4, 2/6, and 8/12
Multiply the numerator and denominator of 3/4 with 3
(3×3) ÷ (4×3) = 9/12
Multiply the numerator and denominator of 2/6 with 2
(2×2) ÷ (6×2) = 4/12
Compare 4/12 < 8/12 < 9/12
So, 2/6 < 8/12 <3/4

Question 16.
c. Show your work.
Type below:
_________

Answer:
2/6 < 8/12 < 3/4

Question 16.
d. Jerry needs more ________ than the other two ingredients.
________

Answer:
Jerry needs more strawberries than the other two ingredients

Question 17.
Angie, Blake, Carlos, and Daisy went running. Angie ran \(\frac{1}{3}\) mile, Blake ran \(\frac{3}{5}\) mile, Carlos ran \(\frac{7}{10}\) mile, and Daisy ran \(\frac{1}{2}\) mile. Which runner ran the shortest distance? Who ran the greatest distance?
The shortest distance: ________
The greatest distance: ________

Answer:
The shortest distance: \(\frac{1}{3}\)
The greatest distance: \(\frac{7}{10}\)

Explanation:
As per the given data,
Angie, Blake, Carlos, and Daisy went running
Angie ran 1/3 mile, Blake ran 3/5 mile, Carlos ran 7/10 mile, and Daisy ran 1/2 mile
Least common denominator of 1/3, 3/5, 7/10, and 1/2 =30
(1x 10)/(3×10), (3×6)/(5×6), (7×3)/(10×3), (1×15)/(2×15)
10/30, 18/30, 21/30, 15/30
10/30 < 15/30 < 18/30 < 21/30
1/3 < 1/2 < 3/5 < 7/10
The shortest distance ran by Angie and that is 1/ 3
The greatest distance ran by Carlos and that is 7/10

Question 18.
Elaine bought \(\frac{5}{8}\) pound of potato salad and \(\frac{4}{6}\) pound of macaroni salad for a picnic. Use the numbers to compare the amounts of potato salad and macaroni salad Elaine bought.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 25
Type below:
_________

Answer:
As per the given data,
Elaine bought 5/8 pound of potato salad and 4/6 pound of macaroni salad for a picnic
Multiply the numerator and denominator of 5/8 with 6
(5×6) / (8×6) = 30/48
Multiply the numerator and denominator of 4/6 with 8
(4×8) / (6×8) = 32/48
30/48 < 32/48
So, 5/8 < 4/6
Elaine bought more macaroni salad than potato salad

Common Core – Compare Fractions – Page No. 369

Compare. Write <, >, or =

Question 1.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Compare Fractions img 26

Answer:
\(\frac{1}{5}\) < \(\frac{2}{10}\)

Explanation:
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Compare Fractions img 26

Question 2.
\(\frac{1}{5}\) _____ \(\frac{2}{10}\)

Answer:
\(\frac{1}{5}\) = \(\frac{2}{10}\)

Explanation:
1/5 and 2/10
Think: 10 is a common denominator
1/5 = (1×2) / (5×2) = 2/10
2/10 = 2/10
So, 1/5 = 2/10

Question 3.
\(\frac{2}{4}\) _____ \(\frac{2}{5}\)

Answer:
\(\frac{2}{4}\) > \(\frac{2}{5}\)

Explanation:
2/4 and 2/5
20 is a common denominator
2/4 = (2×5)/(4×5) = 10/20
2/5 = (2×4)/(5×4) = 8/20
10/20 > 8/20
So, 2/4 > 2/5

Question 4.
\(\frac{3}{5}\) _____ \(\frac{7}{10}\)

Answer:
\(\frac{3}{5}\) < \(\frac{7}{10}\)

Explanation:
3/5 and 7/10
10 is a common denominator
3/5 = (3×2)/(5×2) = 6/10
7/10
6/10 < 7/10
So, 3/5 < 7/10

Question 5.
\(\frac{4}{12}\) _____ \(\frac{1}{6}\)

Answer:
\(\frac{4}{12}\) > \(\frac{1}{6}\)

Explanation:
4/12 and 1/6
12 is a common denominator
4/12
1/6 = (1×2)/(6×2) = 2/12
4/12 > 2/12
So, 4/12 > 1/6

Question 6.
\(\frac{2}{6}\) _____ \(\frac{1}{3}\)

Answer:
\(\frac{2}{6}\) = \(\frac{1}{3}\)

Explanation:
2/6 and 1/3
6 is a common denominator
2/6
1/3 = (1×2)/(3×2) = 2/6
So, 2/6 =2/6
So, 2/6 = 1/3

Question 7.
\(\frac{1}{3}\) _____ \(\frac{2}{4}\)

Answer:
\(\frac{1}{3}\) < \(\frac{2}{4}\)

Explanation:
1/3 and 2/4
12 is a common denominator
1/3 = (1×4)/(3×4) = 4/12
2/4 = (2×3)/(4×3) = 6/12
4/12 < 6/12
So, 1/3 < 2/4

Question 8.
\(\frac{2}{5}\) _____ \(\frac{1}{2}\)

Answer:
\(\frac{2}{5}\) < \(\frac{1}{2}\)

Explanation:
2/5 and 1/2
10 is a common denominator
2/5 = (2×2)/(5×2) = 4/10
1/2 = (1×5)/(2×5) = 5/10
4/10 < 5/10
So, 2/5 < 1/2

Question 9.
\(\frac{4}{8}\) _____ \(\frac{2}{4}\)

Answer:
\(\frac{4}{8}\) = \(\frac{2}{4}\)

Explanation:
4/8 and 2/4
8 is a common denominator
4/8
2/4 = (2×2)/(4×2) = 4/8
2/4 = 4/8
So, 4/8 = 2/4

Question 10.
\(\frac{7}{12}\) _____ \(\frac{2}{4}\)

Answer:
\(\frac{7}{12}\) < \(\frac{2}{4}\)

Explanation:
7/12 and 2/4
12 is a common denominator
7/12
2/4 = (2×3)/(4×3) = 6/12
7/12 < 6/12
So, 7/12 < 2/4

Question 11.
\(\frac{1}{8}\) _____ \(\frac{3}{4}\)

Answer:
\(\frac{1}{8}\) <  \(\frac{3}{4}\)

Explanation:
1/8 and 3/4
8 is a common denominator
1/8
3/4 = (3×2)/(4×2) = 6/8
1/8 < 6/8
So, 1/8 < 3/4

Question 12.
A recipe uses \(\frac{2}{3}\) of flour and \(\frac{5}{8}\) cup of blueberries. Is there more flour or more blueberries in the recipe?
more _____

Answer:
flour

Explanation:
From the given data,
A recipe uses 2/3 of flour and 5/8 cup of blueberries
Common denominator is 24
2/3 = (2×8)/(3×8) = 16/24
5/8 = (5×3)/(8×3) = 15/24
16/24 > 15/24
So, 2/3 > 5/8
So, flour is more in the recipe

Question 13.
Peggy completed \(\frac{5}{6}\) of the math homework and Al completed \(\frac{4}{5}\) of the math homework. Did Peggy or Al complete more of the math homework?
_________

Answer:
Peggy completed more work than Al

Explanation:
As per the given data,
Peggy completed 5/6 of the math homework
A1 completed 4/5 of the math homework
30 is a common denominator
5/6 = (5×5)/(6×5) = 25/30
4/5 = (4×6)/(5×6) =24/30
25/30 > 24/30
So, 5/6 > 4/5
So, Peggy completed more work than Al

Common Core – Compare Fractions – Page No. 370

Question 1.
Pedro fills a glass \(\frac{2}{4}\) full with orange juice. Which of the following fractions is greater than \(\frac{2}{4}\)?
Options:
a. \(\frac{3}{8}\)
b. \(\frac{4}{6}\)
c. \(\frac{5}{12}\)
d. \(\frac{1}{3}\)

Answer:
b. \(\frac{4}{6}\)

Explanation:
\(\frac{4}{6}\) > \(\frac{2}{4}\)

Question 2.
Today Ian wants to run less than \(\frac{7}{12}\) mile. Which of the following distances is less than \(\frac{7}{12}\) mile?
Options:
a. \(\frac{3}{4}\) mile
b. \(\frac{2}{3}\) mile
c. \(\frac{5}{6}\) mile
d. \(\frac{2}{4}\) mile

Answer:
d. \(\frac{2}{4}\) mile

Explanation:
\(\frac{2}{4}\) is less than \(\frac{7}{12}\)

Question 3.
Ms. Davis traveled 372,645 miles last year on business. What is the value of 6 in 372,645?
Options:
a. 6
b. 60
c. 600
d. 6,000

Answer:
c. 600

Explanation:
Ms. Davis traveled 372, 645 miles last year on business
The value of 6 in 372,645 is 600

Question 4.
One section of an auditorium has 12 rows of seats. Each row has 13 seats. What is the total number of seats in that section?
Options:
a. 25
b. 144
c. 156
d. 169

Answer:
c. 156

Explanation:
From the given information
One section of an auditorium has 12 rows of seats
Each row has 13 seats = 13×12 = 156 seats
So, the total number of seats in the auditorium = 156 seats

Question 5.
Sam has 12 black-and-white photos and 18 color photos. He wants to put the photos in equal rows so each row has either black-and-white photos only or color photos only. In how many rows can Sam arrange the photos?
Options:
a. 1, 2, 3, or 6 rows
b. 1, 3, 6, or 9 rows
c. 1, 2, or 4 rows
d. 1, 2, 3, 4, 6, or 9 rows

Answer:
a. 1, 2, 3, or 6 rows

Explanation:
As per the given information
Sam has 12 black and white photos 18 color photos
He wants to put the photos in equal rows
So each row has either black and white photos only or color photos only
H.C.F of 12 and 18 is 6
Rows of 6.
2 rows of black equal 12.
3 rows of white equals 18.

Question 6.
The teacher writes \(\frac{10}{12}\) on the board. He asks students to write the fraction in simplest form. Who writes the correct answer?
Options:
a. JoAnn writes \(\frac{10}{12}\)
b. Karen writes \(\frac{5}{12}\)
c. Lynn writes \(\frac{6}{5}\)
d. Mark writes \(\frac{5}{6}\)

Answer:
d. Mark writes \(\frac{5}{6}\)

Explanation:
As per the given data,
The teacher writes 10/12 on the board
He asks students to write the fraction in simplest form
For the simplest form of 10/12, divide the 10/12 with 2
(10÷2)/(12÷2) = 5/6
5/6 is the simplest form of 10/12
So, Mark writes the correct answer

Page No. 373

Question 1.
Locate and label points on the number line to help you write \(\frac{3}{10}, \frac{11}{12}, \text { and } \frac{5}{8}\) in order from least to greatest.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 27
Type below:
___________

Answer:
chapter 6 - compare fractions and order fractions- image1

Explanation:
3/10, 11/12, 5/8
3/10 is closer to 0
11/12 is closer to 1
5/8 is closer to 1/2
So, 3/10 < 5/8 < 11/12

Write the fraction with the greatest value.

Question 2.
\(\frac{7}{10}, \frac{1}{5}, \frac{9}{10}\)
\(\frac{□}{□}\)

Answer:
\(\frac{9}{10}\)

Explanation:
7/10, 1/5, and 9/10
7/10 is closer to 1/2
1/5 is closer to 0
9/10 is closer to 1
So, 9/10 > 7/10 > 1/5
Greatest value is 9/10

Question 3.
\(\frac{5}{6}, \frac{7}{12}, \frac{7}{10}\)
\(\frac{□}{□}\)

Answer:
\(\frac{5}{6}\)

Explanation:
7/12 is less than 1/2
7/10 and 5/6 are greater than 1/2
Compare 5/6 and 7/12
Multiply the numerator and denominator of 5/6 with 2
(5×2)/(6×2) = 10/12 > 7/12
So, 5/6 > 7/12
Compare 5/6 and 7/10
Multiply the 5/6 with 10
(5×10)/(6×10) = 50/60
Multiply the 7/10 with 6
(7×6)/(10×6) = 42/60
So, 5/6> 7/10
So, 7/12 <7/10<5/6

Question 4.
\(\frac{2}{8}, \frac{1}{8}, \frac{2}{4}, \frac{2}{6}\)
\(\frac{□}{□}\)

Answer:
\(\frac{2}{4}\)

Explanation:
2/8, 1/8, 2/4, 2/6
Common denominator of 4,6,8 = 24
(2×3)/(8×3), (1×3)/(8×3), (2×6)/(4×6), (2×4)/(6×4)
6/24, 3/24, 12/24, 8/24
Compare the numerator values
12/24 > 8/24 > 6/24 > 3/24
So, 2/4 > 2/6 > 2/8 >1/8

Write the fractions in order from least to greatest.

Question 5.
\(\frac{1}{4}, \frac{3}{6}, \frac{1}{8}\)
\(\frac{□}{□}\)
Type below:
________

Answer:
\(\frac{1}{8}, \frac{3}{6}, \frac{1}{4}\)

Explanation:
1/4, 3/6, 1/8
1/ 4 is closer to 1/2
3/6 is equal to 1/2
1/8 is closer to 0
So, 1/8 < 3/6 < 1/4

Question 6.
\(\frac{3}{5}, \frac{2}{3}, \frac{3}{10}, \frac{4}{5}\)
\(\frac{□}{□}\)
Type below:
________

Answer:
\(\frac{4}{5}, \frac{3}{10}, \frac{3}{5}, \frac{2}{3}\)

Explanation:
3/5, 2/3, 3/10, 4/5
3/5 is closer to 1/2
2/3 is greater than 1/2
3/10 is less than 1/2
4/5 is closer to 0
So, 4/5 < 3/10 < 3/5 < 2/3

Question 7.
\(\frac{3}{4}, \frac{7}{12}, \frac{5}{12}\)
\(\frac{□}{□}\)
Type below:
________

Answer:
\(\frac{5}{12}, \frac{7}{12}, \frac{3}{4}\)

Explanation:
3/4, 7/12, 5/12
3/ 4 is closer to 1
7/12 is greater than 1/2
5/ 12 is closer to 1/2
So, 5/12 < 7/12 < 3/4

Write the fractions in order from least to greatest.

Question 8.
\(\frac{2}{5}, \frac{1}{3}, \frac{5}{6}\)
\(\frac{□}{□}\)
Type below:
________

Answer:
\(\frac{1}{3}, \frac{2}{5}, \frac{5}{6}\)

Explanation:
2/5, 1/3, 5/6
2/5 is closer to 1/2
1/3 is closer to 0
5/6 is closer to 1
So, 1/3 < 2/5 < 5/6

Question 9.
\(\frac{4}{8}, \frac{5}{12}, \frac{1}{6}\)
\(\frac{□}{□}\)
Type below:
________

Answer:
\(\frac{1}{6}, \frac{5}{12}, \frac{4}{8}\)

Explanation:
4/8, 5/12, 1/6
4/8 is equal to1/2
5/12 is closer to 1/2
1/6 is closer to 0
So, 1/6 < 5/12 < 4/ 8

Question 10.
\(\frac{7}{100}, \frac{9}{10}, \frac{4}{5}\)
\(\frac{□}{□}\)
Type below:
________

Answer:
\(\frac{7}{100}, \frac{4}{5}, \frac{9}{10}\)

Explanation:
7/100, 9/10, 4/5
7/100 is closer to 0
9/10 is closer to 1
4/5 is greater than 1/2
So, 7/100 < 4/5 < 9/10

Reason Quantitatively Algebra Write a numerator that makes the statement true.

Question 11.
\(\frac{1}{2}<\frac { □ }{ 10 } <\frac{4}{5}\)
□ = _____

Answer:
6 or 7

Explanation:
1/2 < x/10 < 4/5
Common denominator is 10
(1×5)/(2×5) < x/10 < (4×2)/(5×2)
5/10 < x/10 < 8/10
Then, x = 6 or 7

Question 12.
\(\frac{1}{4}<\frac{5}{12}<\frac { □ }{ 6 } \)
□ = _____

Answer:
6

Explanation:
1/4 < 5/12 < x/6
Common denominator is 24
(1×6)/(4×6) < (5×2)/(12×2) < 4x/(6×4)
6/24 < 10/24 < 4x/24
If x = 6, then 4x = 24
So, 6/24 < 10/24 < 24/24

Question 13.
\(\frac { □ }{ 8 } <\frac{3}{4}<\frac{7}{8}\)
□ = _____

Answer:
1,2,3,4,5

Explanation:
x/8 < 3/4 < 7/8
Common denominator is 8
x/8 < (3×2)/(4×2) < 7/8
x/8 < 6/8 < 7/8
so x = 1,2,3,4,5

Page No. 374

Question 14.
Nancy, Lionel, and Mavis ran in a 5-kilometer race. The table shows their finish times. In what order did Nancy, Lionel, and Mavis finish the race?
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 28
a. What do you need to find?

Answer:
In which Nancy, Lionel, and Mavis finished the race?

Question 14.
b. What information do you need to solve the problem?
Type below:
_________

Answer:
the amount of time it took each runner to finish the race

Question 14.
c. What information is not necessary?
Type below:
_________

Answer:
the distance of the race

Question 14.
d. How will you solve the problem?
Type below:
_________

Answer:
By using the running race time of Nancy, Lionel, and Mavis

Question 14.
e. Show the steps to solve the problem.
Type below:
_________

Answer:
Common denominator of 2/3, 7/12, 3/4 is 12
(2×4)/(3×4), (7/12), (3×3)/(4×3)
8/12, 7/12, 9/12
7/12 < 8/12 < 9/12
7/12 < 2/3 < 3/4
Lionel < Nancy < Mavis

Question 14.
f. Complete the sentences.
The runner who finished first is _______.
The runner who finished second is _______.
The runner who finished third is _______.
The first: _______
The second: _______
The third: _______

Answer:
Lionel finished the race first
Nancy finished the race second
Mavis finished the race third
Lionel
Nancy
Mavis

Common Core – Compare and Order Fractions – Page No. 375

Write the fractions in order from least to greatest.

Question 1.
\(\frac{5}{8}, \frac{2}{12}, \frac{8}{10}\)
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Compare and Order Fractions img 29

Answer:
\(\frac{2}{12}, \frac{5}{8}, \frac{8}{10}\)

Explanation:
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Compare and Order Fractions img 29

Question 2.
\(\frac{1}{5}, \frac{2}{3}, \frac{5}{8}\)
Type below:
_________

Answer:
\(\frac{1}{5}, \frac{5}{8}, \frac{2}{3}\)

Explanation:
chapter 6 - compare fractions and order fractions- image4
1/5, 2/3, 5/8
1/5 is closer to 0
2/3 is greater than 1/2
5/8 greater than 1/2
1/5 < 5/8 < 2/3

Question 3.
\(\frac{1}{2}, \frac{2}{5}, \frac{6}{10}\)
Type below:
_________

Answer:
\(\frac{2}{5}, \frac{1}{2}, \frac{6}{10}\)

Explanation:
chapter 6 - compare fractions and order fractions- image5
1/2, 2/5, 6/10
1/2 is equal to 1/2
2/5 is less than 1/2
6/10 is greater than 1/2

Question 4.
\(\frac{4}{6}, \frac{7}{12}, \frac{5}{10}\)
Type below:
_________

Answer:
\(\frac{5}{10}\) < \(\frac{7}{12}\) < \(\frac{4}{6}\)

Explanation:
chapter 6 - compare fractions and order fractions- image6
4/6, 7/12, 5/10
4/6 is closer to 1
7/12 is greater than 1/2
5/10 is equal to 1/2

Question 5.
\(\frac{1}{4}, \frac{3}{6}, \frac{1}{8}\)
Type below:
_________

Answer:
\(\frac{1}{8}\) < \(\frac{1}{4}\) < \(\frac{3}{6}\)

Explanation:
chapter 6 - compare fractions and order fractions- image7
1/4, 3/6, 1/8
1/4 is less than 1/2
3/6 is equal to 1/2
1/8 is closer to 0

Question 6.
\(\frac{1}{8}, \frac{3}{6}, \frac{7}{12}\)
Type below:
_________

Answer:
\(\frac{1}{8}\) < \(\frac{7}{12}\) < \(\frac{3}{6}\)

Explanation:
chapter 6 - compare fractions and order fractions- image8
1/8, 3/6, 7/12
1/8 is closer to 0
3/6 is equal to 1/2
7/12 is greater than 1/2

Question 7.
\(\frac{8}{100}, \frac{3}{5}, \frac{7}{10}\)
Type below:
_________

Answer:
\(\frac{8}{100}\) < \(\frac{3}{5}\) < \(\frac{7}{10}\)

Explanation:
chapter 6 - compare fractions and order fractions- image9
8/100, 3/5, 7/10
8/100 is closer to 0
3/5 is greater than 1/2
7/10 is closer to 1

Question 8.
\(\frac{3}{4}, \frac{7}{8}, \frac{1}{5}\)
Type below:
_________

Answer:
\(\frac{1}{5}\) < \(\frac{3}{4}\) < \(\frac{7}{8}\)

Explanation:
chapter 6 - compare fractions and order fractions- image10
3/4, 7/8, 1/5
3/4 is greater than 1/2
7/8 is closer to 1
1/5 is closer to 0

Question 9.
Amy’s math notebook weighs \(\frac{1}{2}\) pound, her science notebook weighs \(\frac{7}{8}\) pound, and her history notebook weighs \(\frac{3}{4}\) pound. What are the weights in order from lightest to heaviest?
Type below:
_________

Answer:
\(\frac{1}{2}\) pound, \(\frac{3}{4}\) pound, \(\frac{7}{8}\) pound

Explanation:
From the given data,
Amy’s math notebook weighs 1/2 pound
Science notebook weighs 7/8 pound
History notebook weighs 3/4 pound
7/8 is closer to 1
3/4 is greater than 1/2
1/2 < 3/4 < 7/8
So, Amy’s math notebook weight < history notebook weight < science notebook

Question 10.
Carl has three picture frames. The thicknesses of the frames are \(\frac{4}{5}\) inch, \(\frac{3}{12}\) inch, and \(\frac{5}{6}\) inch. What are the thicknesses in order from least to greatest?
Type below:
_________

Answer:
\(\frac{3}{12}\) inch, \(\frac{4}{5}\) inch, \(\frac{5}{6}\) inch

Explanation:
As per the given data,
Carl has three picture frames
The thickness of the frames are 4/5 inch, 3/12 inch, 5/6 inch
4/5 is greater than 1/2
3/12 is less than 1/2
5/6 is closer to 1
3/12 < 4/5 < 5/6

Common Core – Compare and Order Fractions – Page No. 376

Question 1.
Juan’s three math quizzes this week took him \(\frac{1}{3}\) hour, \(\frac{4}{6}\) hour, and \(\frac{1}{5}\) hour to complete. Which list shows the lengths of time in order from least to greatest?
Options:
a. \(\frac{1}{3}\) hour, \(\frac{4}{6}\) hour, \(\frac{1}{5}\) hour
b. \(\frac{1}{5}\) hour, \(\frac{1}{3}\) hour, \(\frac{4}{6}\) hour
c. \(\frac{1}{3}\) hour, \(\frac{1}{5}\) hour, \(\frac{4}{6}\) hour
d. \(\frac{4}{6}\) hour, \(\frac{1}{3}\) hour, \(\frac{1}{5}\) hour

Answer:
b. \(\frac{1}{5}\) hour, \(\frac{1}{3}\) hour, \(\frac{4}{6}\) hour

Explanation:
From the given information
Juan’s three math quizzes this week took him 1/3 hour, 4/6 hour, and 1/5 hour
Compare 1/3 and 1/2
1/3 is less than 1/2
4/6 is greater than 1/2
1/5 is closer to 0
1/5 < 1/3 < 4/6
So, Juan’s math quizzes times from least to greatest is 1/5, 1/3, 4/6

Question 2.
On three days last week, Maria ran \(\frac{3}{4}\) mile, \(\frac{7}{8}\) mile, and \(\frac{3}{5}\) mile. What are the distances in order from least to greatest?
Options:
a. \(\frac{3}{4}\) mile, \(\frac{7}{8}\) mile, \(\frac{3}{5}\) mile
b. \(\frac{3}{5}\) mile, \(\frac{3}{4}\) mile, \(\frac{7}{8}\) mile
c. \(\frac{7}{8}\) mile, \(\frac{3}{4}\) mile, \(\frac{3}{5}\) mile
d. \(\frac{7}{8}\) mile, \(\frac{3}{5}\) mile, \(\frac{3}{4}\) mile

Answer:
b. \(\frac{3}{5}\) mile, \(\frac{3}{4}\) mile, \(\frac{7}{8}\) mile

Explanation:
As per the information
On three days last week, Maria ran 3/4 mile, 7/8 mile, and 3/5 mile
3/4 is greater than 1/2
7/8 is closer to 1
3/5 is greater than 1/2
Compare 3/5 and 3/4
3/4 is greater than 3/5
So, 3/5 < 3/4 < 7/8
Distance from least to greatest is 3/5, 3/4 , 7/8

Question 3.
Santiago collects 435 cents in nickels. How many nickels does he collect?
Options:
a. 58
b. 78
c. 85
d. 87

Answer:
d. 87

Explanation:
As per the given data,
Santiago collects 435 cents in nickels
1 nickel worth is 5 cents
Then, nickels per 435 cents = 435/5 = 87
So, Santiago collects 87 nickels

Question 4.
Lisa has three classes that each last 50 minutes. What is the total number of minutes the three classes last?
Options:
a. 15 minutes
b. 150 minutes
c. 153 minutes
d. 156 minutes

Answer:
b. 150 minutes

Explanation:
From the given data,
Lisa has three classes that each last 50 minutes
The total number of minutes the three classes last = 3×50 =150 minutes

Question 5.
Some students were asked to write a composite number. Which student did NOT write a composite number?
Options:
a. Alicia wrote 2.
b. Bob wrote 9.
c. Arianna wrote 15.
d. Daniel wrote 21.

Answer:
a. Alicia wrote 2.

Explanation:
As per the information
Some students were asked to write a composite number
a. Alicia wrote 2
Factors of 2 is 1 and 2
b. Bob wrote 9
Factors of 9 is 1, 3, 9
c. Arianna wrote 15
Factors of 15 is 1, 3, 5, 15
d. Daniel wrote 21
Factors of 21 is 1,3,7,21
So, Alicia did not write a composite number

Question 6.
Mrs. Carmel serves \(\frac{6}{8}\) of a loaf of bread with dinner. Which fraction is equivalent to \(\frac{6}{8}\)?
Options:
a. \(\frac{2}{4}\)
b. \(\frac{9}{16}\)
c. \(\frac{2}{3}\)
d. \(\frac{3}{4}\)

Answer:
d. \(\frac{3}{4}\)

Explanation:
As per the given information
Mrs. Carmel serves 6/8 of a loaf of bread with dinner
To find the equivalent fraction of 6/8, simplify the 6/8 by dividing with the 2
(6÷2)/(8÷2) = ¾
So, the equivalent fraction of 6/8 is 3/4

Page No. 377

Question 1.
For numbers 1a–1d, tell whether the fractions are equivalent by selecting the correct symbol.
a. \(\frac{4}{16}\) _____ \(\frac{1}{4}\)

Answer:
\(\frac{4}{16}\) = \(\frac{1}{4}\)

Explanation:
4/16 and 1/4
Divide the numerator and denominator of 4/16 with 4
(4÷4)/(16÷4) = 1/4
So, 4/16 = 1/4

Question 1.
b. \(\frac{3}{5}\) _____ \(\frac{12}{15}\)

Answer:
\(\frac{3}{5}\) ≠ \(\frac{12}{15}\)

Explanation:
3/5 and 12/15
Multiply the numerator and denominator of 3/5 with 3
(3×3)/(5×3) = 9/15
So, 3/5 ≠ 12/15

Question 1.
c. \(\frac{5}{6}\) _____ \(\frac{25}{30}\)

Answer:
\(\frac{5}{6}\) = \(\frac{25}{30}\)

Explanation:
c. 5/6 and 25/30
Multiply the numerator and denominator of 5/6 with 5
(5×5)/(6×5) = 25/30
So, 5/6 = 25/30

Question 1.
d. \(\frac{6}{10}\) _____ \(\frac{5}{8}\)

Answer:
\(\frac{6}{10}\) ≠ \(\frac{5}{8}\)

Explanation:
6/10 and 5/8
Divide the numerator and denominator of 6/10 with 2
(6÷2)/(10÷2) = 3/5
6/10 ≠5/8

Question 2.
Juan’s mother gave him a recipe for trail mix.
\(\frac{3}{4}\) cup cereal \(\frac{2}{3}\) cup almonds
\(\frac{1}{4}\) cup peanuts \(\frac{1}{2}\) cup raisins
Order the ingredients used in the recipe from least to greatest.
Type below:
_________

Answer:
As per the given data,
Juan’s mother gave him a recipe for trail mix
3/4 cup cereal and 2/3 cup almonds
1/4 cup peanuts and 1/2 cup raisins
3/4 is closer to 1
2/3 is greater than 1/2
1/4 is less than 1/2
1/2 is equal to 1/2
So, 1/4 < 1/2 <2/3 < 3/4
So, Jaun’s mother gave him a recipe for trail mix in order
1/4 cup of peanuts < 1/2 cup of raisins < 2/3 cup almonds < 3/4 cup of cereals

Question 3.
Taylor cuts \(\frac{1}{5}\) sheet of construction paper for an arts and crafts project. Write \(\frac{1}{5}\) as an equivalent fraction with the denominators shown.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 30
Type below:
_________

Answer:
From the given data,
Taylor cuts 1/5 sheet of construction paper for an arts and crafts project
So, the equivalent fractions of 1/5
Multiply the numerator and denominator of 1/5 with 2
(1×2)/(5×2) = 2/10
Multiply the numerator and denominator of 1/5 with 3
(1×3)/(5×3) = 3/15
Multiply the numerator and denominator of 1/5 with 5
(1×5)/(5×5) = 5/25
Multiply the numerator and denominator of 1/5 with 8
(1×8)/(5×8) = 8/40
So, the equivalent fractions of 1/5 are 2/10, 3/15, 5/25, 8/40

Question 4.
A mechanic has sockets with the sizes shown below. Write each fraction in the correct box.
\(\frac{7}{8} in. \frac{3}{16} in. \frac{1}{4} in. \frac{3}{8} in. \frac{4}{8} in. \frac{11}{16} in.\)
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 31
Type below:
_________

Answer:
chapter 6 - compare fractions and order fractions- image11

Explanation:
As per the given data,
A mechanic has sockets with the sizes 7/8 inch, 3/16 inch, 1/4 inch, 3/8 inch, 4/8 inch, 11/16 inch
7/8 is greater than 1/2
3/16 is less than 1/2
1/4 is less than 1/2
3/8 is less than 1/2
4/8 is equal to 1/2
11/16 is greater than 1/2

Page No. 378

Question 5.
Darcy bought \(\frac{1}{2}\) pound of cheese and \(\frac{3}{4}\) pound of hamburger for a barbecue. Use the numbers to compare the amounts of cheese and hamburger Darcy bought.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 32

Answer:
grade 4 chapter 6 image 3

Explanation:
From the given data,
Darcy bought 1/2 pound of cheese and 3/4 pound of hamburger for a barbecue
3/4 is greater than 1/2

Question 6.
Brad is practicing the piano. He spends \(\frac{1}{4}\) hour practicing scales and \(\frac{1}{3}\) hour practicing the song for his recital. For numbers 6a–6c, select Yes or No to tell whether each of the following is a true statement.
a. 12 is a common denominator of \(\frac{1}{4}\) and \(\frac{1}{3}\).
i. yes
ii. no

Answer:
i. yes

Explanation:
12 is a common denominator of 1/3 and 1/4

Question 6.
b. The amount of time spent practicing scales can be rewritten as \(\frac{3}{12}\).
i. yes
ii. no

Answer:
i. yes

Explanation:
b. The amount of time spent practicing scales can be rewritten as 3/12
Multiply the numerator and denominator of 1/4 with 3
(1×3)/(4×3) = 3/12
Yes, amount of time spent practicing scales can be rewritten as 3/12

Question 6.
c. The amount of time spent practicing the song for the recital can be rewritten as \(\frac{6}{12}\).
i. yes
ii. no

Answer:
ii. no

Explanation:
c. The amount of time spent practicing the song for the recital can be rewritten as 6/12
The amount of time spent practicing for the song for his recital = 1/3
Multiply the numerator and denominator of 1/3 with 4
(1×4)/(3×4) = 4/12
No, time spent practicing the song for the recital can not be written as 6/12

Question 7.
In the school chorus, \(\frac{4}{24}\) of the students are fourth graders. In simplest form, what fraction of the students in the school chorus are fourth graders?
\(\frac{□}{□}\)

Answer:
\(\frac{1}{6}\)

Explanation:
As per the given information,
In the school chorus,
4/24 of the students are fourth graders
For the simplest form of 4/24
Divide the numerator and denominator of 4/24 with 4
(4÷4)/(24÷4) =1/6
The simplest form of 4/24 is 1/6

Question 8.
Which pairs of fractions are equivalent? Mark all that apply.
a. \(\frac{8}{12} \text { and } \frac{2}{3}\)
b. \(\frac{3}{4} \text { and } \frac{20}{24}\)
c. \(\frac{4}{5} \text { and } \frac{12}{16}\)
d. \(\frac{7}{10} \text { and } \frac{21}{30}\)

Answer:
a. \(\frac{8}{12} \text { and } \frac{2}{3}\)

Explanation:
a. 8/12 and 2/3
Multiply the numerator and denominator of 2/3 with 4
(2×4)/(3×4) = 8/12
So, 8/12 = 2/3
b. 3/4 and 20/24
Multiply the numerator and denominator of 3/4 with 6
(3×6)/(4×6) = 18/24
c. 4/5 and 12/16
4/5 ≠ 12/16
d. 7/10 and 21/30
Multiply the numerator and denominator of 7/10 with 3
(7×3)/(10×3) =21/30
So, 7/10 = 21/30

Question 9.
Sam worked on his science fair project for \(\frac{1}{4}\) hour on Friday and \(\frac{1}{2}\) hour on Saturday. What are four common denominators for the fractions? Explain your reasoning.

Answer:
From the given data,
Sam worked on his science fair project for 1/4 hour on Friday and 1/2 hour on Saturday
4,8,12,16 are all common denominators because they all multiples of 2 and 4

Page No. 379

Question 10.
Morita works in a florist shop and makes flower arrangements. She puts 10 flowers in each vase, and \(\frac{2}{10}\) of the flowers are daisies.
Part A
If Morita makes 4 arrangements, how many daisies does she need? Show how you can check your answer.
_____ daisies

Answer:
8 daisies

Explanation:
If Morita makes 4 arrangements, 4 X 2 = 8.

Question 10.
Part B
Last weekend, Morita used 10 daisies to make flower arrangements. How many flowers other than daisies did she use to make the arrangements? Explain your reasoning.
_____ other flowers

Answer:
40 other flowers

Explanation:
If she used 10 daises, she must have made 5 arrangements. In each vase, she put \(\frac{2}{10}\) of the flowers are daisies. So, remaining flowers for each vase = 10 – 2 = 8. If she made 5 arrangements, 8 X 5 = 40 other flowers.

Question 11.
In Mary’s homeroom, \(\frac{10}{28}\) of the students have a cat, \(\frac{6}{12}\) have a dog, and \(\frac{2}{14}\) have a pet bird. For numbers 11a–11c, select True or False for each statement.
a. In simplest form, \(\frac{5}{14}\) of the students have a cat.
i. True
ii. False

Answer:
i. True

Explanation:
In simplest form 5/14 of the students have a cat
From the above, 10/28 of the students have a cat
Divide the numerator and denominator of 10/28 with 2
(10÷2)/(28÷2) = 5/14
True

Question 11.
b. In simplest form, \(\frac{2}{4}\) of the students have a dog.
i. True
ii. False

Answer:
i. True

Explanation:
In simplest form, 2/4 of the students have a dog
From the above, 6/12 of the students have a dog
Divide the 6/12 with 3
(6 = 2/4
True

Question 11.
c. In simplest form, \(\frac{1}{7}\) of the students have a pet bird.
i. True
ii. False

Answer:
i. True

Explanation:
In the simplest form, 1/7 of the students have a pet bird
From the data, 2/14 of the students have a pet bird
Divide the numerator and denominator of 2/14 with 2
(2÷2)/(14÷2) = 1/7
True

Page No. 380

Question 12.
Regina, Courtney, and Ellen hiked around Bear Pond. Regina hiked \(\frac{7}{10}\) of the distance in an hour. Courtney hiked \(\frac{3}{6}\) of the distance in an hour. Ellen hiked 38 of the distance in an hour. Compare the distances hiked by each person by matching the statements to the correct symbol. Each symbol may be used more
than once or not at all.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 33
Type below:
_________

Answer:
chapter 6 - compare fractions and order fractions- image13

Explanation:
From the given information
Regina, Courtney, and Ellen hiked around Bear Pond
Regina hiked 7/10 of the distance in an hour
Courtney hiked 3/6 of the distance in an hour
Ellen hiked 3 /8 of the distance in an hour
Compare 7/10 and 3/6
The common denominator of 7/10 and 3/6 is 30
(7×3)/(10×3) and (3×5)/(6×5)
21/30 and 15/30
So, 21/30 > 15/30
So, 7/10 > 15/30
Compare 3/8 and 3/6
The common denominator of 3/8 and 3/6 is 24
(3×3)/(8×3) and (3×4)/(6×4)
9/24 and 12/24 = 9/24 < 12/24 = 3/8 < 3/6
Compare 7/10 and 3/8
The common denominator of 7/10 and 3/8 is 40
(7×4)/(10×4) and (3×5)/(8×5)
28/40 >15/40 = 7/10 > 3/8

Question 13.
Ramon is having some friends over after a baseball game. Ramon’s job is to make a vegetable dip. The ingredients for the recipe are given.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 34
Part A
Which ingredient does Ramon use the greater amount of, buttermilk or cream cheese? Explain how you found your answer.
Type below:
_________

Answer:
Ramon use 5/8 cup of buttermilk and 1/2 cup cream cheese
By comparing these two ingredients
The common denominator of 5/8 and 1/2 are 8
(1×4)/(2×4) =4/8
So, 5/8 > 4/8
So, 5/8 cup buttermilk is > ½ cup cream cheese

Question 13.
Part B
Ramon says that he needs the same amount of two different ingredients. Is he correct? Support your answer with information from the problem.
______

Answer:
Ramon says that he needs the same amount of two ingredients
Yes, Ramon uses 3/4 cup parsley and 6/8 cup scallions
Multiply the 3/4 with 2
(3×2)/(4×2) = 6/8
So, Ramon uses the same amount that is 3/4 cup for parsley and scallions

Page No. 381

Question 14.
Sandy is ordering bread rolls for her party. She wants \(\frac{3}{5}\) of the rolls to be whole wheat. What other fractions can represent the part of the rolls that will be whole wheat? Shade the models to show your work.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 35
Type below:
_________

Answer:
chapter 6 - compare fractions and order fractions- image15

Explanation:
As per the information,
Sandy is ordering bread rolls for her party
She wants 3/5 of the rolls to be whole wheat
For an equivalent fraction of 3/5, multiply with 5
(3×5)/(5×5) = 15/25
Again multiply the 15/25 with 4
(15×4)/(25×4) = 60/100

Question 15.
Angel has \(\frac{4}{8}\) yard of ribbon and Lynn has \(\frac{3}{4}\) yard of ribbon. Do Angel and Lynn have the same amount of ribbon? Shade the model to show how you found your answer. Explain your reasoning.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 36
Type below:
_________

Answer:
grade 4 chapter 6 image 4
Angel and Lynn didn’t have the same amount of ribbon. 4/8 is a greater fraction compared to 3/4. So, Angel’s ribbon is long compared to Lynn’s ribbon.

Question 16.
Ella used \(\frac{1}{4}\) yard of red ribbon. Fill in each box with a number from the list to show equivalent fractions for \(\frac{1}{4}\). Not all numbers will be used.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 37
Type below:
_________

Answer:
grade 4 chapter 6 image 3

Explanation:
1/4 = 2/8 = 4/16 = 3/12

Page No. 382

Question 17.
Frank has two same-size rectangles divided into the same number of equal parts. One rectangle has \(\frac{3}{4}\) of the parts shaded, and the other has \(\frac{1}{3}\) of the parts shaded.
Part A
Into how many parts could each rectangle be divided? Show your work by drawing the parts of each rectangle.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 38
_____ parts

Answer:
grade 4 chapter 6 image 2
12 parts

Question 17.
Part B
Is there more than one possible answer to Part A? If so, did you find the least number of parts into which both rectangles could be divided? Explain your reasoning.
Type below:
_________

Answer:
Yes, as long it is a multiple of 12.
And yes,12 is the least in order to have 1 rectangle have 3/4 shaded and the other 1/3 shaded.

Question 18.
Suki rode her bike \(\frac{4}{5}\) mile. Claire rode her bike \(\frac{1}{3}\) mile. They want to compare how far they each rode their bikes using the benchmark \(\frac{1}{2}\). For numbers 18a–18c, select the correct answers to describe how to solve the problem.
a. Compare Suki’s distance to the benchmark:
\(\frac{4}{5}\) _____ \(\frac{1}{2}\)

Answer:
\(\frac{4}{5}\) ≠ \(\frac{1}{2}\)

Explanation:
The fraction \(\frac{4}{5}\) is not equal to \(\frac{1}{2}\).

Question 18.
b. Compare Claire’s distance to the benchmark:
\(\frac{1}{3}\) _____ \(\frac{1}{2}\)

Answer:
\(\frac{1}{3}\) ≠ \(\frac{1}{2}\)

Explanation:
The fraction \(\frac{1}{3}\) is not equal to \(\frac{1}{2}\)

Question 18.
c. Suki rode her bike _____ Claire.

Answer:
Suki rode her bike faster than Claire.

Page No. 387

Use the model to write an equation.

Question 1.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 39
Type below:
_________

Answer:
\(\frac{3}{5}\) + \(\frac{1}{5}\) = \(\frac{4}{5}\)

Question 2.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 40
Type below:
_________

Answer:
\(\frac{2}{3}\) – \(\frac{1}{3}\) = \(\frac{1}{3}\)

Question 3.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 41
Type below:
_________

Answer:
\(\frac{1}{4}\) + \(\frac{1}{4}\) = \(\frac{2}{4}\)

Question 4.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 42
Type below:
_________

Answer:
1 – \(\frac{5}{8}\) = \(\frac{8}{8}\) – \(\frac{5}{8}\) = \(\frac{3}{8}\)

Use the model to solve the equation.

Question 5.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 43
\(\frac{3}{4}-\frac{1}{4}\) = \(\frac{□}{□}\)

Answer:
\(\frac{2}{4}\)

Question 6.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 44
\(\frac{5}{6}+\frac{1}{6}\) = \(\frac{□}{□}\)

Answer:
\(\frac{6}{6}\) = 1

Question 7.
Reason Abstractly Sean has \(\frac{1}{5}\) of a cupcake and \(\frac{1}{5}\) of a large cake.
a. Are the wholes the same? Explain.
______

Answer:
Yes; From the given information, the fraction of the cupcake and large cake are the same.

Explanation:

Question 7.
Does the sum \(\frac{1}{5}+\frac{1}{5}=\frac{2}{5}\) make sense in this situation? Explain.
______

Answer:
Yes; it makes sense. From the given data, 1 part is out of 5 parts. So, adding two fractions (1 part is out of 5 parts), the complete fraction becomes 2/5.

Question 8.
Carrie’s dance class learned \(\frac{1}{5}\) of a new dance on Monday, and \(\frac{2}{5}\) of the dance on Tuesday. What fraction of the dance is left for the class to learn on Wednesday?
\(\frac{□}{□}\)

Answer:
\(\frac{3}{5}\)

Explanation:
The fraction of left for the class to learn on Wednesday is \(\frac{3}{5}\).

Page No. 388

Question 9.
Samantha and Kim used different models to help find \(\frac{1}{3}+\frac{1}{6}\). Whose model makes sense? Whose model is nonsense? Explain your reasoning below each model.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 45

Answer:
Both Samantha and Kim’s statements make sense. Because both models have an equal number of fractions for each diagram.

Question 10.
Draw a model you could use to add \(\frac{1}{4}+\frac{1}{2}\).
Type below:
___________

Answer:
grade 4 chapter 6 image 1

Question 11.
Cindy has two jars of paint. One jar is \(\frac{3}{8}\) full. The other jar is \(\frac{2}{8}\) full. Use the fractions to write an equation that shows the amount of paint Cindy has.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 46
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 47
Type below:
___________

Answer:
\(\frac{3}{8}+\frac{2}{8}\) = \(\frac{5}{8}\)

Explanation:

Conclusion:

Download Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison PDF for free. Make your students ready for the test with the practice of Go Math Grade 4 Answers. Get all the types of questions, answers in one place for free.

Go Math Grade 4 Chapter 6 Answer Key Pdf Fraction Equivalence and Comparison Read More »

Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers

Go Math Grade 4 Chapter 3 Answer Key Pdf Multiply 2-Digit Numbers

Go Math Grade 4 Chapter 3 Answer Key Pdf: Do you want real-time learning for your students? Then, you must follow Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers. The unlimited practice with different question types and detailed explanation. HMH Go Math Grade 4 Chapter 3 Multiply 2-Digit Numbers Answer Key is the guide for all students who want to achieve their top grades easily.

Students can learn the easy methods to solve problems using HMH Go Math Grade 4 Answer Key. All the problems are solved per the student’s understanding level and provided every answer with an explanation. Houghton Mifflin Harcourt Go Math Grade 4 Answer key is the one-stop solution for every student who wants to choose the correct path to maths skills.

Multiply 2-Digit Numbers Go Math Grade 4 Chapter 3 Answer Key Pdf

The chapter-wise questions and answers along with mid-chapter solutions and review test questions explanations are given. By solving with the HMH grade 4 Go Math Answer Key, students can get success in solving all kinds of Math problems efficiently. Every problem is mentioned in step-by-step solving. The concepts are very clear and included in an understandable way.

Lesson 1: Multiply by Tens

Lesson 2: Estimate Products

Lesson 3: Investigate • Area Models and Partial Products

Lesson 4: Multiply Using Partial Products

Mid-Chapter Checkpoint

Lesson 5: Multiply with Regrouping

Lesson 6: Choose a Multiplication Method

Lesson 7: Problem Solving • Multiply 2-Digit Numbers

Review/Test

Common Core – Page No. 149

Multiply by Tens

Choose a method. Then find the product.

Question 1.
16 × 60 = 960
Use the halving-and-doubling strategy.
Find half of 16: 16 ÷ 2 = 8.
Multiply this number by 60: 8 × 60 = 480
Double this result: 2 × 480 = 960

Answer:
960

Explanation:
Use the halving-and-doubling strategy.
Find half of 16: 16 ÷ 2 = 8.
Multiply this number by 60: 8 × 60 = 480
Double this result: 2 × 480 = 960

Question 2.
80 × 22 = ______

Answer:
1760

Explanation:
By using the place value method, Multiply 80 x 22
You can think of 80 as 8 tens
80 x 22 = (22 x 8) tens
= 176 tens
= 176 x 10 = 1760
80 x 22 = 1760

Go Math Grade 4 Chapter 3 Lesson 3.1 Multiply by Tens Question 3.
30 × 52 = ______

Answer:
1560

Explanation:
Use the Associative Property
You can think of 30 as 3 x 10
30 x 52 = (3 x 10) x 52
= 3 x (10 x 52)
=  3 x 520
= 1560
30 x 52 = 1560

Question 4.
60 × 20 = ______

Answer:
1200

Explanation:
60 x 20
Use the halving and doubling strategy
half of the 60 to make the problem simpler
60/ 2 = 30
Multiply 30 with 20
30 x 20 = 600
Double the 600
2 x 600= 1200
60 x 20 = 1200

Question 5.
40 × 35 = ______

Answer:
1400

Explanation:
By using the Associative Property 40 x 35
You can think of 40 as 4 x 10
40 x 35 = (4 x 10) x 35
= 4  x (10 x 35)
= 4 x 350
= 1400
40 x 35 = 1400

Question 6.
10 × 90 = ______

Answer:
900

Explanation:
By using the place value method, Multiply 10 x 90
You can think of 90 as 9 tens
10 x 90 = (10 x 9) tens
= 90 tens
= 10 x 90 = 900

Question 7.
31 × 50 = ______

Answer:
1,550

Explanation:
Use the place value method to multiply 31 x 50
You can think of 50 as 5 tens
31 x 50 = 31 x 5 tens
= 155 tens
= 1,550
31 x 50 = 1,550

Problem Solving

Question 8.
Kenny bought 20 packs of baseball cards. There are 12 cards in each pack. How many cards did Kenny buy?
______ cards

Answer:
240 cards

Explanation:
From the given data,
Kenny bought 20 packs of basketball cards
There are 12 cards in each pack = 12 x 20 cards
Use the associative property
You can write 20 as 2 x 10
12 x 20 = 12 x (2 x 10)
= (12 x 2) x 10
= (24) x 10
= 240 cards
Kenny bought 240 cards

Question 9.
The Hart family drove 10 hours to their vacation spot. They drove an average of 48 miles each hour. How many miles did they drive in all?
______ miles

Answer:
480 miles

Explanation:
As per the given data,
Hart family drove 10 hours to their vacation spot
Average speed per each hour is = 48 miles
Total miles = 48 x 10
Use the halving and doubling strategy
Half of the 48 to make the problem simpler
48/ 2 = 24
Multiply 24 with 10 = 24x 10 = 240
Double the value = 2 x 240 = 480 miles
Total miles drove by hart family = 480 miles.

Common Core – Page No. 150

Lesson Check

Question 1.
For the school play, 40 rows of chairs are set up. There are 22 chairs in each row. How many chairs are there in all?
Options:
a. 800
b. 840
c. 880
d. 8,800

Answer:
c. 880

Explanation:
As per the given data
For the school play, 40 rows of chairs are available. 22 chairs are available in each row.
Then total chairs in school play are = 22 x 40
By using the place value method
You can think of 40 as 4 tens
22 x 40 = 22 x 4 tens
= 88 tens
= 880
Total chairs in school are = 880

Question 2.
At West School, there are 20 classrooms. Each classroom has 20 students. How many students are at West School?
Options:
a. 40
b. 400
c. 440
d. 4,000

Answer:
b. 400

Explanation:
From the given data,
Total classrooms in west school = 20
Number of students per each classroom = 20
Then, total students at West School = 20 x 20
By using the associative property
You can think of 20 as 2 x 10
20 x 20 = 20 x (2 x 10)
= (20 x 2) x 10
=(40) x 10
=400
Total number of students at West School = 400

Spiral Review

Question 3.
Alex has 48 stickers. This is 6 times the number of stickers Max has. How many stickers does Max have?
Options:
a. 6
b. 7
c. 8
d. 9

Answer:
c. 8

Explanation:
As per the give data,
Alex has 48 stickers
That means, X= 48
This is 6 times the number of stickers max has = Y = 6X = 48
Then, number of stickers with Max = Y = X = 48/6 = 8
Number of stickers with Max = Y = 8 Stickers.

Question 4.
Ali’s dog weighs 8 times as much as her cat. Together, the two pets weigh 54 pounds. How much does Ali’s dog weigh?
Options:
a. 6 pounds
b. 42 pounds
c. 46 pounds
d. 48 pounds

Answer:
d. 48 pounds

Explanation:
From the given data,
Ali’s cat weight = X
Ali’s dog weight = 8 times as much as Ali’s cat = 8X
Together, the two pets weight = (X+8X) = 54 pounds
= 9X = 54 pounds
= X = 54/9 pounds = 6 pounds
Then, Ali’s dog weight = 8X =8 x 6 = 48 pounds.

Question 5.
Allison has 3 containers with 25 crayons in each. She also has 4 boxes of markers with 12 markers in each box. She gives 10 crayons to a friend. How many crayons and markers does Allison have now?
Options:
a. 34
b. 113
c. 123
d. 133

Answer:
b. 113

Explanation:
As per the given data,
Allison has 3 containers with 25 crayons in each = X = 3 x 25 = 75
Allison has 4 boxes of markers with 12 markers in each box = Y = 4 x 12 = 48
Allison gives 10 crayons to a friend = Z = 75-10 = 65
Now, total number of crayons and markers with Allison = Y + Z = 48 + 65 = 113

Question 6.
The state of Utah covers 82,144 square miles. The state of Montana covers 145,552 square miles. What is the total area of the two states?
Options:
a. 63,408 square miles
b. 223,408 square miles
c. 227,696 square miles
d. 966,992 square miles

Answer:
c. 227,696 square miles

Explanation:
From the given data,
The state of Utah covers 82,144 square miles
The state of Montana covers 145,552 square miles
Then, Total area of the two states = 82,144 + 145,552
The total area of two states = 227,696 square miles.

Page No. 153

Question 1.
To estimate the product of 62 and 28 by rounding, how would you round the factors? What would the estimated product be?
about _____

Answer:
1800

Explanation:
By using rounding and mental math
Estimate 62 x 28
Firstly, round each factor
62 x 28
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers      Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers
60 x 30
Use mental math
6 x 3 = 18
60 x 30 = 1800
So, estimated product of 62 and 28 = 1800

Estimate the product. Choose a method.

Question 2.
96 × 34
Estimate: _____

Answer:
3000

Explanation:
Use mental math and compatible numbers
96 x 34
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers      Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers
100 x 30
Use mental math
1 x 30 = 30
100 x 30= 3000

Go Math Chapter 3 Grade 4 Lesson 2 Estimate Products Question 3.
47 × $39
Estimate: $ _____

Answer:
2000

Explanation:
Round to the nearest ten
47 x $39
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers      Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers
50 x $40
50 x $ 4 = $200
50 x $40 = 2000

Question 4.
78 × 72
Estimate: _____

Answer:
5600

Explanation:
Use rounding and mental math
Round each factor
78 x 72
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers      Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers
80 x 70
Use mental math
8 x 7 = 56
80 x 70 = 5600

Question 5.
41 × 78
Estimate: _____

Answer:
3200

Explanation:
Use compatible numbers and mental math
41 x 78
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers      Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers
40 x 80
Use mental math
40 x 8 = 320
40 x 80 = 3200

Question 6.
51 × 73
Estimate: _____

Answer:
3500

Explanation:
Round to the nearest ten
51 x 73
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers      Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers
50 x 70 = 3500

Question 7.
34 × 80
Estimate: _____

Answer:
2400

Explanation:
Round each factor
34 x 80
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers      Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers
30 x 80
3 x 8 = 240
30 x 80 = 2400

Practice: Copy and Solve Estimate the product. Choose a method.

Question 8.
61 × 31
Estimate: _____

Answer:
1800

Explanation:
Round to the nearest ten
61 x 31
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers      Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers
60 x 30 = 1800

Go Math Key Answers Estimate Products Lesson 3.2 Question 9.
52 × 68
Estimate: _____

Answer:
3500

Explanation:
Round each factor
52 x 68
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers      Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers
50 x 70
Use mental math
5 x 7 =35
50 x 70 = 3500

Question 10.
26 × 44
Estimate: _____

Answer:
1200

Explanation:
Round to the nearest tens
26 x 44
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers      Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers
30 x 40 = 1200

Question 11.
57 × $69
Estimate: $ _____

Answer:
$4200

Explanation:
Round each factor
57 x $69
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers      Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers
60 x $70
Use mental math
6 x $7 = $42
60 x $70 = $4200

Find two possible factors for the estimated product.

Question 12.
2,800
Type below:
___________

Answer:
2800

Explanation:
Let us consider 7 x 4 = 28
70 x 40 = 2800

Question 13.
8,100
Type below:
___________

Answer:
8,100

Explanation:
Let us take 9 x 9 = 81
90 x 90 = 8,100

Question 14.
5,600
Type below:
___________

Answer:
5,600

Explanation:
Let us consider 7 x 8 = 56
70 x 80 = 5,600

Question 15.
2,400
Type below:
___________

Answer:
2,400

Explanation:
Let us take 4 x 6 = 24
40 x 60 = 2400
Or 3 x 8 = 24
30 x 80 = 2,400

Question 16.
Mr. Parker jogs for 35 minutes each day. He jogs 5 days in week 1, 6 days in week 2, and 7 days in week 3. About how many minutes does he jog?
about _____ minutes

Answer:
about 630 minutes

Explanation:
From the given data,
Mr. Parker jogs per day = 35 minutes
He jogs 5 days in week 1 = 5 x 35 = 175 minutes
6 days in week 2 = 6 x 35 = 210 minutes
7 days in week 3 = 7 x 35 = 245 minutes
Total minutes of jog by Mr. Parker = week 1 + week 2 + week 3
= 175 + 210 + 245
= 630 minutes
So, total minutes of jog by Mr. Parker = 630 minutes

Question 17.
There are 48 beads in a package. Candice bought 4 packages of blue, 9 packages of gold, 6 packages of red, and 2 packages of silver beads. About how many beads did Candice buy?
about _____ beads

Answer:
about 1008 beads

Explanation:
As per the given data,
48 beads are there in a package
Candice bought 4 packages of blue beads = 4 x 48 = 192
9 packages of gold beads = 9 x 48 = 432
6 packages of red beads = 6 x 48 = 288
2 packages of silver beads = 2 x 48 = 96
Total beads bought by Candice = 192 + 432 + 288 + 96
= 1008 beads
So, total beads bought by Candice = 1008.

Page No. 154

Question 18.
On average, a refrigerator door is opened 38 times each day. Len has two refrigerators in his house. Based on this average, about how many times in a 3-week period are the refrigerator doors opened?
about _____ times

Answer:
about 1600 times

Explanation:
From the given data,
On average, a refrigerator door is opened per day = 38 times
3-week period = 7 x 3 = 21
Then, a refrigerator door is opened per 21 days = 21 x 38 = 798 times
Len has 2 refrigerators in his house
Then, two refrigerators door are opened per 21 days = 2 x 798
= 1596 times
So, in a 3 – week period refrigerator door is opened about 1600 times

Question 19.
The cost to run a refrigerator is about $57 each year. About how much will it have cost to run by the time it is 15 years old?
about $ _____

Answer:
1200

Explanation:
As per the data,
The cost to run a refrigerator per each year = $57
Cost to run a refrigerator by the time it is 15 years old = $57 * 15
Round to the nearest tens
$57 x 15
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers      Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers
$60 x 20
Use mental math
$6 x 2 = 12
$ 60 x 20 = 1200

Question 20.
If Mel opens his refrigerator door 36 times every day, about how many times will it be opened in April? Will the exact answer be more than or less than the estimate? Explain.
Type below:
___________

Answer:
1200

Explanation:
From the given data,
Mel opens his refrigerator door per day = 36 times
Number of days in April month = 30 days
Refrigerator door opened in April month = 36 * 30
Round the factors
36 x 30
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers      Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers
40 x 30 = 1200

Go Math Grade 4 Chapter 3 Test Question 21.
Represent a Problem What question could you write for this answer? The estimated product of two numbers, that are not multiples of ten, is 2,800.
Type below:
___________

Answer:
2800

Explanation:
Let us take
1.
38 × 21
↓        ↓
40 × 20 = 800
2,800 = 42 x 68
↓    ↓
40 x  70 = 2800

Question 22.
Which is a reasonable estimate for the product? Write the estimate. An estimate may be used more than once.
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 1
26 × 48 __________
28 × 21 __________
21 × 22 __________
51 × 26 __________

Answer:
25 x 50 = 1250
30 x 20 = 600
20 x 20 = 400
50 x 25 = 1250

Explanation:
26 x 48 -> 25 x 50 = 1250
28 x 21 -> 30 x 20 = 600
21 x 22 -> 20 x 20 = 400
51 x 26 -> 50 x 25 = 1250

Common Core – Page No. 155

Estimate Products
Estimate the product. Choose a method.

Question 1.
38 × 21
38 × 21
↓       ↓
40 × 20
800

Answer:
800

Explanation:
38 × 21
↓        ↓
40 × 20
800

Question 2.
63 × 19
Estimate: _____

Answer:
1200

Explanation:
63 x 19
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers      Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers
60 x 20 = 1200
Estimated product of 63 x 19 = 1200

Question 3.
27 × $42
Estimate: $ _____

Answer:
$1000

Explanation:
27 × $42
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers      Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers
25 x $40 = $1000
Estimated Product of 25 x $ 42 = $1000

Question 4.
73 × 67
Estimate: _____

Answer:
4900

Explanation:
73 × 67
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers      Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers
70 x 70 = 4900
Estimated Product of 73 x 67 = 4900

Question 5.
37 × $44
Estimate:$ _____

Answer:
$1600

Explanation:
37 × $44
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers      Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers
40 x $40 = $1600
Estimated Product of 37 x $44 = $1600

Question 6.
85 × 71
Estimate: _____

Answer:
6300

Explanation:
85 × 71
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers      Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers
90 x 70 = 6300
Estimated Product of 85 x 71 = 6300

Question 7.
88 × 56
Estimate: _____

Answer:
4950

Explanation:
88 × 56
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers      Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers
90 x 55 = 4950
Estimated Product of 90 x 55 = 4950

Question 8.
97 × 13
Estimate: _____

Answer:
1,000

Explanation:
97 × 13
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers      Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers
100 x 10 = 1,000

Question 9.
92 × 64
Estimate: _____

Answer:
5850

Explanation:
92 × 64
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers      Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers
90 x 65 = 5850

Problem Solving

Question 10.
A dime has a diameter of about 18 millimeters. About how many millimeters long would a row of 34 dimes be?
about _____ millimeters

Answer:
about 600 millimeters

Explanation:
From the given data,
A dime has a diameter of about 18 millimeters
Then, 34 dimes diameter = 18 * 34
18 x 34
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers      Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers
20 x 30 = 600
So, 34 dimes have a diameter of about 600 millimeters long

Go Math Grade 4 Chapter 3 Mid Chapter Checkpoint Question 11.
A half-dollar has a diameter of about 31 millimeters. About how many millimeters long would a row of 56 half-dollars be?
about _____ millimeters

Answer:
1800 millimeters

Explanation:
As per the given data,
A half–dollar has a diameter of about 31 millimeters
Then, 56 half-dollars diameter = 31 * 56
31 * 56
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers      Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers
30 * 60
So, 56 half-dollars have a diameter of about 1800 millimeters long.

Common Core – Page No. 156

Lesson Check

Question 1.
Which is the best estimate for the product
43 × 68?
Options:
a. 3,500
b. 2,800
c. 2,400
d. 280

Answer:
b. 2,800

Explanation:
Round to the nearest tens
43 x 68
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers      Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers
40 x 70
Use mental math
4 x 7 = 28
40 x 70 = 2800
Estimated product of 43 x 68 = 2800

Question 2.
Marissa burns 93 calories each time she plays fetch with her dog. She plays fetch with her dog once a day. About how many calories will Marissa burn playing fetch with her dog in 28 days?
Options:
a. 4,000
b. 2,700
c. 2,000
d. 270

Answer:
b. 2,700

Explanation:
From the given data,
Marissa burned calories each time when she plays fetch with her dog= 93 calories
Then, Marissa burned calories in 28 days while playing fetch with her dog = 28 x 93
Round to the nearest tens
28 x 93
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers      Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers
30 x 90
Then, estimated burned calories in 28 days by Marissa = 2700 calories

Spiral Review

Question 3.
Use the model to find 3 × 126.
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers Common Core img 2
Options:
a. 368
b. 378
c. 468
d. 478

Answer:
b. 378

Explanation:
From the above Figure,
3 x 126 = 3 x 100 + 3 x 20 + 3 x 6
= 300 + 60 + 18
= 378
3 x 126 = 378

Question 4.
A store sells a certain brand of jeans for $38. One day, the store sold 6 pairs of jeans of that brand. How much money did the store make from selling the 6 pairs of jeans?
Options:
a. $188
b. $228
c. $248
d. $288

Answer:
b. $228

Explanation:
As per the given data,
A store sells a certain brand of jeans for rupees = $38
One day, the store sold 6 pairs of jeans of that brand = 6 x $38
6 x $38 = $228
The total amount of 6 pairs of jeans = $228

Question 5.
The Gateway Arch in St. Louis, Missouri, weighs about 20,000 tons. Which amount could be the exact number of tons the Arch weighs?
Options:
a. 31,093 tons
b. 25,812 tons
c. 17,246 tons
d. 14,096 tons

Answer:
c. 17,246 tons

Explanation:
From the given data,
The Gateway Arch in St.Louis, Missouri weight = about 20,000 tons
From the available options, 17,246 tons is closer to 20,000 tons
Then, the exact number of tons the Arch weighs = 17,246 tons

Question 6.
Which is another name for 23 ten thousands?
Options:
a. 23,000,000
b. 2,300,000
c. 230,000
d. 23,000

Answer:
c. 230,000

Explanation:
As per the data,
Another name for 23 ten thousands = 23 x 10,000
= 230,000
Another name for 23 ten thousand = 2,30,000

Page No. 159

Find the product.

Question 1.
16 × 19
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 3
16 × 19 = _____

Answer:
304

Explanation:
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 3
16 x 19 = 304

Question 2.
18 × 26
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 4
18 × 26 = _____

Answer:
468

Explanation:
Chapter 3 - Common core - Image 1. jpg
200 + 160 + 60 + 48 = 468

Question 3.
27 × 39
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 5
27 × 39 = ______

Answer:
1,053

Explanation:
Chapter 3 - Common core - image 2
600 + 210 + 180 +63 = 1053

Draw a model to represent the product.
Then record the product.

Question 4.
14 × 16 = ______

Answer:
224

Explanation:
Chapter 3 - Common core - Image 3
100 + 40 + 60 + 24 = 224

Question 5.
23 × 25 = ______

Answer:
575

Explanation:
Chapter 3 - Common core - Image 4
400 + 60 + 100 + 15 = 575

Question 6.
Explain how modeling partial products can be used to find the products of greater numbers.
Type below:
__________

Answer:
You can use mental math to find the partial products and then find the sum of the partial products.

Explanation:

Question 7.
Emma bought 16 packages of rolls for a party. There were 12 rolls in a package. After the party there were 8 rolls left over. How many rolls were eaten? Explain.
______ rolls

Answer:
184 rolls were eaten

Explanation:
From the given data,
Emma bought 16 packages of rolls for a party
There were 12 rolls in a package
Then, total rolls = 16 x 12 = 192
Chapter 3 - Common core - Image 5
100 + 60 + 20 + 12 =192
After the party there were 8 rolls left over
Then, total eaten rolls are = 192 – 8 = 184

Page No. 160

Question 8.
Jamal and Kim used different ways to solve 12 × 15 by using partial products. Whose answer makes sense? Whose answer is nonsense? Explain your reasoning.
Jamal’s Work
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 6
100 + 20 + 10 = 130

Kim’s Work
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 7
120 + 60 = 180
a. For the answer that is nonsense, write an answer that makes sense.
Type below:
__________

Answer:
a. Jamal’s work makes nonsense.
100 + 20 + 50 + 10 = 180 it makes sense

Question 8.
b. Look at Kim’s method. Can you think of another way Kim could use the model to find the product? Explain.
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 8
Type below:
__________

Answer:
Other method: 12 x 15
10 x 12 = 120
5 x 12 = 60
120 + 60 = 180.

Explanation:
Kim follows another method to find 12 x 15
That is, 100 + 50 = 150
20 + 10 = 30
Then, 150 + 30 =180
12 x 15 = 180

Question 9.
Look at the model in 8b. How would the partial products change if the product was 22 × 15? Explain why you think the products changed.
Type below:
__________

Answer:
330

Explanation:
Following the 8b method
22 x 15 =330
Chapter 3 - Common core - Image 6
200 + 100 = 300
20 + 10 = 30
Now, 300 + 30 = 330
Finally, 22 x 15 = 330
The factor of 15 is increased in present problem. So, the product also increases for 15 x 22.

Common Core – Page No. 161

Area Models and Partial Products

Draw a model to represent the product.
Then record the product.

Question 1.
13 × 42
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers Common Core img 9

Answer:
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers Common Core img 9

Question 2.
18 × 34 = ______

Answer:
chapter 3 - Area models and partial products- image 1. jpg
300 + 40 + 240 + 32 = 612

Question 3.
22 × 26 = ______

Answer:
chapter 3 - Area models and partial products- image 2. jpg
400 + 120 + 40 + 12 = 572

Question 4.
1 5 × 33 = ______

Answer:
chapter 3 - Area models and partial products- image 3. jpg
300 + 30 + 150 + 15 = 495

Question 5.
23 × 29 = ______

Answer:
chapter 3 - Area models and partial products- image 4. jpg
400 + 180 + 60 + 27 = 667

Question 6.
19 × 36 = ______

Answer:
chapter 3 - Area models and partial products- image 5. jpg
300 + 60 + 270 + 54 = 684

Problem Solving

Question 7.
Sebastian made the following model to find the product 17 × 24.
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers Common Core img 10
Is his model correct? Explain.
a. yes
b. no

Answer:
b. no

Explanation:
chapter 3 - Area models and partial products- image 6. jpg
200 + 40 + 140 + 28 = 408

Question 8.
Each student in Ms. Sike’s kindergarten class has a box of crayons. Each box has 36 crayons. If there are 18 students in Ms. Sike’s class, how many crayons are
there in all?
______ crayons

Answer:
648 crayons

Explanation:
From the given information,
Each student in Ms.Sike’s kindergarten class has a box of crayons
Crayons in each box = 36 Crayons
Number of students in Mr.Sike’s class = 18 students
Total crayons = 18 x 36
chapter 3 - Area models and partial products- image 7. jpg
300 + 60 + 240 + 48 = 648

Common Core – Page No. 162

Lesson Check

Question 1.
Which product does the model below represent?
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers Common Core img 11
Options:
a. 161
b. 230
c. 340
d. 391

Answer:
d. 391

Explanation:
200 + 30 + 140 + 21 = 391
17 x 23 = 391

Question 2.
Which product does the model below represent?
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 12 img 12
Options:
a. 219
b. 225
c. 244
d. 275

Answer:
b. 225

Explanation:
130 + 20 + 65 + 10 = 225
15 x 15 = 225

Spiral Review

Question 3.
Mariah builds a tabletop using square tiles. There are 12 rows of tiles and 30 tiles in each row. How many tiles in all does Mariah use?
Options:
a. 100
b. 180
c. 360
d. 420

Answer:
c. 360

Explanation:
From the given data,
Mariah builds a tabletop using square tiles
The square contains 12 rows of tiles and 30 tiles in each row = 12 x 30
12 x 30 = 360 tiles
Total tiles used by Mariah = 360 tiles

Go Math Answer Key Chapter 3 Review Test Answer Key Question 4.
Trevor bakes 8 batches of biscuits, with 14 biscuits in each batch. He sets aside 4 biscuits from each batch for a bake sale and puts the rest in a jar. How many biscuits does Trevor put in the jar?
Options:
a. 112
b. 80
c. 50
d. 32

Answer:
b. 80

Explanation:
As per the given data,
Number of biscuits baked by Trevor = 8 batches
Number of biscuits in each batch = 14 biscuits
So, total biscuits = 14 x 8 = 112
Trevor sets aside 4 biscuits from each batch for a bake = 8*4 = 32 biscuits are aside for a bake
Trevor kept rest of biscuits in a jar = 112 – 32 = 80
So, 80 biscuits are put in the jar by the Trevor

Question 5.
Li feeds her dog 3 cups of food each day. About how many cups of food does her dog eat in 28 days?
Options:
a. 60 cups
b. 70 cups
c. 80 cups
d. 90 cups

Answer:
c. 80 cups

Explanation:
As per the given data,
Li feeds her dog per day = 3 cups of food
Then, Li feeds her dog for 28 days = 3 x 28
= 84 cups of food
So, Li feeds her dog with 84 cups of food in 28 days

Question 6.
Which symbol makes the number sentence true?
4 ■ 0 = 0
Options:
a. +
b. –
c. ×
d. ÷

Answer:
c. ×

Explanation:
4 x 0 = 0

Page No. 165

Question 1.
Find 24 × 34.
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 13
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 14
_____

Answer:
816

Explanation:
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 13
chapter 3 - Area models and partial products- image 9. jpg

Question 2.
1 2
× 1 2
——–
_____

Answer:
144

Explanation:
chapter 3 - Area models and partial products- image 10. jpg
chapter 3 - Area models and partial products- image 11. jpg

Question 3.
3 1
× 2 4
——-
_____

Answer:
744

Explanation:
chapter 3 - Area models and partial products- image 12. jpg
chapter 3 - Area models and partial products- image 13. jpg

Question 4.
2 5
× 4 3
——-
_____

Answer:
1,075

Explanation:
chapter 3 - Area models and partial products- image 14. jpg
chapter 3 - Area models and partial products- image 15. jpg

Multiply Using Partial Products Lesson 3.4 Answer Key Question 5.
3 7
× 2 4
——-
_____

Answer:
888

Explanation:
chapter 3 - Area models and partial products- image 16. jpg
chapter 3 - Area models and partial products- image 17. jpg

Question 6.
5 4
× 1 5
——-
_____

Answer:
810

Explanation:
chapter 3 - Area models and partial products- image 18. jpg
chapter 3 - Area models and partial products- image 19. jpg

Question 7.
8 7
× 1 6
——-
_____

Answer:
1,392

Explanation:
chapter 3 - Area models and partial products- image 20. jpg
chapter 3 - Area models and partial products- image 21. jpg

Question 8.
6 2
× 5 6
——-
_____

Answer:
3,472

Explanation:
chapter 3 - Area models and partial products- image 22. jpg
chapter 3 - Area models and partial products- image 23. jpg

Question 9.
4 9
× 6 3
——-
_____

Answer:
3,087

Explanation:
chapter 3 - Area models and partial products- image 24. jpg
chapter 3 - Area models and partial products- image 25. jpg

Practice: Copy and Solve Record the product.

Question 10.
38 × 47
_____

Answer:
1,786

Explanation:
chapter 3 - Area models and partial products- image 26. jpg
chapter 3 - Area models and partial products- image 27. jpg

Question 11.
46 × 27
_____

Answer:
1,242

Explanation:
chapter 3 - Area models and partial products- image 28. jpg
chapter 3 - Area models and partial products- image 29. jpg

Question 12.
72 × 53
_____

Answer:
3,816

Explanation:
chapter 3 - Area models and partial products- image 30. jpg
chapter 3 - Area models and partial products- image 31. jpg

Question 13.
98 × 69
_____

Answer:
6,762

Explanation:
chapter 3 - Area models and partial products- image 32. jpg
chapter 3 - Area models and partial products- image 33. jpg

Multiply Using Partial Products Lesson 3.4 Question 14.
53 × 68
_____

Answer:
3,604

Explanation:
chapter 3 - Area models and partial products- image 34. jpg
chapter 3 - Area models and partial products- image 35. jpg

Question 15.
76 × 84
_____

Answer:
6,384

Explanation:
chapter 3 - Area models and partial products- image 36. jpg
chapter 3 - Area models and partial products- image 37. jpg

Question 16.
92 × 48
_____

Answer:
4,416

Explanation:
chapter 3 - Area models and partial products- image 38. jpg
chapter 3 - Area models and partial products- image 39. jpg

Question 17.
37 × 79
_____

Answer:
2,923

Explanation:
chapter 3 - Area models and partial products- image 40. jpg
chapter 3 - Area models and partial products- image 41. jpg

Reason Abstractly Algebra Find the unknown digits. Complete the problem.

Question 18.
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 15
Type below:
___________

Answer:
1,824

Explanation:
chapter 3 - Area models and partial products- image 42. jpg

Question 19.
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 16
Type below:
___________

Answer:
7,954

Explanation:
chapter 3 - Area models and partial products- image 43. jpg

Question 20.
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 17
Type below:
___________

Answer:
1,908

Explanation:
chapter 3 - Area models and partial products- image 44. jpg

Question 21.
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 18
Type below:
___________

Answer:
952

Explanation:
chapter 3 - Area models and partial products- image 45. jpg

Page No. 166

Use the picture graph for 22–24.
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 19

Question 22.
Use Graphs A fruit-packing warehouse is shipping 15 boxes of grapefruit to a store in Santa Rosa, California. What is the total weight of the shipment?
______ pounds

Answer:
1275 pounds

Explanation:
From the given data,
A fruit packing warehouse is shipping 15 boxes of grapefruit to store in Santa Rose, California
Grapefruit weight per box = 85 pounds
Total weight of the shipment = 85 x 15
chapter 3 - Area models and partial products- image 46. jpg
So, the total weight of the shipment = 1275 pounds

Question 23.
How much less do 13 boxes of tangelos weigh than 18 boxes of tangerines?
______ pounds

Answer:
450 pounds

Explanation:
As per the given data,
Tangelos weight per box = 90 pounds
Then, the weight of the 13 boxes of tangelos = 90 x 13
chapter 3 - Area models and partial products- image 47. jpg
And, the weight of the 18 boxes of tangelos = 90 x 18
chapter 3 - Area models and partial products- image 48. jpg
1620 – 1170 = 450
So, 13 boxes of tangelos weight are 450 pounds less than 18 boxes of tangelos weight

Question 24.
What is the weight of 12 boxes of oranges?
______ pounds

Answer:
1,080 pounds

Explanation:
The weight of the oranges per box = 90 pounds
then, weight of 12 boxes oranges = 90 x 12
chapter 3 - Area models and partial products- image 49. jpg
So, weight of 12 boxes oranges = 1,080 pounds

Question 25.
Each person in the United States eats about 65 fresh apples each year. Based on this estimate, how many apples do 3 families of 4 eat each year?
______ apples

Answer:
780 apples

Explanation:
From the given data,
Each person in the united states eats fresh apples per year = 65
3 families of 4 persons = 3 x 4 = 12 persons
Then, the number of apples eat by 12 persons = 65 x 12
chapter 3 - Area models and partial products- image 50. jpg
So, the total number of apples eat by 12 persons per year = 780

Question 26.
The product 26 × 93 is greater than 25 × 93. How much greater? Explain how you know without multiplying.
______

Answer:
The difference is 93
26 x 93 is one more group of 93 than 25 x 93

Question 27.
Margot wants to use partial products to find 22 × 17. Write the numbers in the boxes to show 22 × 17.
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 20
Type below:
__________

Answer:
chapter 3 - Area models and partial products- image 51. jpg

Explanation:
22 x 17
(20 + 2) x 17
20 x 17 + 2 x 17
20 x (10 + 7) + 2 x (10 + 7)
(20 x 10) + (20 x 7) + (2 x 10) + (2 x 7)
chapter 3 - Area models and partial products- image 51. jpg

Common Core – Page No. 167

Multiply Using Partial Products

Record the product.

Question 1.
2 3
× 7 9
———
1, 4 0 0
2 1 0
1 8 0
+ 2 7
——–
1, 8 1 7

Answer:
1, 8 1 7

Explanation:
2 3
× 7 9
———
1, 4 0 0
2 1 0
1 8 0
+ 2 7
——–
1, 8 1 7

Question 2.
5 6
× 3 2
——-
_______

Answer:
1,792

Explanation:
Chapter 3 - Common core - Image 7

Question 3.
8 7
× 6 4
——-
_______

Answer:
5,568

Explanation:
Chapter 3 - Common core - Image 8

Question 4.
3 3
× 2 5
——-
_______

Answer:
825

Explanation:
Chapter 3 - Common core - Image 9

Question 5.
9 4
× 1 2
——-
_______

Answer:
1,128

Explanation:
Chapter 3 - Common core - Image 10

Question 6.
5 1
× 7 7
——-
_______

Answer:
3,927

Explanation:
Chapter 3 - Common core - Image 11

Question 7.
6 9
× 4 9
——-
_______

Answer:
3,381

Explanation:
Chapter 3 - Common core - Image 12

Question 8.
8 6
× 8 4
——-
_______

Answer:
7,224

Explanation:
Chapter 3 - Common core - Image 13

Question 9.
9 8
× 4 2
——-
_______

Answer:
4,116

Explanation:
Chapter 3 - Common core - Image 14

Question 10.
7 3
× 3 7
——-
_______

Answer:
2,701

Explanation:
Chapter 3 - Common core - Image 15

Question 11.
8 5
× 5 1
——-
_______

Answer:
4,335

Explanation:
Chapter 3 - Common core - Image 16

Problem Solving

Question 12.
Evelyn drinks 8 glasses of water a day, which is 56 glasses of water a week. How many glasses of water does she drink in a year? (1 year = 52 weeks)
_______ glasses

Answer:
2,912 glasses

Explanation:
As per the given data,
Evelyn drinks 8 glasses of water a day
Evelyn drinks water per week = 56 glasses
Then, the number of glasses per 52 weeks = 52 x 56
Chapter 3 - Common core - Image 17
Total number of glasses of water drink by Evelyn per year = 2912 glasses of water

Multiply Using Partial Products Lesson 3.4 Answer Key Question 13.
Joe wants to use the Hiking Club’s funds to purchase new walking sticks for each of its 19 members. The sticks cost $26 each. The club has $480. Is this enough money to buy each member a new walking stick? If not, how much more money is needed?
Is the money enough? _______
How much more is needed? _______

Answer:
This amount is not enough to buy walking sticks
Still, $14 amount is needed to buy walking sticks

Explanation:
From the given data,
Joe wants to use the Hiking club funds to purchase new walking sticks for each of its 19 members
Cost per each stick = $26
Total walking sticks cost per 19 members = $26 x 19
Chapter 3 - Common core - Image 18
Total cost for walking sticks for 19 members = $494
The club has = $480
This amount is not enough to buy walking sticks
Still, $14 amount is needed to buy walking sticks

Common Core – Page No. 168

Lesson Check

Question 1.
A carnival snack booth made $76 selling popcorn in one day. It made 22 times as much selling cotton candy. How much money did the snack booth make selling
cotton candy?
Options:
a. $284
b. $304
c. $1,562
d. $1,672

Answer:
d. $1,672

Explanation:
As per the given data,
A carnival snack booth made popcorn in one day = $76
It made 22 times as much selling cotton candy
Then, total selling cotton candy made by snack booth = $76 x 22
Chapter 3 - Common core - Image 19
So, $1672 money snack booth will get for selling cotton candy

Question 2.
What are the partial products of
42 × 28?
Options:
a. 800, 80, 40, 16
b. 800, 16
c. 800, 40, 320, 16
d. 80, 16

Answer:
c. 800, 40, 320, 16

Explanation:
Chapter 3 - Common core - Image 20
So, partial products of 42 x 28 are 800, 40, 320, 16

Spiral Review

Question 3.
Last year, the city library collected 117 used books for its shelves. This year, it collected 3 times as many books. How many books did it collect this year?
Options:
a. 832
b. 428
c. 351
d. 72

Answer:
c. 351

Explanation:
From the given data,
Last year, the number of used books collected by city library by its shelves = 117 books
This year, it collected 3 times as many books = 3 x 117 =351 books
Total number of books collected by the city library for this year = 351 books

Question 4.
Washington Elementary has 232 students. Washington High has 6 times as many students. How many students does Washington High have?
Options:
a. 1,392
b. 1,382
c. 1,292
d. 1,281

Answer:
a. 1,392

Explanation:
As per the given data,
The number of students in Washington elementary = 232 students
Washington High has 6 times as many students = 6 x 232 = 1392
Total number of students in Washington High = 1392 students

Question 5.
What are the partial products of 35 × 7?
Options:
a. 10, 12
b. 21, 35
c. 210, 35
d. 350, 21

Answer:
c. 210, 35

Explanation:
Partial products of 35 x 7 are 210, 35

Question 6.
Shelby has ten $5 bills and thirteen $10 bills. How much money does Shelby have in all?
Options:
a. $15
b. $60
c. $63
d. $180

Answer:
d. $180

Explanation:
From the given data,
Shelby has ten $5 bills and thirteen $10 bills = (10 x $5) + (13 x $10)
= ($50) + ($130)
=$180
Total money with Shelby = $180

Page No. 169

Question 1.
Explain how to find 40 × 50 using mental math.
Type below:
__________

Answer:
200

Explanation:
40 x 50
By using mental math
4 x 5 = 20
40 x 50 = 200

Question 2.
What is the first step in estimating 56 × 27?
Type below:
__________

Answer:
18 centimeters

Explanation:
Round to the nearest values.
So, the first step of the estimated 56 x 27 is rounding to the nearest values that is 60 x 30

Choose a method. Then find the product.

Question 3.
35 × 10 = _____

Answer:
350

Explanation:
By using the place value method
You can take 10 as 1 ten
35 x 10 = 35 x 1 ten
= 35 ten
35 x 10 = 350

Question 4.
19 × 20 = _____

Answer:
380

Explanation:
19 x 20
By using the associative property
You can think of 20 as (2 x 10)
19 x 20 = 19 x (2 x 10)
= (19 x 2) x 10
= 38 x 10
19 x 20 = 380

Question 5.
12 × 80 = _____

Answer:
960

Explanation:
Use the halving and doubling strategy
half of the 80 to make the problem simpler
80/ 2 = 40
Multiply 40 with 12
40*12 = 480
Double the 480
2*480= 960
12*80 = 960

Question 6.
70 × 50 = _____

Answer:
3,500

Explanation:
70 x 50
By using the place value method
You can take 50 as 5 tens
70 x 50 = 70 x 5 tens
= 350 tens
70 x 50 = 3,500

Question 7.
58 × 40 = _____

Answer:
2,320

Explanation:
By using the associative property
You can think of 40 as (4 x 10)
58 x 40 = 58 x (4 x 10)
= (58 x 4) x 10
= 232 x 10
58 x 40 = 2,320

Question 8.
30 × 40 = _____

Answer:
1,200

Explanation:
Use the halving and doubling strategy
half of the 40 to make the problem simpler
40/ 2 = 20
Multiply 20 with 30
20*30 = 600
Double the 600
2*600= 1200
30*40 = 1,200

Question 9.
14 × 60 = _____

Answer:
840

Explanation:
By using the place value method
You can take 60 as 6 tens
14 x 60 = 14 x 6 tens
= 84 tens
14 x 60 = 840

Question 10.
20 × 30 = _____

Answer:
600

Explanation:
By using the associative property
You can think of 30 as (3 x 10)
20 x 30 = 20 x (3 x 10)
= (20 x 3) x 10
= 60 x 10
20 x 30 = 600

Question 11.
16 × 90 = _____

Answer:
1,440

Explanation:
Use the halving and doubling strategy
half of the 90 to make the problem simpler
90/ 2 = 45
Multiply 45 with 16
16*45 = 720
Double the 720
2*720= 1440
16*90 = 1,440

Estimate the product. Choose a method.

Question 12.
81 × 38
Estimate: _____

Answer:
3,200

Explanation:
Round to the nearest tens.
81 is close to 80; 38 is close to 40;
80 x 40 = 3,200

Question 13.
16 × $59
Estimate: $ _____

Answer:
$120

Explanation:
Round to the nearest tens.
16 is close to 20; $59 is close to $60;
Use the mental math to find the product of 20 x $60
2 x $6 = $12
20 x $60 = $120
Estimated product of 16 x $59 = $120

Question 14.
43 × 25
Estimate: _____

Answer:
1,000

Explanation:
Round to the nearest tens.
43 is close to 40; 25 is close to 25;
40 x 25 = 1000
Estimated product of 43 x 25 = 1,000

Question 15.
76 × 45
Estimate: _____

Answer:
3,200

Explanation:
Round to the nearest tens.
76 is close to 80; 45 is close to 40;
Use the mental math
8 x 4 = 32
80 x 40 = 3200
So, the estimated product of 76 x 45 = 3,200

Question 16.
65 × $79
Estimate: _____

Answer:
$4,800

Explanation:
Round to the nearest tens.
65 is close to 60; $79 is close to $80;
Use the mental math
6 x $8 = $48
60 x $80 = $4800
So, estimated product of 65 x $79 = $4,800

Question 17.
92 × 38
Estimate: _____

Answer:
3,600

Explanation:
Round to the nearest tens.
92 is close to 90; 38 is close to 40;
Use the mental math, then
9 x 4 = 36
90 x 40 = 3,600
So, estimated product of 92 x 38 = 3,600

Question 18.
37 × 31
Estimate: _____

Answer:
1,200

Explanation:
Round to the nearest tens.
37 is close to 40; 31 is close to 30;
Use the mental math, then
4 x 3 = 12
40 x 30 = 1,200
So, estimated product of 37 x 31 = 1,200

Question 19.
26 × $59
Estimate: _____

Answer:
$1,800

Explanation:
Round to the nearest tens.
26 is close to 30; $59 is close to $60;
Use the mental math, then
3 x $6 = $18
30 x $60 = $1,800
So, estimated product of 26 x $59 = $1,800

Question 20.
54 × 26
Estimate: _____

Answer:
18 centimeters

Explanation:
Round to the nearest tens.
54 is close to 50; 26 is close to 30;
Use the mental math
5 x 3 = 15
50 x 30 = 1,500
So, estimated product of 54 x 26 = 1,500

Question 21.
52 × 87
Estimate: _____

Answer:
4,500

Explanation:
Round to the nearest tens.
52 is close to 50; 87 is close to 90;
Use the mental math
5 x 9 = 45
50 x 90 = 4500
So, estimated product of 52 x 87 = 4,500

Question 22.
39 × 27
Estimate: _____

Answer:
18 centimeters

Explanation:
Round to the nearest tens.
39 is close to 40; 27 is close to 30;
Use the mental math
4 x 3 = 12
40 x 30 = 1,200
So, estimated product of 39 x 27 = 1,200

Question 23.
63 × 58
Estimate: _____

Answer:
3,600

Explanation:
Round to the nearest tens.
63 is close to 60; 58 is close to 60;
Use the mental math
6 x 6 = 36
60 x 60 = 3,600
So, estimated product of 63 x 58 = 3,600

Page No. 170

Question 24.
Ms. Traynor’s class is taking a field trip to the zoo. The trip will cost $26 for each student. There are 22 students in her class. What is a good estimate for the cost of the students’ field trip?
Type below:
__________

Answer:
18 centimeters

Explanation:
As per the given data,
Ms. Traynor’s class is taking a field trip to the zoo
Cost of the trip for each student = $26
Total number of students in her class = 22
The total cost of the trip for students = $26 x 22
Round to the nearest tens.
26 is close to 30; 22 is close to 20;
Use the mental math
$3 x 2 = $6
$30 x 20 = $600
Then, the total estimated cost for the trip for students = $600

Go Math Grade 4 Chapter 3 Test Pdf Question 25.
Tito wrote the following on the board. What is the unknown number?
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 21
______

Answer:
400

Explanation:
An unknown number is 50 x 8 = 400

Question 26.
What are the partial products that result from multiplying 15 × 32?
Type below:
__________

Answer:
Partial products are 300, 150, 20, 10

Explanation:
Chapter 3 - Common core - Image 36
Partial products are 300, 150, 20, 10

Question 27.
A city bus company sold 39 one-way tickets and 20 round-trip tickets from West Elmwood to East Elmwood. One-way tickets cost $14. Round trip tickets cost $25. How much money did the bus company collect?
$ ______

Answer:
$1,046

Explanation:
As per the given data,
Number of one – way tickets sold by the city bus company = 39
Round trip tickets from west Elmwood to east Elmwood = 20
Cost of one – way tickets = $14
Then, cost of 39 one – way tickets = 39 x $14 =$546
Cost of round trip tickets = $25
Then, cost of 20 round trip tickets = $25 x 20 = $500
Total money collected by the city bus company = $546 + $500 = $1,046

Page No. 173

Question 1.
Look at the problem. Complete the sentences.
Multiply ____ and ____ to get 0.
Multiply ____ and ____ to get 1,620.
Add the partial products.
0 + 1,620 = ____
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 22
_____

Answer:
Multiply 27 and 0 to get 0.
Multiply 27 and 6 to get 1,620.
Add the partial products. 0 + 1,620 = 1,620.

Estimate. Then find the product.

Question 2.
6 8
× 5 3
——-
Estimate: _________
Product: __________

Answer:
Estimate: 3,500
Product: 3,604

Explanation:
68 is closer to 70 and 53 is closer to 50
Estimate: 70 x 50 = 3,500
60 x 53 = 3180
8 x 53 = 424
3180 + 424 = 3604
Product 3,604

Question 3.
6 1
× 5 4
——-
Estimate: _________
Product: __________

Answer:
Estimate: 3,000
Product: 3,294

Explanation:
61 is closer to 60 and 54 is closer to 50
Estimate: 60 x 50 = 3,000
60 x 54 = 3240
1 x 54 = 54
3240 + 54 = 3294
Product 3,294

Question 4.
9 0
× 2 7
——-
Estimate: _________
Product: __________

Answer:
Estimate: 2,700
Product: 2,430

Explanation:
27 is closer to 30
Estimate: 90 x 30 = 2,700
90 x 27 = 2430
Product 2,430

Question 5.
3 0
× 4 7
——-
Estimate: _________
Product: __________

Answer:
Estimate: 1,500
Product: 1,410

Explanation:
47 is closer to 50
Estimate: 30 x 50 = 1,500
30 x 47 = 1410
Product 1,410

Question 6.
7 8
× 5 6
——-
Estimate: _________
Product: __________

Answer:
Estimate: 4,800
Product: 4,368

Explanation:
78 is closer to 80 and 56 is closer to 60
Estimate: 80 x 60 = 4,800
70 x 56 = 3920
8 x 56 = 448
3920 + 448 = 4368
Product 4,368

Question 7.
2 7
× 2 5
——-
Estimate: _________
Product: __________

Answer:
Estimate: 600
Product: 675

Explanation:
27 is closer to 30 and 25 is closer to 20
Estimate: 30 x 20 = 600
20 x 25 = 500
7 x 25 = 175
500 + 175 = 675
Product 675

Practice: Copy and Solve Estimate. Then find the product.

Question 8.
34 × 65
Estimate: _________
Product: __________

Answer:
Estimate: 1,800
Product: 2,210

Explanation:
34 is closer to 30 and 65 is closer to 60
Estimate: 30 x 60 = 1,800
30 x 65 = 1950
4 x 65 = 260
1950 + 260 = 2210
Product 2,210

Question 9.
42 × $13
Estimate: $ _________
Product: $ _________

Answer:
Estimate: $400
Product: $546

Explanation:
42 is closer to 40 and 13 is closer to 10
Estimate: 40 x 10 = 400
40 x $13 = $520
2 x $13= $26
$520 + $26 = $546
Product $546

Question 10.
60 × 17
Estimate: _________
Product: __________

Answer:
Estimate: 1,200
Product: 1,020

Explanation:
17 is closer to 20
Estimate: 60 x 20 = 1,200
60 x 17 = 1020
Product = 1,020

Question 11.
62 × 45
Estimate: _________
Product: __________

Answer:
Estimate: 2,400
Product: 2,790

Explanation:
62 is closer to 60 and 45 is closer to 40
Estimate: 60 x 40 = 2,400
60 x 45 = 2700
2 x 45= 90
2700 + 90 = 2790
Product 2,790

Question 12.
57 × $98
Estimate: $ _________
Product: $ _________

Answer:
Estimate: 6,000
Product: 5,586

Explanation:
57 is closer to 60 and 98 is closer to 100
Estimate: 60 x 100 = 6,000
50 x 98 = 4900
7 x 98= 686
4900 + 686 = 5586
Product 5,586

Look for a Pattern Algebra Write a rule for the pattern.
Use your rule to find the unknown numbers.

Question 13.
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 23
Rule _____________
Type below:
_________

Answer:
Chapter 3 - Common core - Image 37

Explanation:
1 hour = 60 min
Then, 5hr = 5 x 60 = 300 min
10hr = 10 x 60 = 600 min
15hr = 15 x 60 = 900 min
20hr = 20 x 60 = 1200 min
25hr = 25 x 60 = 1500 min

Question 14.
Owners of a summer camp are buying new cots for their cabins. There are 16 cabins. Each cabin needs 6 cots. Each cot costs $92. How much will the new cots cost?
$ _______

Answer:
$8,832

Explanation:
As per the given data,
Owners pf a summer camp are buying new cots for their cabins
Number of cabins = 16
Each cabin needs 6 cots
Then, total cots = 16 x 6 = 96
Each cot cost = $92
Then, cost for total cots = $92 x 96
92 is closer to 90 and 96 is closer to 100
Estimate = 90 x 100 = 9,000
90 x 96 = 8640
2 x 96 = 192
8640 + 192 = 8832
Product = 8,832

Question 15.
A theater has 28 rows of 38 seats downstairs and 14 rows of 26 seats upstairs. How many seats does the theater have?
______ seats

Answer:
1,428 seats

Explanation:
As per the given data,
A theatre has 28 rows of 38 seats downstairs = 28 x 38 = 1064
14 rows of 26 seats upstairs = 14 x 26 = 364
Total number of seats = 1064 + 364 = 1,428 seats

Page No. 174

Question 16.
Machine A can label 11 bottles in 1 minute. Machine B can label 12 bottles in 1 minute. How many bottles can both machines label in 15 minutes?
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 24
a. What do you need to know?
Type below:
__________

Answer:
number of bottles labeled by Machine A and Machine B in 15 minutes

Question 16.
b. What numbers will you use?
Type below:
__________

Answer:
15x 11 and 15 x 12

Question 16.
c. Tell why you might use more than one operation to solve the problem.
Type below:
__________

Answer:
To find out the total number of bottle made by both machines A & B

Question 16.
d. Solve the problem.
So, both machines can label ____ bottles in ____ minutes.
Type below:
__________

Answer:
Machine A can label 11 bottles in 1 minute
Then, the number of bottles labeled by machine A in 15 minutes = 15 x 11 = 165
Machine B can label 12 bottles in 1 minute
Then, number of bottles labelled by Machine B in 15 minutes = 15 x 12 = 180
Total bottles labelled by both the machines in 15 minutes = 165 + 180 = 345

Question 17.
Make Sense of Problems
A toy company makes wooden blocks. A carton holds 85 blocks. How many blocks can 19 cartons hold?
______ blocks

Answer:
1,615 blocks

Explanation:
From the given data,
A toy company makes wooden blocks
A carton holds 85 blocks
Then, number of blocks hold by 19 cartons = 19 x 85 = 1615
Total number of blocks held by 19 cartons = 1,615

Question 18.
A company is packing cartons of candles. Each carton can hold 75 candles. So far, 50 cartons have been packed, but only 30 cartons have been loaded on a truck. How many more candles are left to load on the truck?
______ candles

Answer:
1,500 candles

Explanation:
As per the given data,
A company is packing cartons of candles
Each carton can hold 75 candles
Then, number of candles hold by 50 cartons = 50 x 75 = 3750
Number of candles hold by 30 cartons = 30 x 75 = 2250
50 cartons have been packed, but only 30 cartons have been loaded on a truck
Remaining candles are left to load on truck = 3750 – 2250 = 1,500

Question 19.
Mr. Garcia’s class raised money for a field trip to the zoo. There are 23 students in his class. The cost of the trip will be $17 for each student. What is the cost for all the students? Explain how you found your answer.
$ ______

Answer:
$391

Explanation:
As per the given data,
Mr. Garcia’s class raised money for a field trip to the zoo
Total number of students in his class = 23 students
Cost of the trip for each student = $17
Then, total cost for all the students = $17 x 23 = $391

Common Core – Page No. 175

Multiply with Regrouping
Estimate. Then find the product.

Question 1.
Estimate: 2,700
Think: 87 is close to 90 and 32 is close to 30.
90 × 30 = 2,700
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers Common Core img 25

Answer:
2,784

Explanation:
Think: 87 is close to 90 and 32 is close to 30.
90 × 30 = 2,700
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers Common Core img 25

Question 2.
7 3
× 2 8
——–
Estimate: ______
Product: _______

Answer:
Estimate: 2,100
Product: 2,044

Explanation:
Estimate: 73 is close to 70; 28 is close to 30.
So, 70 x 30 = 2,100.
Product: Write 73 as 7 tens and 3 ones. Multiply 28 by 3 ones.
2
28
x 73
——–
84 <– 3 x 28
Multiply 28 by 7 tens
5
28
x 73
——–
1960 <– 70 x 28
Add the partial products.
84 + 1960 = 2,044.
So, 73 x 28 = 2,044.

Go Math Grade 4 Chapter 3 Answer Key Pdf Question 3.
4 8
× 3 8
——–
Estimate: ______
Product: _______

Answer:
Estimate: 2,000
Product: 1,824

Explanation:
48 is close to 50 and 38 is close to 40.
Estimate: 50 × 40 = 2,000
40 x 38 = 1520
8 x 38 = 304
1520 + 304 = 1824.
Product: 1,824

Question 4.
5 9
× 5 2
——–
Estimate: ______
Product: _______

Answer:
Estimate: 3,000
Product: 3,068

Explanation:
59 is close to 60 and 52 is close to 50.
Estimate: 60 × 50 = 3,000
50 x 52 = 2600
9 x 52 = 468
2600 + 468 = 3068.
Product: 3,068.

Question 5.
8 4
× 4 0
——–
Estimate: ______
Product: _______

Answer:
Estimate: 3,200
Product: 3,360

Explanation:
84 is close to 80 and 40 is close to 40.
Estimate: 80 × 40 = 3,200
80 x 40 = 3,200
4 x 40 = 160
3200 + 160 = 3,360.
Product: 3,360.

Question 6.
8 3
× 7 7
——–
Estimate: ______
Product: _______

Answer:
Estimate: 6,400
Product: 6,391

Explanation:
83 is close to 80 and 77 is close to 80.
Estimate: 80 × 80 = 6,400
80 x 77 = 6,160
3 x 77 = 231
6,160 + 231 = 6,391.
Product: 6,391.

Question 7.
9 1
× 1 9
——–
Estimate: ______
Product: _______

Answer:
Estimate: 1,800
Product: 1,729

Explanation:
91 is close to 90 and 19 is close to 20.
Estimate: 90 × 20 = 1,800
90 x 19 = 1,710
1 x 19 = 19
1,710+ 19 = 1,729.
Product: 1,729.

Problem Solving

Question 8.
Baseballs come in cartons of 84 baseballs. A team orders 18 cartons of baseballs. How many baseballs does the team order?
_______ baseballs

Answer:
1,512 baseballs

Explanation:
To find total baseballs, 84 x 18
80 x 18 = 1,440
4 x 18 = 72
84 x 18 = 1,512

Question 9.
There are 16 tables in the school lunch room. Each table can seat 22 students. How many students can be seated at lunch at one time?
_______ students

Answer:
352 students

Explanation:
Total Students = 16 x 22
10 x 22 = 220
6 x 22 = 132
220 + 132 = 352.
352 students can be seated at lunch at one time

Common Core – Page No. 176

Lesson Check

Question 1.
The art teacher has 48 boxes of crayons. There are 64 crayons in each box. Which is the best estimate of the number of crayons the art teacher has?
Options:
a. 2,400
b. 2,800
c. 3,000
d. 3,500

Answer:
c. 3,000

Explanation:
1. Total number of crayons = 48 x 64
48 is close to 50; 64 is close to 60
50 x 60 = 3,000.
The art teacher has about to 3, 000 crayons.

Question 2.
A basketball team scored an average of 52 points in each of 15 games. How many points did the team score in all?
Options:
a. 500
b. 312
c. 780
d. 1,000

Answer:
c. 780

Explanation:
Total Points = 52 x 15
50 x 15 = 750
2 x 15 = 30
750 + 30 = 780.
The basketball team scored 780 points in total.

Spiral Review

Question 3.
One Saturday, an orchard sold 83 bags of apples. There are 27 apples in each bag. Which expression represents the total number of apples sold?
Options:
a. 16 + 6 + 56 + 21
b. 160 + 60 + 56 + 21
c. 160 + 60 + 560 + 21
d. 1,600 + 60 + 560 + 21

Answer:
d. 1,600 + 60 + 560 + 21

Explanation:
Total number of apples sold = 83 x 27
80 x 27 = 2,160
3 x 27 = 81
2,160 + 81 = 2,241.
The total number of apples sold = 2,241.
16 + 6 + 56 + 21 = 99 not equal to 2,241
160 + 60 + 56 + 21 = 297 not equal to 2,241
160 + 60 + 560 + 21 = 801 not equal to 2,241
1,600 + 60 + 560 + 21 = 2,241 equal to 2,241
1,600 + 60 + 560 + 21 = 2,241 is correct.

Question 4.
Hannah has a grid of squares that has 12 rows with 15 squares in each row. She colors 5 rows of 8 squares in the middle of the grid blue. She colors the rest of
the squares red. How many squares does Hannah color red?
Options:
a. 40
b. 140
c. 180
d. 220

Answer:
b. 140

Explanation:
Hannah has a grid of squares that has 12 rows with 15 squares in each row = 12 x 15 = 180.
The grid of squares in blue = 5 x 8 = 40.
The grid of squares in red = 180 – 40 = 140.

Question 5.
Gabriella has 4 times as many erasers a Leona. Leona has 8 erasers. How many erasers does Gabriella have?
Options:
a. 32
b. 24
c. 12
d. 2

Answer:
a. 32

Explanation:
Gabriella have 4 x 8 = 32 erasers.

Question 6.
Phil has 3 times as many rocks as Peter. Together, they have 48 rocks. How many more rocks does Phil have than Peter?
Options:
a. 36
b. 24
c. 16
d. 12

Answer:
b. 24

Explanation:
Phil has 3 times as many rocks as Peter. Together, they have 48 rocks
If Peter has x rocks, Phil has 3x rocks
3x + x = 48.
4x = 48.
x = 48/4 = 12.
Peter has 12 rocks. Phil has 3 x 12 = 36 rocks.
Phil has 36 – 12 = 24 more rocks than Peter.

Page No. 179

Question 1.
Find the product.
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 26
Estimate: ______
Product: _______

Answer:
Estimate: 1,500
Product: 1,566

Explanation:
54 x 29
Estimate: Think 54 is close to 50; 29 is close to 30.
50 x 30 = 1,500
Product:
20 x 5 tens = 100 tens
20 x 4 ones = 80 ones
9 x 5 tens = 45 tens
9 x 4 ones = 36 ones.
Add partial products.
1000 + 80 + 450 + 36 = 1,566.

Estimate. Then choose a method to find the product.

Question 2.
3 6
× 1 4
——-
Estimate: ______
Product: _______

Answer:
Estimate: 400
Product: 504

Explanation:
36 x 14
Estimate: Think 36 is close to 40; 14 is close to 10.
40 x 10 = 400
Product:
10 x 3 tens = 30 tens
10 x 6 ones = 60 ones
4 x 3 tens = 12 tens
4 x 6 ones = 24 ones.
Add partial products.
300 + 60 + 120 + 24 = 504.

Go Math Grade 4 Chapter 3 Answer Key Question 3.
6 3
× 4 2
——-
Estimate: ______
Product: _______

Answer:
Estimate: 2,400
Product: 2646

Explanation:
63 x 42
Estimate: Think 63 is close to 60; 42 is close to 40.
60 x 40 = 2400
Product:
40 x 6 tens = 240 tens
40 x 3 ones = 120 ones
2 x 6 tens = 12 tens
2 x 3 ones = 6 ones.
Add partial products.
2400 + 120 + 120 + 6 = 2646.

Question 4.
8 4
× 5 3
——-
Estimate: ______
Product: _______

Answer:
Estimate: 4,000
Product: 4,452

Explanation:
84 x 53
Estimate: Think 84 is close to 80; 53 is close to 50.
80 x 50 = 4,000
Product:
50 x 8 tens = 400 tens
50 x 4 ones = 200 ones
3 x 8 tens = 24 tens
3 x 4 ones = 12 ones.
Add partial products.
4000 + 200 + 240 + 12 = 4,452.

Question 5.
7 1
× 1 3
——-
Estimate: ______
Product: _______

Answer:
Estimate: 700
Product: 923

Explanation:
71 x 13
Estimate: Think 71 is close to 70; 13 is close to 10.
70 x 10 = 700
Product:
10 x 7 tens = 70 tens
10 x 1 ones = 10 ones
3 x 7 tens = 21 tens
3 x 1 ones = 3 ones.
Add partial products.
700 + 10 + 210 + 3 = 923.

Practice: Copy and Solve Estimate. Find the product.

Question 6.
29 × $82
Estimate: $ _______
Product: $ _______

Answer:
Estimate: $2,400
Product: $2,378

Explanation:
29 x $82
Estimate: Think 29 is close to 30; $82 is close to $80.
30 x $80 = $2,400
Product:
$80 x 2 tens = $160 tens
$80 x 9 ones = $720 ones
$2 x 2 tens = $4 tens
$2 x 9 ones = $18 ones.
Add partial products.
$1600 + $720 + $40 + $18 = $2,378.

Question 7.
57 × 79
Estimate: _______
Product: _______

Answer:
Estimate: 4,800
Product: 4,503

Explanation:
57 x 79
Estimate: Think 57 is close to 60; 79 is close to 80.
60 x 80 = 4,800
Product:
70 x 5 tens = 350 tens
70 x 7 ones = 490 ones
9 x 5 tens = 45 tens
9 x 7 ones = 63 ones.
Add partial products.
3500 + 490 + 450 + 63 = 4,503.

Question 8.
80 × 27
Estimate: _______
Product: _______

Answer:
Estimate: 2,400
Product: 2,160

Explanation:
80 x 27
Estimate: Think 27 is close to 30.
30 x 80 = 2,400
Product:
20 x 8 tens = 160 tens
20 x 0 ones = 0 ones
7 x 8 tens = 56 tens
7 x 0 ones = 0 ones.
Add partial products.
1600 + 0 + 560 + 0 = 2,160.

Question 9.
32 × $75
Estimate: $ _______
Product: $ _______

Answer:
Estimate: $2,100
Product: $2,400

Explanation:
32 × $75
Estimate: Think 32 is close to 30; $75 is close to $70.
30 x $70 = $2,100
Product:
$70 x 3 tens = $210 tens
$70 x 2 ones = $140 ones
$5 x 3 tens = $15 tens
$5 x 2 ones = $10 ones.
Add partial products.
$2100 + $140 + $150 + $10 = $2,400.

Question 10.
55 × 48
Estimate: _______
Product: _______

Answer:
Estimate: 2,750
Product: 2,640

Explanation:
55 × 48
Estimate: Think 48 is close to 50.
55 x 50 = 2,750
Product:
40 x 5 tens = 200 tens
40 x 5 ones = 200 ones
8 x 5 tens = 40 tens
8 x 5 ones = 40 ones.
Add partial products.
2000 + 200 + 400 + 40 = 2,640.

Question 11.
19 × $82
Estimate: $ _______
Product: $ _______

Answer:
Estimate: $1,600
Product: $1,558

Explanation:
19 × $82
Estimate: Think 19 is close to 20; $82 is close to $80.
20 x $80 = $1,600
Product:
$80 x 1 tens = $80 tens
$80 x 9 ones = $720 ones
$2 x 1 tens = $2 tens
$2 x 9 ones = $18 ones.
Add partial products.
$800 + $720 + $20 + $18 = $1,558.

Question 12.
25 × $25
Estimate: $ _______
Product: $ _______

Answer:
Estimate: $625
Product: $625

Explanation:
25 × $25
Estimate:
25 x $25 = $625
Product:
$20 x 2 tens = $40 tens
$20 x 5 ones = $100 ones
$5 x 2 tens = $10 tens
$5 x 5 ones = $25 ones.
Add partial products.
$400 + $100 + $100 + $25 = $625.

Question 13.
41 × 98
Estimate: _______
Product: _______

Answer:
Estimate: 4,000
Product: 4,018

Explanation:
41 × 98
Estimate: Think 41 is close to 40; 98 is close to 100.
40 x 100 = 4,000
Product:
90 x 4 tens = 360 tens
90 x 1 ones = 90 ones
8 x 4 tens = 32 tens
8 x 1 ones = 8 ones.
Add partial products.
3600 + 90 + 320 + 8 = 4,018.

Identify Relationships Algebra Use mental math to find the number.

Question 14.
30 × 14 = 420, so
30 × 15 = ______

Answer:
30 × 15 = 450

Explanation:
30 × 15 = 30 + 420
30 × 15 = 450

Question 15.
25 × 12 = 300, so
25 × ______ = 350

Answer:
25 x 14 = 350

Explanation:
25 × 12 = 300
For every next multiplication, the product value is increased by 25.
25 x 13 = 325.
25 x 14 =350.

Question 16.
The town conservation manager bought 16 maple trees for $26 each. She paid with five $100 bills. How much change will the manager receive? Explain.
$ ______

Answer:
$84

Explanation:
The town conservation manager bought 16 maple trees for $26 each = 16 x $26 = $416.
She paid with five $100 bills = 5 x $100 = $500.
The manager receive = $500 – $416 = $84.

Question 17.
Each of 25 students in Group A read for 45 minutes. Each of 21 students in Group B read for 48 minutes. Which group read for more minutes? Explain.
_________

Answer:
Group A read for more minutes than Group B.

Explanation:
Group A read for 25 x 45 = 1125 minutes.
Group B read for 21 x 48 = 1008 minutes.
Group A read for more minutes than Group B.

Page No. 180

Question 18.
Martin collects stamps. He counted 48 pages in his collector’s album. The first 20 pages each have 35 stamps in 5 rows. The rest of the pages each have 54 stamps. How many stamps does Martin have in his album?
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 27
a. What do you need to know?
Type below:
_________

Answer:
The total stamps in the first 20 pages + The total stamps in the remaining pages.

Question 18.
b. How will you use multiplication to find the number of stamps?
Type below:
_________

Answer:
The first 20 pages each have 35 stamps in 5 rows.
So, 35 x 5 = 175 stamps.

Question 18.
c. Tell why you might use addition and subtraction to help solve the problem.
Type below:
_________

Answer:
As mentioned that the number of stamps available in the first 20 pages and the number of stamps available in the rest of the pages. We need to add all pages to get 48 pages stamps.

Question 18.
d. Show the steps to solve the problem.
Type below:
_________

Answer:
Martin has 48 pages in his collector’s album.
The first 20 pages each have 35 stamps in 5 rows.
So, 35 x 5 = 175 stamps.
The first 20 pages have 175 stamps.
The rest of the pages each have 54 stamps.
So, total stamps = 175 + 54 = 229 stamps.

Question 18.
e. Complete the sentences.
Martin has a total of _____ stamps on the first 20 pages.
There are _____ more pages after the first 20 pages in Martin’s album.
There are _____ stamps on the rest of the pages.
There are _____ stamps in the album.
Type below:
_________

Answer:
Martin has a total of __175___ stamps on the first 20 pages.
There are __24___ more pages after the first 20 pages in Martin’s album.
There are __54___ stamps on the rest of the pages.
There are ___229__ stamps in the album.

Question 19.
Select the expressions that have the same product as 35 × 17. Mark all that apply.
Options:
a. (30 × 10) + (30 × 7) + (5 × 10) + (5 × 7)
b. (30 × 17) + (5 × 17)
c. (35 × 30) + (35 × 5) + (35 × 10) + (35 × 7)
d. (35 × 10) + (35 × 7)
e. (35 × 10) + (30 × 10) + (5 × 10) + (5 × 7)
f. (35 × 30) + (35 × 5)

Answer:
a. (30 × 10) + (30 × 7) + (5 × 10) + (5 × 7)
b. (30 × 17) + (5 × 17)
d. (35 × 10) + (35 × 7)

Explanation:
35 × 17
30 x 10 =300
30 x 7 = 210
5 x 10 = 50
5 x 7 = 35
300 + 210 + 50 + 35 = 595.
a. (30 × 10) + (30 × 7) + (5 × 10) + (5 × 7) = 300 + 210 + 50 + 35 = 595 equal to 595.
b. (30 × 17) + (5 × 17) = 510 + 85 = 595 equal to 595.
c. (35 × 30) + (35 × 5) + (35 × 10) + (35 × 7) = 1050 + 175 + 350 + 245 = 1820 not equal to 595.
d. (35 × 10) + (35 × 7) = 350 + 245 = 595 equal to 595
e. (35 × 10) + (30 × 10) + (5 × 10) + (5 × 7) = 350 + 300 + 50 + 35 = 735 not equal to 595.
f. (35 × 30) + (35 × 5) = 1050 + 175 = 1,225 not equal to 595.

Common Core – Page No. 181

Choose a Multiplication Method

Estimate. Then choose a method to find the product.

Question 1.
Estimate: 1,200
3 1
× 4 3
——-
9 3
+ 1, 2 4 0
————
1, 3 3 3

Answer:
Estimate: 1,200
Product: 1, 3 3 3

Explanation:
Estimate: 1,200
3 1
× 4 3
——-
9 3
+ 1, 2 4 0
————
1, 3 3 3

Question 2.
6 7
× 8 5
——-
Estimate: _____
Product: ______

Answer:
Estimate: 6,300
Product: 5,695

Explanation:
Estimate: 67 is close to 70; 85 is close to 90.
70 x 90 = 6,300.
Product: 67 x 85
80 x 6 tens = 480 tens
80 x 7 ones = 560 ones
5 x 6 tens = 30 tens
5 x 7 ones = 35 ones.
Add partial products.
4800 + 560 + 300 + 35 = 5,695.

Question 3.
6 8
× 3 8
——-
Estimate: _____
Product: ______

Answer:
Estimate: 2,800
Product: 2,584

Explanation:
Estimate: 68 is close to 70; 38 is close to 40.
70 x 40 = 2,800.
Product: 68 x 38
30 x 6 tens = 180 tens
30 x 8 ones = 240 ones
8 x 6 tens = 48 tens
8 x 8 ones = 64 ones.
Add partial products.
1800 + 240 + 480 + 64 = 2,584.

Question 4.
9 5
× 1 7
——-
Estimate: _____
Product: ______

Answer:
Estimate: 1,700
Product: 1,615

Explanation:
Estimate: 95 is close to 100.
100 x 17 = 1,700.
Product: 95 x 17
10 x 9 tens = 90 tens
10 x 5 ones = 50 ones
7 x 9 tens = 63 tens
7 x 5 ones = 35 ones.
Add partial products.
900 + 50 + 630 + 35 = 1,615.

Question 5.
4 9
× 5 4
——-
Estimate: _____
Product: ______

Answer:
Estimate: 2,500
Product: 2,646

Explanation:
Estimate: 49 is close to 50; 54 is close to 50.
50 x 50 = 2,500.
Product: 49 x 54
50 x 4 tens = 200 tens
50 x 9 ones = 450 ones
4 x 4 tens = 16 tens
4 x 9 ones = 36 ones.
Add partial products.
2000 + 450 + 160 + 36 = 2,646.

Go Math Grade 4 Answer Key Chapter 3 Question 6.
9 1
× 2 6
——-
Estimate: _____
Product: ______

Answer:
Estimate: 2,700
Product: 2,366

Explanation:
Estimate: 91 is close to 90; 26 is close to 30.
90 x 30 = 2,700.
Product: 49 x 54
20 x 9 tens = 180 tens
20 x 1 ones = 20 ones
6 x 9 tens = 54 tens
6 x 1 ones = 6 ones.
Add partial products.
1800 + 20 + 540 + 6 = 2,366.

Question 7.
8 2
× 1 9
——-
Estimate: _____
Product: ______

Answer:
Estimate: 1,600
Product: 1,558

Explanation:
Estimate: 82 is close to 80; 19 is close to 20.
80 x 20 = 1,600.
Product: 82 x 19
10 x 8 tens = 80 tens
10 x 2 ones = 20 ones
9 x 8 tens = 72 tens
9 x 2 ones = 18 ones.
Add partial products.
800 + 20 + 720 + 18 = 1,558.

Question 8.
4 6
× 2 7
——-
Estimate: _____
Product: ______

Answer:
Estimate: 1,500
Product: 1,242

Explanation:
Estimate: 46 is close to 50; 27 is close to 30.
50 x 30 = 1,500.
Product: 46 x 27
20 x 4 tens = 80 tens
20 x 6 ones = 120 ones
7 x 4 tens = 28 tens
7 x 6 ones = 42 ones.
Add partial products.
800 + 120 + 280 + 42 = 1,242.

Question 9.
4 1
× 3 3
——-
Estimate: _____
Product: ______

Answer:
Estimate: 1,200
Product: 1,353

Explanation:
Estimate: 41 is close to 40; 33 is close to 30.
40 x 30 = 1,200.
Product: 41 x 33
30 x 4 tens = 120 tens
30 x 1 ones = 30 ones
3 x 4 tens = 12 tens
3 x 1 ones = 3 ones.
Add partial products.
1200 + 30 + 120 + 3 = 1,353.

Question 10.
9 7
× 1 3
——-
Estimate: _____
Product: ______

Answer:
Estimate: 1,300
Product: 1,261

Explanation:
Estimate: 97 is close to 100.
100 x 13 = 1,300.
Product: 97 x 13
10 x 9 tens = 90 tens
10 x 7 ones = 70 ones
3 x 9 tens = 27 tens
3 x 7 ones = 21 ones.
Add partial products.
900 + 70 + 270 + 21 = 1,261.

Question 11.
7 5
× 6 9
——-
Estimate: _____
Product: ______

Answer:
Estimate: 5,600
Product: 5,195

Explanation:
Estimate: 75 is close to 80; 69 is close to 70.
80 x 70 = 5,600.
Product: 75 x 69
60 x 7 tens = 420 tens
60 x 5 ones = 300 ones
9 x 7 tens = 63 tens
9 x 5 ones = 45 ones.
Add partial products.
4200 + 300 + 630 + 45 = 5,195.

Problem Solving

Question 12.
A movie theatre has 26 rows of seats. There are 18 seats in each row. How many seats are there in all?
______ seats

Answer:
468 seats

Explanation:
26 x 18 = 468 seats.
20 x 18 = 360
6 x 18 = 108
108+360 = 468.

Question 13.
Each class at Briarwood Elementary collected at least 54 cans of food during the food drive. If there are 29 classes in the school, what was the least number of
cans collected?
______ cans

Answer:
1,566 cans

Explanation:
Each class at Briarwood Elementary collected at least 54 cans of food.
If there are 29 classes in the school,
the least number of cans collected = 54 x 29 = 1,566 cans.

Common Core – Page No. 182

Lesson Check

Question 1.
A choir needs new robes for each of its 46 singers. Each robe costs $32. What will be the total cost for all 46 robes?
Options:
a. $1,472
b. $1,372
c. $1,362
d. $230

Answer:
a. $1,472

Explanation:
46 x $32
40 x $32 = $1,280
6 x $32 = $192
$1,280 + $192 = $1,472

Question 2.
A wall on the side of a building is made up of 52 rows of bricks with 44 bricks in each row. How many bricks make up the wall?
Options:
a. 3,080
b. 2,288
c. 488
d. 416

Answer:
b. 2,288

Explanation:
52 x 44
50 x 44 = 2,200
2 x 44 = 88
2,200 + 88 = 2,288.
2,288 bricks make up the wall.

Spiral Review

Question 3.
Which expression shows how to multiply 4 × 362 by using place value and expanded form?
Options:
a. (4 × 3) + (4 × 6) + (4 × 2)
b. (4 × 300) + (4 × 600) +(4 × 200)
c. (4 × 300) + (4 × 60) + (4 × 20)
d. (4 × 300) + (4 × 60) + (4 × 2)

Answer:
d. (4 × 300) + (4 × 60) + (4 × 2)

Explanation:
4 × 362 = 1,448
a. (4 × 3) + (4 × 6) + (4 × 2) = 12 + 24 + 8 = 44 not equal to 1,448.
b. (4 × 300) + (4 × 600) +(4 × 200) = 1200 + 2400 + 800 = 4,400 not equal to 1,448.
c. (4 × 300) + (4 × 60) + (4 × 20) = 1200 + 240 + 80 = 1,520 not equal to 1,448.
d. (4 × 300) + (4 × 60) + (4 × 2) = 1200 + 240 + 8 = 1,448 equal to 1,448.

Question 4.
Use the model below. What is the product 4 x 492?
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers Common Core img 28
Options:
a. 16 + 36 + 8 = 60
b. 160 + 36 + 8 = 204
c. 160 + 360 + 8 = 528
d. 1,600 + 360 + 8 = 1,968

Answer:
d. 1,600 + 360 + 8 = 1,968

Explanation:
Grade 4 Chapter 3 Common Core 182
1,600 + 360 + 8 = 1,968

Question 5.
What is the sum 13,094 + 259,728?
Options:
a. 272,832
b. 272,822
c. 262,722
d. 262,712

Answer:
c. 262,722

Explanation:
13,094 + 259,728 = 262,722

Question 6.
During the 2008–2009 season, there were 801,372 people who attended the home hockey games in Philadelphia. There were 609,907 people who attended the home hockey games in Phoenix. How much greater was the home attendance in Philadelphia than in Phoenix that season?
Options:
a. 101,475
b. 191,465
c. 201,465
d. 202,465

Answer:
b. 191,465

Explanation:
801,372 – 609,907 = 191,465
Philadelphia attendance is 191,465 greater than in Phoenix that season.

Page No. 185

Question 1.
An average of 74 reports with bird counts were turned in each day in June. An average of 89 were turned in each day in July. How many reports were turned in for both months? (Hint: There are 30 days in June and 31 days in July.)
First, write the problem for June.
Type below:
__________

Answer:
Given that An average of 74 reports with bird counts was turned in each day in June.
For June Month, there are 30 days = 30 x 74 = 2,220.

Question 1.
Next, write the problem for July.
Type below:
__________

Answer:
An average of 89 reports with bird counts was turned in each day in July.
For July Month, there are 31 days = 31 x 89 = 2,759.

Question 1.
Last, find and add the two products.
____________ reports were turned in for both months.
Type below:
__________

Answer:
Given that An average of 74 reports with bird counts was turned in each day in June.
For June Month, there are 30 days = 30 x 74 = 2,220.
An average of 89 reports with bird counts was turned in each day in July.
For July Month, there are 31 days = 31 x 89 = 2,759.
Add two products to get the total number of reports that were turned in for both months.
2,220 + 2,759 = 4,979.

Question 2.
What if an average of 98 reports were turned in each day for the month of June? How many reports were turned in for June? Describe how your answer for June would be different.
______ reports

Answer:
720 more reports

Explanation:
Given that an average of 98 reports was turned in each day for the month of June.
June has 30 days.
Total number of reports were turned in for June = 30 x 98 = 2, 940.
From the above answer, 98 − 74 = 24. So, there would be 30 × 24, or 720 more reports.

Question 3.
There are 48 crayons in a box. There are 12 boxes in a carton. Mr. Johnson ordered 6 cartons of crayons for the school. How many crayons did he get?
______ crayons

Answer:
3,456 crayons

Explanation:
There are 48 crayons in a box.
There are 12 boxes in a carton.
So, 1 carton = 48 x 12 = 576 crayons.
If Mr. Johnson ordered 6 cartons of crayons for the school, 6 x 576 crayons = 3,456 crayons.
He gets 3,456 crayons.

Question 4.
Make Sense of Problems Each of 5 birdwatchers reported seeing 15 roseate spoonbills in a day. If they each reported seeing the same number of roseate spoonbills over 14 days, how many would be reported?
______ roseate spoonbills

Answer:
1,050 roseate spoonbills

Explanation:
Given that, 1 day –>5 birdwatchers reported 15 roseate spoonbills = 5 x 15 = 75 roseate spoonbills.
So, in 14 days –> 5 birdwatchers reported 75 x 14 = 1,050 roseate spoonbills.

Page No. 186

Question 5.
On each of Maggie’s bird-watching trips, she has seen at least 24 birds. If she has taken 4 of these trips each year over the past 16 years, at least how many birds has Maggie seen?
at least ______ birds

Answer:
Maggie seen 1,536 birds

Explanation:
Given that, 1 trip –> Maggie seen 24 birds.
For 1 year she goes for 4 bird-watching trips.
So, she has seen 4 x 24 = 96 birds for 1 year.
For 16 years, 16 x 96 = 1,536 birds have Maggie seen.

Question 6.
Make Sense of Problems There are 12 inches in a foot. In September, Mrs. Harris orders 32 feet of ribbon for the Crafts Club. In January, she orders 9 feet less. How many inches of ribbon does Mrs. Harris order? Explain how you found your answer.
______ inches

Answer:
660 inches

Explanation:
There are 12 inches in a foot.
In September, Mrs. Harris orders 32 feet of ribbon for the Crafts Club = 32 x 12 = 384.
In January, she orders 9 feet less = 32 – 9 = 23.
So, in January, she orders 23 x 12 = 276.
Mrs. Harris order 276 + 384 = 660 inches of ribbon in total.
(or)
9 less than 32 is 23, so I added 23 + 32 = 55.
Then, I multiplied 55 × 12 = 660.

Question 7.
Lydia is having a party on Saturday. She decides to write a riddle on her invitations to describe her house number on Cypress Street. Use the clues to find Lydia’s address.
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 29
______ Cypress Street

Answer:
14827 Cypress Street

Explanation:
Given that tens digit is 5 less than 7 = 7 – 5 = 2. 2 is the tens digit.
The thousands digit is twice the digit in the tens place = 2 x 2 = 4.
The hundreds digit is the greatest even number that is less than 10 i.e, 8.
The ones digit is the product of 7 and 1 = 7 x 1 = 7.
The ten thousands digit is the difference between the hundreds digit and the ones digit. So, 8 – 7 = 1.
Add the products to get the final answer = 14827.
Lydia’s address ( house number ) is 14827 Cypress Street.

Question 8.
A school is adding 4 rows of seats to the auditorium. There are 7 seats in each row. Each new seat costs $99. What is the total cost for the new seats? Show your work.
$ ______

Answer:
$2,772

Explanation:
Given that A school is adding 4 rows of seats to the auditorium. There are 7 seats in each row.
So, 7 x 4 = 28 seats are available in an auditorium.
Each new seat costs $99.
28 x $99 = $2,772 for total cost of the new seats.

Common Core – Page No. 187

Problem Solving Multiply 2 – Digit numbers

Solve each problem. Use a bar model to help.

Question 1.
Mason counted an average of 18 birds at his bird feeder each day for 20 days. Gloria counted an average of 21 birds at her bird feeder each day for 16 days. How many more birds did Mason count at his feeder than Gloria counted at hers?
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers Common Core img 30
Birds counted by Mason: 18 × 20 = 360
Birds counted by Gloria: 21 × 16 = 336
Draw a bar model to compare.
Subtract. 360 – 336 = 24
So, Mason counted 24 more birds.

Answer:
Birds counted by Mason: 18 × 20 = 360
Birds counted by Gloria: 21 × 16 = 336
Draw a bar model to compare.
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers Common Core img 30
Subtract. 360 – 336 = 24
So, Mason counted 24 more birds.

Question 2.
The 24 students in Ms. Lee’s class each collected an average of 18 cans for recycling. The 21 students in Mr. Galvez’s class each collected an average of 25 cans for recycling. How many more cans were collected by Mr. Galvez’s class than Ms. Lee’s class?
______ more cans

Answer:
The number of cans collected by Ms. Lee’s class = 18 x 24 = 432.
The number of cans collected by Mr. Galvez’s class = 25 x 21 = 525.
Use Bar Model
Grade 4 Chapter 3 Common Core 187
Subtract. 525 – 432 = 93 more cans.
So, Mr. Galvez’s class collected 93 more cans than Ms. Lee’s class.

Question 3.
At East School, each of the 45 classrooms has an average of 22 students. At West School, each of the 42 classrooms has an average of 23 students. How many more students are at East School than at West School?
______ more students

Answer:
Students in East school = 45 x 22 = 990.
Students in West School = 42 x 23 = 966.
Use Bar Model
Grade 4 Chapter 3 Common Core image 2 187
Subtract. 990 – 966 = 24.
So, East School has 24 students more than West School.

Question 4.
A zoo gift shop orders 18 boxes of 75 key rings each and 15 boxes of 80 refrigerator magnets each. How many more key rings than refrigerator magnets does the gift shop order?
______ more key rings

Answer:
Number of Key Rings = 75 x 18 = 1,350.
Number of Refrigerator Magnets= 80 x 15 = 1,200.
Use Bar Model
Grade 4 Chapter 3 Common Core image 3 187
Subtract. 1,350 – 1,200 = 150.
So, key rings are 150 more than refrigerator magnets.

Common Core – Page No. 188

Lesson Check

Question 1.
Ace Manufacturing ordered 17 boxes with 85 ball bearings each. They also ordered 15 boxes with 90 springs each. How many more ball bearings than springs did they order?
Options:
a. 5
b. 85
c. 90
d. 95

Answer:
d. 95

Explanation:
Number of ball bearings = 85 x 17 = 1,445.
Number of springs = 90 x 15 = 1,350.
Use Bar Model
Grade 4 Chapter 3 Common Core image 1 188
Subtract. 1,445 – 1,350 = 95.
So, ball bearings are 95 more than springs.

Question 2.
Elton hiked 16 miles each day on a 12-day hiking trip. Lola hiked 14 miles each day on her 16-day hiking trip. In all, how many more miles did Lola hike than Elton hiked?
Options:
a. 2 miles
b. 18 miles
c. 32 miles
d. 118 miles

Answer:
c. 32 miles

Explanation:
Hiking trip by Elton = 12 x 16 = 192.
Hiking trip by Lola = 16 x 14 = 224.
Use Bar Model
Grade 4 Chapter 3 Common Core image 2 188
Subtract. 224 – 192 = 32.
So, the Hiking trip by Lola is 32 times more than the Hiking trip by Elton.

Spiral Review

Question 3.
An orchard has 24 rows of apple trees. There are 35 apple trees in each row. How many apple trees are in the orchard?
Options:
a. 59
b. 192
c. 740
d. 840

Answer:
d. 840

Explanation:
An orchard has 24 rows of apple trees. There are 35 apple trees in each row.
24 x 35 = 840 apple trees are in the orchard.

Question 4.
An amusement park reported 354,605 visitors last summer. What is this number rounded to the nearest thousand?
Options:
a. 354,600
b. 355,000
c. 360,000
d. 400,000

Answer:
b. 355,000

Explanation:
An amusement park reported 354,605 visitors last summer. 4,605 is close to 5,000. So, the answer is 355,000.

Question 5.
Attendance at the football game was 102,653. What is the value of the digit 6?
Options:
a. 6
b. 60
c. 600
d. 6,000

Answer:
c. 600

Explanation:
Digit 6 is at hundreds of positions. So, the answer is 6 x 100 = 600.

Question 6.
Jill’s fish weighs 8 times as much as her parakeet. Together, the pets weigh 63 ounces. How much does the fish weigh?
Options:
a. 7 ounces
b. 49 ounces
c. 55 ounces
d. 56 ounces

Answer:
d. 56 ounces

Explanation:
Let Jill’s parakeet = X.
Jill’s fish weighs 8 times as much as her parakeet = 8X.
Together, the pets weigh 63 ounces.
X + 8X = 63.
9X = 63.
X = 63/9 = 7.
So, Jill’s parakeet =7.
Jill’s fish = 7 x 8 = 56 ounces.

Review/Test – Page No. 189

Question 1.
Explain how to find 40 × 50 using mental math
Type below:
_________

Answer:
200

Explanation:
40 x 50
By using mental math
4 x 5 = 20
40 x 50 = 200

Mrs. Traynor’s class is taking a field trip to the zoo. The trip will cost $26 for each student. There are 22 students in her class.

Question 2.
Part A
Round each factor to estimate the total cost of the students’ field trip.
$ ______

Answer:
$600

Explanation:
Total cost of the students’ field trip = 22 x $26.
22 x $26
20 x $30 = $600
The total cost would be about $600.

Question 2.
Part B
Use compatible numbers to estimate the total cost of the field trip.
$ ______

Answer:
$500

Explanation:
If we use compatible numbers to estimate the total cost of the field trip.
22 x $26
20 × 25 = 500
The total cost would be about $500.

Question 2.
Part C
Which do you think is the better estimate? Explain.
Better estimate: _________

Answer:
Using rounded numbers is a better estimate. When rounded numbers are used, one estimated factor was $4 more than the actual factor and the other estimated factor was $2 that is less than the actual factor. So, the estimate should be close to the actual one. When compatible numbers are used both estimated factors were less than the actual factors. So, the product will be an underestimate.

Review/Test – Page No. 190

For numbers 3a–3e, select Yes or No to show if the answer is correct.

Question 3.
3a. 35 × 10 = 350
i. yes
ii. no

Answer:
i. yes

Explanation:
35 x 10 = 350
30 x 10 = 300.
5 x 10 = 50.
300 + 50 = 350.

Question 3.
3b. 19 × 20 = 380
i. yes
ii. no

Answer:
i. yes

Explanation:
19 × 20 = 380
19 x 20 = 19 x 2 tens.
19 x 20 = 38 tens = 380.

Question 3.
3c. 12 × 100 = 120
i. yes
ii. no

Answer:
ii. no

Explanation:
12 x 100 = 120.
10 x 100 = 1000
2 x 100 = 200.
1000 + 200 = 1200.

Question 3.
3d. 70 × 100 = 7,000
i. yes
ii. no

Answer:
i. yes

Explanation:
70 x 100 = 7,000
100 x 7 tens = 700 tens = 7,000

Question 3.
3e. 28 × 30 = 2,100
i. yes
ii. no

Answer:
ii. no

Explanation:
28 × 30
20 x 30 = 600
8 x 30 = 240
600 + 240 = 840

Question 4.
There are 23 boxes of pencils in Mr. Shaw’s supply cabinet. Each box contains 100 pencils. How many pencils are in the supply cabinet?
_____ penciles

Answer:
2,300 pencils

Explanation:
23 x 100 = 2,300 pencils are in the supply cabinet.

Question 5.
Which would provide a reasonable estimate for each product? Write the estimate beside the product. An estimate may be used more than once
23 × 38 __________
31 × 32 __________
46 × 18 __________
39 × 21 __________

Answer:
23 × 38 –> 25 x 40
31 x 32 –> 30 × 30
46 × 18 –> 50 × 20
39 × 21 –> 25 × 40

Explanation:
23 × 38; 23 is close to 25; 38 is close to 40.
So, the estimated product is 25 x 40
31 x 32; 31 is close to 30; 32is close to 30.
So, the estimated product is 30 × 30
46 × 18; 46 is close to 50; 18 is close to 20.
So, the estimated product is 50 × 20
39 × 21; 39 is close to 40; 21 is close to 25.
So, the estimated product is 25 × 40

Question 6.
There are 26 baseball teams in the league. Each team has 18 players. Write a number sentence that will provide a reasonable estimate for the number of players in the league. Explain how you found your estimate.
Type below:
__________

Answer:
There are 26 baseball teams in the league. Each team has 18 players.
26 x 18
25 x 20
We Rounded each factor to its close factor, then simplified the multiplication.

Question 7.
The model shows 48 × 37. Write the partial products.
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers Review/Test img 31
Type below:
__________

Answer:
Grade 4 Chapter 3 Common Core image 1 190
Partial Products are 1200, 240, 280, 56

Review/Test – Page No. 191

Question 8.
Jess made this model to find the product 32 × 17. Her modelis incorrect.
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers Review/Test img 32
Part A
What did Jess do wrong?
Type below:
__________

Answer:
Jess added the numbers in the model instead of multiplying.

Question 8.
Part B
Redraw the model so that it is correct.
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers Review/Test img 33
Type below:
__________

Answer:
Grade 4 Chapter 3 Common Core image 2 190

Question 8.
Part C
What is the actual product 32 × 17?
______

Answer:
544

Explanation:
32 × 17
10 x 32 = 320
7 x 32 = 224
320 + 224 = 544.

Question 9.
Tatum wants to use partial products to find 15 × 32. Write the numbers in the boxes to show 15 × 32.
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers Review/Test img 34
Type below:
__________

Answer:
Grade 4 Chapter 3 Common Core image 4 190

Review/Test – Page No. 192

Question 10.
Which product is shown by the model? Write the letter of the product on the line below the model.
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers Review/Test img 35
Type below:
__________

Answer:
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers Review/Test img 35
C                                              A                                                  B
10 + 3 = 13
10 + 3 = 13
13 x 13
2. 10 + 7 = 17
30 + 6 = 36
17 x 36
3. 20 + 4 = 24
10 + 4 = 14
24 x 14

Question 11.
Mrs. Jones places 3 orders for school T-shirts. Each order has 16 boxes of shirts and each box holds 17 shirts. How many T-shirts does Mrs. Jones order? Use partial products to help you.
Type below:
__________

Answer:
816 T-shirts

Explanation:
Mrs. Jones places 3 orders for school T-shirts. Each order has 16 boxes of shirts and each box holds 17 shirts.
Each box has 17 shirts.
16 boxes = 16 x 17 = 272.
Each order = 16 boxes = 272 shirts.
3 orders = 3 x 272 = 816 shirts.
Mrs. Jones order 816 T-shirts.

Question 12.
Write the unknown digits. Use each digit exactly once.
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers Review/Test img 36
Type below:
__________

Answer:
Grade 4 Chapter 3 Common Core image 1 192
90 x 40 = 3,600
90 x 6 = 540
3 x 40 = 120
3 x 6 = 18.
3,600 + 540 + 120 + 8 = 4,278.

Question 13.
Mike has 16 baseball cards. Niko has 17 times as many baseball cards as Mike does. How many baseball cards does Niko have?
________ baseball cards

Answer:
272 baseball cards

Explanation:
Mike has 16 baseball cards. Niko has 17 times as many baseball cards as Mike does.
Niko have 16 x 17 = 272 baseball cards.

Question 14.
Multiply.
36 × 28 = ________

Answer:
1,008

Explanation:
36 x 28
20 x 30 = 600
20 x 6 = 120
8 x 30 = 240
8 x 6 = 48
600 + 120 + 240 + 48 = 1,008

Review/Test – Page No. 193

Question 15.
A farmer planted 42 rows of tomatoes with 13 plants in each row. How many tomato plants did the farmer grow?
42 × 13 = ______ tomato plants

Answer:
420 + 126 = 546 tomato plants

Explanation:
42 × 13
10 x 42 = 420
3 x 42 = 126
420 + 126 = 546 tomato plants

Question 16.
Select another way to show 25 × 18. Mark all that apply.
Options:
a. (20 × 10) + (20 × 8) + (5 × 10) + (5 × 8)
b. (25 × 20) + (25 × 5) + (25 × 10) + (25 × 8)
c. (20 × 18) + (5 × 10) + (5 × 8)
d. (25 × 10) + (25 × 8)
e. (25 × 20) + (25 × 5)

Answer:
a. (20 × 10) + (20 × 8) + (5 × 10) + (5 × 8)
c. (20 × 18) + (5 × 10) + (5 × 8)
d. (25 × 10) + (25 × 8)

Explanation:
25 × 18
10 x 25 = 250
8 x 25 = 200
250 + 200 = 450.
a. (20 × 10) + (20 × 8) + (5 × 10) + (5 × 8) = 200 + 160 + 50 + 40 = 450
b. (25 × 20) + (25 × 5) + (25 × 10) + (25 × 8) = 500 + 125 + 250 + 200 = 1,075
c. (20 × 18) + (5 × 10) + (5 × 8) = 360 + 50 + 40 = 450
d. (25 × 10) + (25 × 8) = 250 + 200 = 450
e. (25 × 20) + (25 × 5) = 500 + 125 = 625

Question 17.
Terrell runs 15 sprints. Each sprint is 65 meters. How many meters does Terrell run? Show your work.
______ meters

Answer:
975 meters

Explanation:
Terrell run 15 x 65 = 975 meters.

Question 18.
There are 3 new seats in each row in a school auditorium. There are 15 rows in the auditorium. Each new seat cost $74. What is the cost for the new seats? Explain how you found your answer.
$ ______

Answer:
$3,330

Explanation:
Given that There are 3 new seats in each row in a school auditorium. There are 15 rows in the auditorium. Each new seat cost $74.
So, 3 x 15 = 45 seats are available in an auditorium.
Each new seat costs $74.
45 x $74 = $3,330 for total cost of the new seats.

Question 19.
Ray and Ella helped move their school library to a new building. Ray packed 27 boxes with 25 books in each box. Ella packed 23 boxes with 30 books in each box. How many more books did Ella pack? Show your work.
______ books

Answer:
15 books

Explanation:
Ray packed 27 x 25 = 675 books.
Ella packed 23 x 30 = 690 books
Ella packed 690 – 675 = 15 books more than Ray.

Review/Test – Page No. 194

Question 20.
Julius and Walt are finding the product of 25 and 16.
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers Review/Test img 37
Part A
Julius’ answer is incorrect. What did Julius do wrong?
Type below:
__________

Answer:
Julius multiplied 25 by 10 and then multiplied 25 by 6 correctly. He added the two partial products incorrectly.

Question 20.
Part B
What did Walt do wrong?
Type below:
__________

Answer:
Walt multiplied 6 by 5 and got 300 instead of 30

Question 20.
Part C
What is the correct product?
Type below:
__________

Answer:
25 x 16 = 400

Question 21.
A clothing store sells 26 shirts and 22 pairs of jeans. Each item of clothing costs $32.
Part A
What is a reasonable estimate for the total cost of the clothing?
Show or explain how you found your answer.
$ ______

Answer:
$1500

Explanation:
A clothing store sells 26 shirts and 22 pairs of jeans. 26 + 22 = 48 clothes.
Each item of clothing costs $32.
48 x $32
50 x $30 = $1500

Question 21.
Part B
What is the exact answer for the total cost of the clothing? Show or explain how you found your answer.
$ ______

Answer:
$1,536

Explanation:
48 x $32
40 x $32 = $1,280
8 x $32 = $256
$1,280 + $256 = $1,536

Page No. 199

Question 1.
A restaurant has 68 chairs. There are six chairs at each table. About how many tables are in the restaurant?
Estimate. 68 ÷ 6
Think: What number times 6 is about 68?
10 × 6 = ___
11 × 6 = ___
12 × 6 = ___
68 is closest to ______, so the best estimate is about _______ tables are in the restaurant.
Type below:
__________

Answer:
68 is close to 70 and 6 is close to 5.
So, 70/5 = 12.
10 × 6 = __60_
11 × 6 = _66__
12 × 6 = _72__
68 is closest to ___66___, so the best estimate is about 11 x 6 = 66 tables are in the restaurant.

Find two numbers the quotient is between. Then estimate the quotient.

Question 2.
41 ÷ 3
between _______ and _______

Answer:
between 13 and 14
about 14

Explanation:
13 x 3 = 39; 14 x 3 = 42.
The quotient of 41 ÷ 3 is between 13 and 14.

Question 3.
192 ÷ 5
between _______ and _______

Answer:
between 30 and 40
about 40

Explanation:
30 x 5 = 150; 40 x 5 = 200.
The quotient of 192 ÷ 5 is between 30 and 40.

Find two numbers the quotient is between. Then estimate the quotient.

Question 4.
90 ÷ 7
between _______ and _______

Answer:
between 12 and 13
about 13

Explanation:
12 x 7 = 84; 13 x 7 = 91.
The quotient of 90 ÷ 7 is between 12 and 13.

Question 5.
67 ÷ 4
between _______ and _______

Answer:
between 16 and 17
about 17

Explanation:
16 x 4 = 64; 17 x 4 = 68.
The quotient of 67 ÷ 4 is between 16 and 17.

Question 6.
281 ÷ 9
between _______ and _______

Answer:
between 30 and 40
about 30

Explanation:
30 x 9 = 270; 40 x 9 = 360.
The quotient of 281 ÷ 9 is between 30 and 40.

Question 7.
102 ÷ 7
between _______ and _______

Answer:
between 14 and 15
about 15

Explanation:
14 x 7 = 98; 15 x 7 = 105.
The quotient of 102 ÷ 7 is between 14 and 15.

Question 8.
85 ÷ 6
between _______ and _______

Answer:
between 14 and 15
about 14

Explanation:
14 x 6 = 84; 15 x 6 = 90.
The quotient of 85 ÷ 6 is between 14 and 15.

Question 9.
220 ÷ 8
between _______ and _______

Answer:
between 20 and 30
about 30

Explanation:
20 x 8 = 160; 30 x 8 = 240.
The quotient of 220 ÷ 8 is between 20 and 30.

Decide whether the actual quotient is greater than or less than the estimate given. Write < or >.

Question 10.
83 ÷ 8 _______ 10

Answer:
>

Explanation:
83 ÷ 8 = 10.375 > 10

Question 11.
155 ÷ 4 _______ 40

Answer:
<

Explanation:
155 ÷ 4 = 38.75 < 40

Question 12.
70 ÷ 6 _______ 11

Answer:
>

Explanation:
70 ÷ 6 = 11.666 > 11

Question 13.
What’s the Question? A dolphin’s heart beats 688 times in 6 minutes. Answer: about 100 times.
Type below:
__________

Answer:
About how many times does a dolphin’s heart beats in 1 minute?

Question 14.
Analyze A mother bottlenose ate about 278 pounds of food in one week. About how much food did she eat in a day?
about _____ pounds

Answer:
about 40 pounds

Explanation:
278 ÷ 7
The quotient of 278 ÷ 7 is between 39 and 40.

Question 15.
Tanya has $42 to spend at the Dolphin Island store. T-shirts sell for $7 each and a pair of sunglasses sells for $6. Tanya buys 3 T-shirts. How many pairs of sunglasses can she buy with the amount of money she has left?
_____ pairs of sunglasses

Answer:
3 pairs of sunglasses

Explanation:
Given that Tanya has $42 to spend at the Dolphin Island store. T-shirts sell for $7 each and a pair of sunglasses sell for $6.
Tanya buys 3 T-shirts = 3 x $7 = $21.
pair of sunglasses = $42 – $21 = $21.
1 pair of sunglasses sells for $6.
So, $21 ÷ $7 = 3.
3 pairs of sunglasses can Tanya buy with the amount of money she has left.

Page No. 200

Question 16.
If a bottlenose dolphin can eat 175 pounds of fish, squid, and shrimp in a week, about how many pounds of food does it eat in a day? Milo says the answer is about 20 pounds. Leah says the answer is about 30 pounds. Who is correct? Explain.
Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers img 38
________

Answer:
The bottlenose dolphin can eat 25 pounds for 1 day.
Both answers are correct. Because the 25 pounds is in between 20 and 30 pounds.

Explanation:
1 week = 7 days.
The bottlenose dolphin can eat 175 pounds for 7 days.
For 1 day = 175 ÷ 7 = 25 pounds.
The bottlenose dolphin can eat 25 pounds for 1 day.
Both answers are correct. Because the 25 pounds is in between 20 and 30 pounds.

Question 17.
Four families went out for lunch. The total food bill came to $167. The families also left a $30 tip for the waitress. If each family spent the same amount, about how much did each family spend on dinner? Explain how you found your answer.
$ ______

Answer:
$98.5

Explanation:
Four families went out for lunch. The total food bill came to $167. The families also left a $30 tip for the waitress.
So, total amount = $167 + $30 = $197.
If each family spent the same amount = $197 ÷ 2 = $98.5
Each family spent $98.5.

Question 18.
There are 6 showings of a film about Van Gogh at the Art Museum. A total of 459 people saw the film. The same number of people were at each showing. About how many people were at each showing? Circle the numbers the quotient is between. Then explain how you found your answer.
40 50 60 70 80
Type below:
_________

Answer:
40 50 60 70 80
I found multiples of 6 that 459 is between. 70 × 6 = 420 and 80 × 6 = 480. Since 459 is closer to 480, 459 ÷ 6 is about 80.

Conclusion

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Go Math Grade 5 Chapter 3 Answer Key Pdf Add and Subtract Decimals

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Add and Subtract Decimals Go Math Grade 5 Chapter 3 Answer Key Pdf

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Lesson 1: Investigate • Thousandths

Lesson 2: Place Value of Decimals

Lesson 3: Compare and Order Decimals

Lesson 4: Round Decimals

Lesson 5: Investigate • Decimal Addition

Lesson 6: Investigate • Decimal Subtraction

Mid-Chapter Checkpoint

Lesson 7: Estimate Decimal Sums and Differences

Lesson 8: Add Decimals

Lesson 9: Subtract Decimals

Lesson 10: Algebra • Patterns with Decimals

Lesson 11: Problem Solving • Add and Subtract Money

Lesson 12: Choose a Method

Review/Test

Share and Show – Page No. 111

Write the decimal shown by the shaded parts of each model.

Question 1.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 1
______

Answer:
0.665

Explanation:
The given picture shows
6 hundredths, 6 tenths, and 5 thousandths are shaded
665/1000 = 0.665

Question 2.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 2
______

Answer:
0.398

Explanation:
The given picture shows
3 hundredths, 9 tenths, and 8 thousandths are shaded
398/1000 = 0.398

Go Math Grade 5 Chapter 3 Answer Key Pdf Question 3.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 3
______

Answer:
0.181

Explanation:
The given picture shows
1 hundredth, 8 tenths, and 1 thousandth are shaded
181/1000 = 0.181

Question 4.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 4
______

Answer:
0.990

Explanation:
The given picture shows
9 hundredth, 9 tenths, and 0 thousandths are shaded
990/1000 = 0.990

Complete the sentence.

Question 5.
0.6 is 10 times as much as ______ .
______

Answer:
\(\frac{6}{100}\) = 0.06

Explanation:
Let the unknown number is S
0.6 = 10S
S = 0.6/10 = \(\frac{6}{10}\) x \(\frac{1}{10}\)
S = \(\frac{6}{100}\) = 0.06

Question 6.
0.007 is \(\frac{1}{10}\) of _______ .
______

Answer:
0.07

Explanation:
Let the unknown number is S
0.007 = \(\frac{1}{10}\)S
S = 0.007 x 10 = 0.07

Question 7.
0.008 is \(\frac{1}{10}\) of ________ .
______

Answer:
0.08

Explanation:
Let the unknown number is S
0.008 = \(\frac{1}{10}\)S
S = 0.008 x 10 = 0.08

Go Math Grade 5 Chapter 3 Pdf Question 8.
0.5 is 10 times as much as ______.
______

Answer:
0.05

Explanation:
Let the unknown number is S
0.5 = 10S
S = 0.5/10 = \(\frac{5}{10}\) x \(\frac{1}{10}\)
S = \(\frac{5}{100}\) = 0.05

Use place-value patterns to complete the table.

Question 9.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 5
Type below:
_________

Answer:
grade 5 chapter 3 Add and Subtract Decimals image 1

Explanation:
0.2 is 10 times as much as
Let the unknown number is S
0.2 = 10S
S = 0.2/10 = 0.02
0.2 is 1/10 of
0.2 = S/10
S = 0.2 x 10 = 2
0.07 is 10 times as much as
Let the unknown number be S
0.07 = 10S
S = 0.07/10 = 0.007
0.07 is 1/10 of
0.07 = S/10
S = 0.07 x 10 = 0.7
0.05 is 10 times as much as
Let the unknown number be S
0.05 = 10S
S = 0.05/10 = 0.005
0.05 is 1/10 of
0.05 = S/10
S = 0.05 x 10 = 0.5
0.4 is 10 times as much as
Let the unknown number be S
0.4 = 10S
S = 0.4/10 = 0.04
0.4 is 1/10 of
0.4 = S/10
S = 0.4 x 10 = 4

Question 10.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 6
Type below:
_________

Answer:
grade 5 chapter 3 Add and Subtract Decimals image 2

Explanation:
0.06 is 10 times as much as
Let the unknown number is S
0.06 = 10S
S = 0.06/10 = 0.006
0.06 is 1/10 of
0.06 = S/10
S = 0.06 x 10 = 0.6
0.9 is 10 times as much as
Let the unknown number is S
0.9 = 10S
S = 0.9/10 = 0.09
0.9 is 1/10 of
0.9 = S/10
S = 0.9 x 10 = 9
0.3 is 10 times as much as
Let the unknown number is S
0.3 = 10S
S = 0.3/10 = 0.03
0.3 is 1/10 of
0.3 = S/10
S = 0.3 x 10 = 3
0.08 is 10 times as much as
Let the unknown number is S
0.08 = 10S
S = 0.08/10 = 0.006
0.08 is 1/10 of
0.08 = S/10
S = 0.08 x 10 = 0.8

Problem Solving Applications – Page No. 112

Use the table for 17 and 20.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 7

Question 17.
A science teacher showed an image of a carpenter bee on a wall. The image is 10 times as large as the actual bee. Then he showed another image of the bee that is 10 times as large as the first image. What is the length of the bee in the second image?
______ meters

Answer:
2.5 meters

Explanation:
A science teacher showed an image of a carpenter bee on a wall. The image is 10 times as large as the actual bee.
carpenter bee = 0.025
The first image = 0.025 x 10 = 0.25
The second image = 10 times as large as the first image = 0.25 x 10 = 2.5

Go Math Grade 5 Chapter 3 Answer Key Question 18.
Math Explain how you can use place value to describe how 0.05 and 0.005 compare.
Type below:
_________

Answer:
Both numbers have 0 ones. So, we cannot compare these two numbers.
Look at the tenths. Both numbers have 0 tenths. So, we cannot compare these numbers.
Look at the hundredths.
The first number has 5 hundredths. The second number has 0 hundredths.
So, 0.05 > 0.005

Question 19.
Use Repeated Reasoning Terry, Sasha, and Harry each chose a number. Terry’s number is ten times as much as Sasha’s. Harry’s number is \(\frac{1}{10}\) of Sasha’s. Sasha’s number is 0.4. What number did each person choose?
Terry’s number: ______
Harry’s number: ______

Answer:
Terry’s number: 4
Harry’s number: 0.04

Explanation:
Sasha’s number is 0.4
Terry’s number is ten times as much as Sasha’s.
Terry’s number = 10 x 0.4 = 10 x \(\frac{4}{10}\) = 4
Harry’s number is \(\frac{1}{10}\) of Sasha’s.
Harry’s number = \(\frac{1}{10}\) x 0.4 = \(\frac{1}{10}\) x \(\frac{4}{10}\) = \(\frac{4}{100}\) = 0.04
Sasha’s number is 0.4
Terry’s number is 4
Harry’s number is 0.04

Question 20.
An atlas beetle is about 0.14 of a meter long. How does the length of the atlas beetle compare to the length of a leafcutting bee?
Type below:
_________

Answer:
An atlas beetle is about 0.14 of a meter long.
length of a leafcutting bee = 0.014
1 tenth is greater than 0 tenths.
So, 0.14 > 0.014
So, atlas beetle length is greater than the length of a leafcutting bee

Question 21.
Choose the numbers that make the statement true.
0.65 is 10 times as much as Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 8 and \(\frac{1}{10}\) of Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 9
Type below:
_________

Answer:
0.65 is 10 times as much as 0.065
0.65 is \(\frac{1}{10}\) of 6.5

Explanation:
0.65 is 10 times as much as
0.65 = 10S
S = 0.65/10 = 0.065
0.65 is \(\frac{1}{10}\) of
0.65 x 10 = 6.5
So, 0.65 is 10 times as much as 0.065
0.65 is \(\frac{1}{10}\) of 6.5

Share and Show – Page No. 115

Question 1.
Complete the place-value chart to find the value of each digit.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 10
Type below:
_________

Answer:
grade 5 chapter 3 Add and Subtract Decimals 115image 1

Explanation:
3 x 1 = 3
5 Tenths = 5 x 1/10 = 0.5
2 hundredths = 2 x 1/100 = 0.02
3 thousandths = 3 x 1/1000 = 0.003

Write the value of the underlined digit.

Question 2.
0.543
Type below:
_________

Answer:
0.04

Explanation:
(0 x 1) + (5 x \(\frac{1}{10}\)) + (4 x \(\frac{1}{100}\)) + (3 x \(\frac{1}{1000}\))
4 x \(\frac{1}{100}\) = 4 hundredths = 0.04

Question 3.
6.234
Type below:
_________

Answer:
0.2

Explanation:
(6 x 1) + (2 x \(\frac{1}{10}\)) + (3 x \(\frac{1}{100}\)) + (4 x \(\frac{1}{1000}\))
2 x \(\frac{1}{10}\) = 2 tenths = 0.2

Go Math Grade 5 Chapter 3 Review Test Question 4.
3.954
Type below:
_________

Answer:
0.004

Explanation:
(3 x 1) + (9 x \(\frac{1}{10}\)) + (5 x \(\frac{1}{100}\)) + (4 x \(\frac{1}{1000}\))
4 x \(\frac{1}{1000}\) = 4 thousandths = 0.004

Write the number in two other forms.

Question 5.
0.253
Type below:
_________

Answer:
Word Form: two hundred fifty-three thousandths
Expanded Form: (0 x 1) + (2 x \(\frac{1}{10}\)) + (5 x \(\frac{1}{100}\)) + (3 x \(\frac{1}{1000}\))

Question 6.
7.632
Type below:
_________

Answer:
Word Form: seven and six hundred thirty-two thousandths
Expanded Form: (7 x 1) + (6 x \(\frac{1}{10}\)) + (3 x \(\frac{1}{100}\)) + (2 x \(\frac{1}{1000}\))

On Your Own

Write the value of the underlined digit.

Question 7.
0.496
Type below:
_________

Answer:
0.09

Explanation:
(0 x 1) + (4 x \(\frac{1}{10}\)) + (9 x \(\frac{1}{100}\)) + (6 x \(\frac{1}{1000}\))
9 x \(\frac{1}{100}\) = 9 hundredths = 0.09

Question 8.
2.726
Type below:
_________

Answer:
0.7

Explanation:
(2 x 1) + (7 x \(\frac{1}{10}\)) + (2 x \(\frac{1}{100}\)) + (6 x \(\frac{1}{1000}\))
7 x \(\frac{1}{10}\) = 0.7

Question 9.
1.066
Type below:
_________

Answer:
0.006

Explanation:
(1 x 1) + (0 x \(\frac{1}{10}\)) + (6 x \(\frac{1}{100}\)) + (6 x \(\frac{1}{1000}\))
6 x \(\frac{1}{1000}\) = 0.006

Go Math Grade 5 Chapter 3 Mid Chapter Checkpoint Answer Key Question 10.
6.399
Type below:
_________

Answer:
0.3

Explanation:
(6 x 1) + (3 x \(\frac{1}{10}\)) + (9 x \(\frac{1}{100}\)) + (9 x \(\frac{1}{1000}\))
3 x \(\frac{1}{10}\) = 0.3

Question 11.
0.002
Type below:
_________

Answer:
0.002

Explanation:
(0 x 1) + (0 x \(\frac{1}{10}\)) + (0 x \(\frac{1}{100}\)) + (2 x \(\frac{1}{1000}\))
2 x \(\frac{1}{1000}\) = 0.002

Question 12.
4.371
Type below:
_________

Answer:
0.001

Explanation:
(4 x 1) + (3 x \(\frac{1}{10}\)) + (7 x \(\frac{1}{100}\)) + (1 x \(\frac{1}{1000}\))
1 x \(\frac{1}{1000}\) = 0.001

Write the number in two other forms.

Question 13.
0.489
Type below:
_________

Answer:
Word Form: four hundred eighty-nine thousandths
Expanded Form: (0 x 1) + (4 x \(\frac{1}{10}\)) + (8 x \(\frac{1}{100}\)) + (9 x \(\frac{1}{1000}\))

5th Grade Go Math Chapter 3 Review Test Question 14.
5.916
Type below:
_________

Answer:
Word Form: five and nine hundred sixteen thousandths
Expanded Form: (5 x 1) + (9 x \(\frac{1}{10}\)) + (1 x \(\frac{1}{100}\)) + (6 x \(\frac{1}{1000}\))

Problem Solving Applications – Page No. 116

Use the table for 15–16.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 11

Question 15.
What is the value of the digit 7 in New Mexico’s average annual rainfall?
Type below:
_________

Answer:
0.07

Explanation:
New Mexico’s average annual rainfall = 0.372
(0 x 1) + (3 x \(\frac{1}{10}\)) + (7 x \(\frac{1}{100}\)) + (2 x \(\frac{1}{1000}\))
7 x \(\frac{1}{100}\) = 0.07

Question 16.
Which of the states has an average annual rainfall with the least number in the thousandths place? What is another way to write the total annual rainfall in this state?
_________

Answer:
Wisconsin
(0 x 1) + (8 x \(\frac{1}{10}\)) + (2 x \(\frac{1}{100}\)) + (0 x \(\frac{1}{1000}\))

Explanation:
California = 0.564
New Mexico = 0.372
New York = 1.041
Wisconsin = 0.820
Maine = 1.074
The state that has an average annual rainfall with the least number in the thousandths place
0 < 1 < 2 < 4. So, the state is Wisconsin.
Another way to write the total annual rainfall in Wisconsin state is (0 x 1) + (8 x \(\frac{1}{10}\)) + (2 x \(\frac{1}{100}\)) + (0 x \(\frac{1}{1000}\))

Question 17.
Verify the Reasoning of Others Damian wrote the number four and twenty-three thousandths as 4.23. Describe and correct his error.
Type below:
_________

Answer:
four and twenty-three thousandths = 4 ones and 0 tenths, 2 hundredths, three thousandths = 4.023.
He has written 4.23 which is wrong.

Go Math 5th Grade Chapter 3 Add and Subtract Decimals Question 18.
Dan used a meter stick to measure some seedlings in his garden. One day, a corn stalk was 0.85 m tall. A tomato plant was 0.850 m. A carrot top was 0.085 m. Which plant was the shortest?
_________

Answer:
the carrot top is the shortest plant

Explanation:
Dan used a meter stick to measure some seedlings in his garden. One day, a corn stalk was 0.85 m tall. A tomato plant was 0.850 m. A carrot top was 0.085 m. 0 tenths are less than the 8 tenths. So, 0.085 is less than 0.85 or 0.850. So, the carrot top is the shortest plant.

Question 19.
Math Explain how you know that the digit 6 does not have the same value in the numbers 3.675 and 3.756.
Type below:
_________

Answer:
In 3.675, the digit of 6 is in the tenths place. So, its value is 6 x 1/10 or 0.6.
In 3.756, the digit of 6 is in the thousandths place, so its value is 6 x 1/1000 or 0.006.

Question 20.
What is the value of the underlined digit? Mark all that apply.
0.589
Options:
a. 0.8
b. 0.08
c. eight tenths
d. eight hundredths
e. 8 × (\(\frac{1}{10}\))

Answer:
b. 0.08
d. eight hundredths

Explanation:
(0 x 1) + (5 x \(\frac{1}{10}\)) + (8 x \(\frac{1}{100}\)) + (9 x \(\frac{1}{1000}\))
8 x \(\frac{1}{100}\) = 8 hundredths = 0.08

Share and Show – Page No. 119

Question 1.
Use the place-value chart to compare the two numbers. What is the greatest place-value position where the digits differ?
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 12
Type below:
_________

Answer:
3.472 > 3.445
They differ in hundredths position

Explanation:
Compare the ones; 3 = 3
Compare the tenths; 4 = 4
Compare the hundredths; 7 > 4
So, 3.472 > 3.445

Compare. Write <, >, or =.

Question 2.
4.563 ______ 4.536

Answer:
4.563 > 4.536

Explanation:
Compare the ones; 4 = 4
Compare the tenths; 5 = 5
Compare the hundredths; 6 > 3
So, 4.563 > 4.536

Go Math Grade 5 Chapter 3 Review/Test Answer Key Pdf Question 3.
5.640 ______ 5.64

Answer:
5.640 = 5.64

Explanation:
Compare the ones; 5 = 5
Compare the tenths; 6 = 6
Compare the hundredths; 4 = 4
Compare the thousandths; 0 = 0
So, 5.640 = 5.64

Question 4.
8.673 ______ 8.637

Answer:
8.673 > 8.637

Explanation:
Compare the ones; 8 = 8
Compare the tenths; 6 = 6
Compare the hundredths; 7 > 3
So, 8.673 > 8.637

Name the greatest place-value position where the digits differ.

Name the greater number.

Question 5.
3.579; 3.564
______

Answer:
3.579 > 3.564
The greatest place-value position where the digits differ are hundredths

Explanation:
Compare the ones; 3 = 3
Compare the tenths; 5 = 5
Compare the hundredths; 7 > 6
So, 3.579 > 3.564
The greatest place-value position where the digits differ are hundredths

Question 6.
9.572; 9.637
______

Answer:
9.572 < 9.637
The greatest place-value position where the digits differ are tenths

Explanation:
Compare the ones; 9 = 9
Compare the tenths; 5 < 6
So, 9.572 < 9.637
The greatest place-value position where the digits differ are tenths

Question 7.
4.159; 4.152
______

Answer:
4.159 > 4.152
The greatest place-value position where the digits differ are thousandths

Explanation:
Compare the ones; 4 = 4
Compare the tenths; 1 = 1
Compare the hundredths; 5 = 5
Compare the thousandths; 9 > 2
So, 4.159 > 4.152
The greatest place-value position where the digits differ are thousandths

Order from least to greatest.

Question 8.
4.08; 4.3; 4.803; 4.038

Answer:
4.038, 4.08, 4.3, 4.803

Explanation:
Compare the ones; All are equal
Compare the tenths; 0 < 3 < 8.
So, 4.08, 4.038, 4.3, 4.803
Compare the hundredths of 4.08 and 4.038; 8 > 3
So, 4.038, 4.08, 4.3, 4.803

Go Math Grade 5 Chapter 3 Test Question 9.
1.703; 1.037; 1.37; 1.073

Answer:
1.037, 1.073, 1.37, 1.703

Explanation:
Compare the ones; All are equal
Compare the tenths; 0 < 3 < 7.
So, 1.037; 1.073; 1.37; 1.703
Compare the hundredths of 1.037 and 1.073; 3 < 7
So, 1.037, 1.073, 1.37, 1.703

On Your Own

Compare. Write <, >, or =.

Question 10.
8.72 ______ 8.720

Answer:
8.72 = 8.720

Explanation:
Compare the ones; 8 = 8
Compare the tenths; 7 = 7
Compare the hundredths; 2 = 2
Compare the thousands; 0 = 0
So, 8.72 = 8.720

Question 11.
5.4 ______ 5.243

Answer:
5.4 > 5.243

Explanation:
Compare the ones; 5 = 5
Compare the tenths; 4 > 2
So, 5.4 > 5.243

Question 12.
1.036 ______ 1.306

Answer:
1.036 < 1.306

Explanation:
Compare the ones; 1 = 1
Compare the tenths; 0 < 3
So, 1.036 < 1.306

Question 13.
2.573 ______ 2.753

Answer:
2.573 < 2.753

Explanation:
Compare the ones; 2 = 2
Compare the tenths; 5 < 7
So, 2.573 < 2.753

Question 14.
9.300 ______ 9.3

Answer:
9.300 = 9.3

Explanation:
Compare the ones; 9 = 9
Compare the tenths; 3 = 3
Compare the hundredths; 0 = 0
Compare the thousands; 0 = 0
So, 9.300 = 9.3

Go Math Pdf Grade 5 Chapter 3 Lesson 3.3 Answer Key Question 15.
6.76 ______ 6.759

Answer:
6.76 > 6.759

Explanation:
Compare the ones; 6 = 6
Compare the tenths; 7 = 7
Compare the hundredths; 6 > 5
So, 6.76 > 6.759

Order from greatest to least.

Question 16.
2.007; 2.714; 2.09; 2.97
______ ; ______ ; ______ ; ______

Answer:
2.97; 2.714; 2.09; 2.007

Explanation:
Compare the ones; All are equal
Compare the tenths; 0 < 7 < 9.
So, 2.007; 2.09; 2.714; 2.97
Compare the hundredths of 2.007 and 2.09; 0 < 9
So, 2.007; 2.09; 2.714; 2.97
Order from greatest to least = 2.97; 2.714; 2.09; 2.007

Question 17.
0.386; 0.3; 0.683; 0.836
______ ; ______ ; ______ ; ______

Answer:
0.836; 0.683; 0.386; 0.3

Explanation:
Compare the ones; All are equal
Compare the tenths; 0 < 3 < 6 < 8.
So, 0.386; 0.3; 0.683; 0.836
Compare the hundredths of 0.386 and 0.3; 8 > 0
So, 0.3; 0.386; 0.683; 0.836
Order from greatest to least = 0.836; 0.683; 0.386; 0.3

Question 18.
5.249; 5.43; 5.340; 5.209
______ ; ______ ; ______ ; ______

Answer:
5.43; 5.340; 5.249; 5.209

Explanation:
Compare the ones; All are equal
Compare the tenths; 2 < 3 < 4.
So, 5.249; 5.209; 5.340; 5.43
Compare the hundredths of 5.249 and 5.209; 4 > 0
So, 5.209; 5.249; 5.340; 5.43
Order from greatest to least = 5.43; 5.340; 5.249; 5.209

Question 19.
0.678; 1.678; 0.587; 0.687
______ ; ______ ; ______ ; ______

Answer:
1.678; 0.687; 0.678; 0.587

Explanation:
Compare the ones; 0 < 1
So, 0.678; 0.587; 0.687; 1.678
Compare the tenths of 0.678; 0.587; 0.687; 5 < 6.
So, 0.587; 0.678; 0.687; 1.678
Compare the hundredths of 0.678 and 0.687; 7 < 8
So, 0.587; 0.678; 0.687; 1.678
Order from greatest to least = 1.678; 0.687; 0.678; 0.587

Use Reasoning Algebra Find the unknown digit to make each statement true.

Question 20.
3.59 > 3.5 ______ 1 > 3.572

Answer:
3.59 > 3.581 > 3.572

Explanation:
The possible values are
3.573; 3.574; 3.575; 3.578; 3.579; 3.580; 3.581; 3.582; 3.583; 3.584; 3.585; 3.586; 3.587; 3.588; 3.589;
The digit that ends with 1 is 3.581.
So, the unknown digit is 3.581

Go Math Grade 5 Answer Key Chapter 3 Compare and Order Decimals Lesson 3.3 Question 21.
6.837 > 6.83 ______ > 6.835

Answer:
6.837 > 6.836 > 6.835

Explanation:
The value must be 6.836. Because 6 is the only digit between 5 and 7.
So, the unknown digit is 6.836

Question 22.
2.45 < 2 ______ 6 < 2.461

Answer:
2.45 < 2.456 < 2.461

Explanation:
2.451; 2.452; 2.453; 2.454; 2.455; 2.456; 2.457; 2.458; 2.459; 2.460; 2.461
The digit that ends with 6 is 2.456.
So, the unknown digit is 2.456

Problem Solving Applications – Page No. 120

Use the table for 23–26.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 13

Question 23.
In comparing the height of the mountains, which is the greatest place value where the digits differ?
_________

Answer:
The greatest place value where the digits differ is hundredths

Explanation:
3.104; 3.134; 3.152
0 hundredths < 3 hundredths < 5 hundredths
3.152; Mount Steele, Yukon is the greatest mountain.
The greatest place value where the digits differ is hundredths.

Question 24.
Use Math Vocabulary How does the height of Mount Steele compare to the height of Mount Blackburn? Compare the heights using words.
Type below:
_________

Answer:
The Height of Mount Steele is greater than Height of Mount Blackburn.

Explanation:
Height of Mount Steele = 3.152
Height of Mount Blackburn = 3.104
3.152 > 3.104
The Height of Mount Steele is greater than the Height of Mount Blackburn.

Lesson 3 Add and Subtract Whole Numbers Answer Key Question 25.
Explain how to order the heights of the mountains from greatest to least.
Type below:
_________

Answer:
3.152 > 3.134 > 3.104

Explanation:
3.104; 3.134; 3.152
0 hundredths < 3 hundredths < 5 hundredths
3.152 > 3.134 > 3.104

Question 26.
What if the height of Mount Blackburn were 0.05 miles greater? Would it then be the mountain with the greatest height? Explain.
______

Answer:
Height of Mount Blackburn = 3.104 + 0.05 = 3.154
3.154 > 3.152 > 3.134.
Yes, Mount Blackburn would have the greatest height if it had been 0.05 miles greater.

Question 27.
Orlando kept a record of the total rainfall each month for 5 months.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 14
Order the months from the least amount of rainfall to the greatest amount of rainfall.
Least ______ ______ ______ ______ ______ Greatest

Answer:
Least: 3.09; 3.75; 4.04; 4.09; 4.42 Greatest

Explanation:
3.75; 4.42; 4.09; 3.09; 4.04
3 < 4
3.75; 3.09; 4.42; 4.09; 4.04
Compare tenths of 3.75 and 3.09; 0 < 7
3.09; 3.75; 4.42; 4.09; 4.04
Compare tenths of 4.42; 4.09; 4.04; 0 <4
3.09; 3.75; 4.09; 4.04; 4.42
Compare hundredths of 4.09 and 4.04; 4 < 9
So, 3.09; 3.75; 4.04; 4.09; 4.42

Share and Show – Page No. 123

Write the place value of the underlined digit. Round each number to the place of the underlined digit.

Question 1.
0.673
Place value: ________
Round: ________

Answer:
Place value: 7 hundredths = 0.07
Round: 0.670

Explanation:
0.673
(0 x 1) + (6 x \(\frac{1}{10}\)) + (7 x \(\frac{1}{100}\)) + (3 x \(\frac{1}{1000}\))
Place Value: 7 x \(\frac{1}{100}\) = 7 hundredths = 0.07
0.673
3 < 5
0.670

Question 2.
4.282
Place value: ________
Round: ________

Answer:
Place value: 2 tenths = 0.2
Round: 4.300

Explanation:
4.282
(4 x 1) + (2 x \(\frac{1}{10}\)) + (8 x \(\frac{1}{100}\)) + (2 x \(\frac{1}{1000}\))
Place Value: 2 x \(\frac{1}{10}\) = 2 tenths = 0.2
4.282
8 > 5
4.300

Go Math Grade 5 Chapter 3 Lesson 3.4 Answer Key Question 3.
12.917
Place value: ________
Round: ________

Answer:
Place value: 2 ones = 2
Round: 13

Explanation:
12.917
(1 x 10) + (2 x 1) + (9 x \(\frac{1}{10}\)) + (1 x \(\frac{1}{100}\)) + (7 x \(\frac{1}{1000}\))
Place Value: 2 x 1 = 2 ones = 2
12.917
9 > 5
13

Name the place value to which each number was rounded.

Question 4.
0.982 to 0.98
________

Answer:
The hundredths

Explanation:
As 2 < 5, We round 0.982 to 0.98.
The place value of the digit 8 is hundredths.
The hundredths

Question 5.
3.695 to 4
________

Answer:
The ones

Explanation:
As 6 > 5, We round 3.695 to 4.
The place value of the digit 3 is ones.
The ones

Question 6.
7.486 to 7.5
________

Answer:
The tenths

Explanation:
As 8 > 5, We round 7.486 to 7.5.
The place value of the digit 4 is tenths.
The tenths

On Your Own

Write the place value of the underlined digit. Round each number to the place of the underlined digit.

Question 7.
0.592
Place value: ________
Round: ________

Answer:
Place value: 5 tenths = 0.5
Round: 0.6

Explanation:
0.592
(0 x 1) + (5 x \(\frac{1}{10}\)) + (9 x \(\frac{1}{100}\)) + (2 x \(\frac{1}{1000}\))
Place Value: 5 x \(\frac{1}{10}\) = 5 tenths = 0.5
0.592
9 > 5
0.6

Go Math Grade 5 Lesson 3.4 Answer Key Question 8.
6.518
Place value: ________
Round: ________

Answer:
Place value: 6 ones = 6
Round: 7

Explanation:
6.518
(6 x 1) + (5 x \(\frac{1}{10}\)) + (1 x \(\frac{1}{100}\)) + (8 x \(\frac{1}{1000}\))
Place Value: 6 x 1 = 6 ones = 6
6.518
5 = 5
7

Question 9.
0.809
Place value: ________
Round: ________

Answer:
Place value: 0 hundredths = 0
Round: 0.8

Explanation:
0.809
(0 x 1) + (8 x \(\frac{1}{10}\)) + (0 x \(\frac{1}{100}\)) + (9 x \(\frac{1}{1000}\))
Place Value: 0 x \(\frac{1}{100}\) = 0 hundredths = 0
0.809
0 < 5
0.800

Question 10.
3.334
Place value: ________
Round: ________

Answer:
Place value: 7 tenths = 0.7
Round: 3

Explanation:
3.334
(3 x 1) + (3 x \(\frac{1}{10}\)) + (3 x \(\frac{1}{100}\)) + (4 x \(\frac{1}{1000}\))
Place Value: 3 x \(\frac{1}{10}\) = 7 tenths = 0.7
3.334
3 < 5
3.000

Question 11.
12.074
Place value: ________
Round: ________

Answer:
Place value: 0 tenths = 0
Round: 12.1

Explanation:
12.074
(1 x 10) + (2 x 1) + (0 x \(\frac{1}{10}\)) + (7 x \(\frac{1}{100}\)) + (4 x \(\frac{1}{1000}\))
Place Value: 0 x \(\frac{1}{10}\) = 0 tenths = 0
12.074
7 > 5
12.1

Question 12.
4.494
Place value: ________
Round: ________

Answer:
Place value: 9 hundredths = 0.09
Round: 4.49

Explanation:
4.494
(4 x 1) + (4 x \(\frac{1}{10}\)) + (9 x \(\frac{1}{100}\)) + (4 x \(\frac{1}{1000}\))
Place Value: 9 x \(\frac{1}{100}\) = 9 hundredths = 0.09
4.494
4 < 5
4.49

Name the place value to which each number was rounded.

Question 13.
0.328 to 0.33
________

Answer:
The hundredths

Explanation:
As 8 > 5, We round 0.328 to 0.33.
The place value of the digit 2 is hundredths.
The hundredths

Question 14.
2.607 to 2.61
________

Answer:
The hundredths

Explanation:
As 7 > 5, We round 2.607 to 2.61.
The place value of the digit 0 is hundredths.
The hundredths

Question 15.
12.583 to 13
________

Answer:
The ones

Explanation:
As 5 = 5, We round 12.583 to 13.
The place value of the digit 2 is one.
The ones

Round 16.748 to the place named.

Question 16.
tenths: ______

Answer:
16.7

Explanation:
Round 16.748 to the nearest tenths
The tenth digit is 7. So, 4 < 5
16.7

Question 17.
hundredths: ______

Answer:
16.75

Explanation:
Round 16.748 to the nearest hundredths
The hundredth digit is 4. So, 8 > 5
16.75

Question 18.
ones: ______

Answer:
17

Explanation:
Round 16.748 to the nearest ones
The ones digit is 6. So, 7 > 5
17

Question 19.
Explain what happens when you round 4.999 to the nearest tenth.
Type below:
_________

Answer:
5

Explanation:
round 4.999 to the nearest tenth
The tenth digit is 9. So, 9 > 5
5

Problem Solving Applications – Page No. 124

Use the table for 20–22.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 15

Question 20.
The speeds of two insects when rounded to the nearest whole number are the same. Which two insects are they?
_________
_________

Answer:
Bumblebee
Honeybee

Explanation:
Dragonfly = 6.974 meters; nearest whole number = 7
Horsefly = 3.934 meters; nearest whole number = 4
Bumblebee = 2.861 meters; nearest whole number = 3
Honeybee = 2.548 meters; nearest whole number = 3
Housefly = 1.967 meters; nearest whole number = 2
Bumblebee and Honeybee speeds are the same if their rounded to the nearest whole number.

Question 21.
What is the speed of the housefly rounded to the nearest hundredth?
______ meters per second

Answer:
3.93 meters per second

Explanation:
Horsefly = 3.934 meters rounded to the nearest hundredth
The hundredth digit is 3. So, 4 < 5
3.93

Question 22.
What’s the Error? Mark said that the speed of a dragonfly rounded to the nearest tenth was 6.9 meters per second. Is he correct? If not, what is his error?
Type below:
_________

Answer:
Dragonfly = 6.974 meters rounded to the nearest tenth.
The tenth digit is 9. So, 7 > 5
7.
So, Mark said is wrong.

Question 23.
A rounded number for the speed of an insect is 5.67 meters per second. What are the fastest and slowest speeds to the thousandths that could round to 5.67 meters per second? Explain.
Type below:
_________

Answer:
The slowest speed to the thousandths that could round to 5.67 meters per second is 5.671
The fastest speed to the thousandths that could round to 5.67 meters per second is 5.674

Explanation:
To find the slowest speed to the thousandths that could round to 5.67 meters per second we need to find the lowest digit which will not affect the digit in the hundredths place, and that is 1. So, the slowest speed to the thousandths that could round to 5.67 meters per second is 5.671.
To find the fastest speed to the thousandths that could round to 5.67 meters per second we need to find the greatest digit which will not affect the digit in the hundredths place, and that is 4. So, the fastest speed to the thousandths that could round to 5.67 meters per second is 5.674.

Question 24.
The price of a certain box of cereal at the grocery store is $0.258 per ounce. For numbers 24a–24c, select True or False for each statement.
a. Rounded to the nearest whole number, the price is $1 per ounce.
i. yes
ii. no

Answer:
ii. no

Explanation:
$0.258
2 < 5.
So, if we rounded to the nearest whole number, the value becomes 0.

Question 24.
b. Rounded to the nearest tenth, the price is $0.3 per ounce.
i. yes
ii. no

Answer:
i. yes

Explanation:
$0.258
5 = 5
So, $3 is the answer.

Question 24.
c. Rounded to the nearest hundredth, the price is $0.26 per ounce.
i. yes
ii. no

Answer:
i. yes

Explanation:
$0.258
8 > 5
$0.26

Share and Show – Page No. 127

Complete the quick picture

Question 1.
1.37 + 1.85 =
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 16
______

Answer:
grade 5 chapter 3 Add and Subtract Decimals 127 image 1

Explanation:
1.37 + 1.85 = 3. 22
Add hundredths; 7 + 5 = 12; Regroup
Add tenths; 3 + 8 + 1 = 12; Regroup
Add tens; 1 + 1 + 1 = 3

Add. Draw a quick picture.

Question 2.
0.9 + 0.7 =
______

Answer:
0.9 + 0.7 = 1.6
grade 5 chapter 3 Add and Subtract Decimals 127 image 2

Explanation:
0.9 + 0.7 =
Add tenths 9 + 7 = 16; Regroup
Add ones 0 + 0 + 1 = 1
0.9 + 0.7 = 1.6

Go Math Chapter 3 Test Grade 5 Lesson 3.5 Thousandths Question 3.
0.65 + 0.73 =
______

Answer:
0.65 + 0.73 = 1.38
grade 5 chapter 3 Add and Subtract Decimals 127 image 3

Explanation:
0.65 + 0.73 = 1.38
Add hundredths 5 + 3 = 8;
Add tenths 6 + 7 = 13; Regroup
Add ones 0 + 0 + 1 = 1
0.65 + 0.73 = 1.38

Question 4.
1.3 + 0.7 =
______

Answer:
1.3 + 0.7 = = 2
grade 5 chapter 3 Add and Subtract Decimals 127 image 4

Explanation:
Add tenths 3 + 7 = 10; Regroup
Add ones 1 + 1 = 2
1.3 + 0.7 = = 2

Question 5.
2.72 + 0.51 =
______

Answer:
2.72 + 0.51 = 3.23
grade 5 chapter 3 Add and Subtract Decimals 127 image 5

Explanation:
Add hundredths 2 + 1 = 3
Add tenths 5 + 7 = 12; Regroup
Add ones 2 + 0 + 1 = 3
2.72 + 0.51 = 3.23

Problem Solving Applications

Question 6.
Carissa bought 2.35 pounds of chicken and 2.7 pounds of turkey for lunch this week. She used a quick picture to and the amount of lunch meat. Does Carissa’s work make sense? Explain.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 17
______

Answer:
Yes; Because she bought 2.35 pounds of chicken and 2.7 pounds
2.35 + 2.7 = 5.05 pounds.
there is 5 ones and 5 hundredths.

Sense or Nonsense? – Page No. 128

Question 7.
Robyn and Jim used quick pictures to model 1.85 + 2.73.
Robyn’s Work
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 18
1.85 + 2.73 = 3.158
Does Robyn’s work make sense?
Explain your reasoning.
Type below:
_________

Answer:
Robyn’s work doesn’t make sense. Because 7 + 8 = 15. So, he needs to regroup and then add 1 to the one’s digits.
1 + 2 + 1 = 4
1.85 + 2.73 = 4.58 is the correct answer.

Jim’s Work
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 19
1.85 + 2.73 = 4.58
Does Jim’s work make sense?
Explain your reasoning.

Answer:
Jim’s work makes sense.
Add: 1.85 + 2.73 = 4.58.
4 ones, 5 tenths, and 8 hundredths.

Go Math Book 5th Grade Lesson 3.5 Answer Key Question 8.
Make Arguments Explain how you would help Robyn understand that regrouping is important when adding decimals.
Type below:
_________

Answer:
Regrouping is important when adding decimals. When you add two digits, if their addition is more than 10 then we need to regroup the values to find the correct answer.

Question 9.
Write a decimal addition problem that requires regrouping the hundredths. Explain how you know you will need to regroup.
Type below:
_________

Answer:
Let’s add 1.47 and 1.35 As we have more than 9 hundredths we have to regroup and mid the tenths.
So, now we have 8 tenths and two-hundredths left.
Also, as we have less than 9 tenths we do not have to regroup and add the ones.
The answer is 2.82.
As we have more than 9 hundredths we have to regroup and mid the tenths.

Share and Show – Page No. 131

Complete the quick picture to find the difference.

Question 1.
0.62 − 0.18 =
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 20
______

Answer:
grade 5 chapter 3 Add and Subtract Decimals 131 image 1

Explanation:
0.62 − 0.18
Subtract hundredths:  2 – 8;
There are not enough hundredths. So, regroup
12 – 8 = 4
Subtract tenths: 5 – 1 = 4
Subtract ones: 0 – 0 = 0
So, 0.62 − 0.18 = 0.44

Subtract. Draw a quick picture.

Question 2.
3.41 − 1.74 =
______

Answer:
grade 5 chapter 3 Add and Subtract Decimals 131 image 2

Explanation:
3.41 − 1.74
Subtract hundredths:  1 – 4;
There are not enough hundredths. So, regroup
11 – 4 = 7
Subtract tenths: 3 – 7
There are not enough tenths. So, regroup
13 – 7 = 6
Subtract ones: 2 – 1 = 1
So, 3.41 − 1.74 = 1.67

Question 3.
0.84 − 0.57 =
______

Answer:
grade 5 chapter 3 Add and Subtract Decimals 131 image 3

Explanation:
0.84 − 0.57
Subtract hundredths:  4 – 7;
There are not enough hundredths. So, regroup
14 – 7 = 7
Subtract tenths: 7 – 5 = 2
Subtract ones: 0 – 0 = 0
So, 0.84 − 0.57 = 0.27

Go Math Grade 5 Chapter 3 Lesson 3.6 Answer Key Question 4.
4.05 − 1.61 =
______

Answer:
grade 5 chapter 3 Add and Subtract Decimals 131 image 4

Explanation:
4.05 − 1.61
Subtract hundredths:  5 – 1 = 4;
Subtract tenths: 0 – 6
There are not enough hundredths. So, regroup
10 – 6 = 4
Subtract ones: 3 – 1 = 2
So, 4.05 − 1.61 = 2.44

Problem Solving Applications

Question 6.
Write a decimal subtraction equation that requires regrouping from the tenths. Explain how you know you will need to regroup.
Type below:
__________

Answer:
Subtract 0.32 and 0.05
Subtract hundredths. As there are not enough hundredths we have to regroup. So, we have 10 more hundredths and one-tenth I.
Subtract tenths. As there are enough tenths we do not have to regroup.
The answer: 0.27

Pose a Problem – Page No. 132

Question 7.
Antonio left his MathBoard on his desk during lunch. The quick picture below shows the problem he was working on when he left.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 21
Write a word problem that can be solved using the quick picture above.
Pose a problem.          Solve your problem.
Type below:
__________

Answer:
From the given picture, he has drawn eight-hundredths and crosses two-hundredths. Then, he has drawn six tenths and crossed four-tenths. When comes to ones. he has taken three ones and crossed two out of them.
there are 7 – 2 = 5 hundredths
6 – 4 = 2 tenths
3 – 2 = 1 ones
1.25

Question 7.
Use Reasoning Describe how you can change the problem by changing the quick picture.
Type below:
__________

Answer:
By changing the quick picture, the value of place value is changed.

Question 8.
The price of a box of markers at a retail store is $4.65. he price of a box of markers at the school bookstore is $3.90. How much more do the markers cost at the retail store? Explain how you can use a quick picture to solve the problem.
$ ______

Answer:
The price of a box of markers at a retail store is $4.65. he price of a box of markers at the school bookstore is $3.90.
$4.65 – $3.90 = $0.75
grade 5 chapter 3 Add and Subtract Decimals 131 image 5

Concepts and Skills – Page No. 133

Question 1.
Explain how you can use base-ten blocks to find 1.54 + 2.37.
Type below:
__________

Answer:
1.54 + 2.37
Add hundredths 4 + 7 = 11; Regroup
Add tenths 5 + 3 + 1 = 9;
Add ones 2 + 1 = 3
1.54 + 2.37 = 3.91
We have to use three square boxes to show three ones, 9 lines to show 9 tenths, and 1 dot to show one hundredth

Complete the sentence.

Question 2.
0.04 is \(\frac{1}{10}\) of

Answer:
0.04 is \(\frac{1}{10}\) of 0.4

Explanation:
Let the unknown number is S
0.04 = \(\frac{1}{10}\)S
S = 0.04 x 10 = 0.4

Question 3.
0.06 is 10 times as much as

Answer:
\(\frac{6}{1000}\) = 0.006

Explanation:
Let the unknown number is S
0.06 = 10S
S = 0.06/10
S = \(\frac{6}{100}\) x \(\frac{1}{10}\)
S = \(\frac{6}{1000}\) = 0.006

Write the value of the underlined digit.

Question 4.
6.54
Type below:
__________

Answer:
4 hundredths = 0.04

Explanation:
(6 x 1) + (5 x \(\frac{1}{10}\)) + (4 x \(\frac{1}{100}\))
4 x \(\frac{1}{100}\) = 4 hundredths = 0.04

Question 5.
0.837
Type below:
__________

Answer:
8 tenths = 0.8

Explanation:
(0 x 1) + (8 x \(\frac{1}{10}\)) + (3 x \(\frac{1}{100}\)) + (7 x \(\frac{1}{1000}\))
8 x \(\frac{1}{10}\) = 8 tenths = 0.8

Question 6.
8.702
Type below:
__________

Answer:
2 thousandths = 0.002

Explanation:
(8 x 1) + (7 x \(\frac{1}{10}\)) + (0 x \(\frac{1}{100}\)) + (2 x \(\frac{1}{1000}\))
2 x \(\frac{1}{1000}\) = 2 thousandths = 0.002

Question 7.
9.173
Type below:
__________

Answer:
9 ones = 9

Explanation:
(9 x 1) + (1 x \(\frac{1}{10}\)) + (7 x \(\frac{1}{100}\)) + (3 x \(\frac{1}{1000}\))
9 x 1 = 9 ones = 9

Compare. Write <, >, or =.

Question 8.
6.52 _____ 6.520

Answer:
6.52 = 6.520

Explanation:
Compare the ones; 6 = 6
Compare the tenths; 5 = 5
Compare the hundredths; 2 = 2
Compare the thousandths; 0 = 0
So, 6.52 = 6.520

Question 9.
3.589 _____ 3.598

Answer:
3.589 < 3.598

Explanation:
Compare the ones; 3 = 3
Compare the tenths; 5 = 5
Compare the hundredths; 8 < 9
So, 3.589 < 3.598

Question 10.
8.483 _____ 8.463

Answer:
8.483 > 8.463

Explanation:
Compare the ones; 8 = 8
Compare the tenths; 4 = 4
Compare the hundredths; 8 > 6
So, 8.483 > 8.463

Write the place value of the underlined digit. Round each number to the place of the underlined digit.

Question 11.
0.724
Place value: __________
Round: __________

Answer:
Place value: 7 tenths = 0.7
Round: 0.7

Explanation:
0.724
(0 x 1) + (7 x \(\frac{1}{10}\)) + (2 x \(\frac{1}{100}\)) + (4 x \(\frac{1}{1000}\))
Place Value: 7 x \(\frac{1}{10}\) = 7 tenths = 0.7
0.724
2 < 5
0.7

Question 12.
2.576
Place value: __________
Round: __________

Answer:
Place value: 2 ones = 2
Round: 3

Explanation:
2.576
(2 x 1) + (5 x \(\frac{1}{10}\)) + (7 x \(\frac{1}{100}\)) + (6 x \(\frac{1}{1000}\))
Place Value: 2 x 1 = 2 ones = 2
2.576
5 = 5
3

Question 13.
4.769
Place value: __________
Round: __________

Answer:
Place value: 6 hundredths = 0.06
Round: 4.77

Explanation:
4.769
(4 x 1) + (7 x \(\frac{1}{10}\)) + (6 x \(\frac{1}{100}\)) + (9 x \(\frac{1}{1000}\))
Place Value: 6 x \(\frac{1}{100}\)) = 6 hundredths = 0.06
4.769
9 > 5
4.77

Draw a quick picture to find the sum or difference.

Question 14.
2.46 + 0.78 =

Answer:
grade 5 chapter 3 Add and Subtract Decimals 133 image 1

Explanation:
2.46 + 0.78 = 3.24

Question 15.
3.27 − 1.84 =

Answer:
grade 5 chapter 3 Add and Subtract Decimals 133 image 2

Explanation:
3.27 − 1.84 = 1.43

Page No. 134

Question 16.
Marco read that a honeybee can fly up to 2.548 meters per second. He rounded the number to 2.55. To which place value did Marco round the speed of a honeybee?
__________

Answer:
Marco read that a honeybee can fly up to 2.548 meters per second. He rounded the number to 2.55.
The speed of a honeybee is 2.548.
Marco has to round this number to the nearest hundredth to get 2.55.
The digit in the hundredths places increases by 1.
The 8 > 5
So, the rounded number is 2.55.

Question 17.
What is the relationship between 0.04 and 0.004?
Type below:
__________

Answer:
Compare ones; 0 = 0
Compare tenths; 0 = 0
Compare hundredths; 4 > 0
So, 0.04 > 0.004

Go Math Grade 5 Workbook Lesson 3.7 Answer Key Question 18.
Jodi drew a quick picture to model the answer for 3.14 − 1.75. Draw what her picture might look like.
Type below:
__________

Answer:
grade 5 chapter 3 Add and Subtract Decimals 133 image 3

Explanation:
Jodi drew a quick picture to model the answer for 3.14 − 1.75
3.14 – 1.75 = 1.39

Question 19.
The average annual rainfall in California is 0.564 of a meter per year. What is the value of the digit 4 in that number?
Type below:
__________

Answer:
The average annual rainfall in California is 0.564 of a meter per year.
(0 x 1) + (5 x \(\frac{1}{10}\)) + (6 x \(\frac{1}{100}\)) + (4 x \(\frac{1}{1000}\))
4 x \(\frac{1}{1000}\) = 4 thousandths = 0.004

Question 20.
Jan ran 1.256 miles on Monday, 1.265 miles on Wednesday, and 1.268 miles on Friday. What were her distances from greatest to least?
_____ mi; _____ mi; _____ mi

Answer:
1.268 mi; 1.265 mi; 1.256 mi

Explanation:
Jan ran 1.256 miles on Monday, 1.265 miles on Wednesday, and 1.268 miles on Friday.
Compare hundredths: 6 > 5
So, 1.265; 1.268; 1.256
Compare thousandths in 1.265 and 1.268
8 > 5
1.268 mi; 1.265 mi; 1.256 mi

Share and Show – Page No. 137

Use rounding to estimate.

Question 1.
2.3 4
1.9
+5.2 3
————
Estimate: _____

Answer:
Estimate: About 9

Explanation:
2.34; 3 < 5; 2
1.9; 9 > 5; 2
5.23; 2 < 5; 5
Add: 2 + 2 + 5 = 9

Question 2.
10.3 9
-4.2 8
————
Estimate: _____

Answer:
Estimate: About 6

Explanation:
10.39; 3 < 5; 10
4.28; 2 < 5; 4
Subtract: 10 – 4 = 6

Go Math Lesson 3.7 5th Grade Answer Key Question 3.
$ 19.7 5
+$3.9 8
————
Estimate: $ _____

Answer:
Estimate: About $24

Explanation:
19.7 5; 7 > 5; 20
3.98; 9 > 5; 4
20 + 4 = 24

Use benchmarks to estimate.

Question 4.
0.3 4
0.1
+0.2 5
————
Estimate: _____

Answer:
Estimate: About 0.55

Explanation:
0.3 4 is closer to 0.35
0.1 is closer to 0
0.25
0.35 + 0 + 0.25 = 0.55

Question 5.
10.3 9
-4.2 8
————
Estimate: _____

Answer:
Estimate: About 6

Explanation:
10.3 9 is closer to 10
4.2 8 is closer to 4
10 – 4 = 6

On Your Own

Use rounding to estimate.

Question 6.
0.9 3
+0.1 8
————
Estimate: _____

Answer:
Estimate: About 1

Explanation:
0.93; 9 >5; 1
0.18; 1 < 5; 0
1 + 0 = 1

Question 7.
7.4 1
-3.8 8
————
Estimate: _____

Answer:
Estimate: About 3

Explanation:
7.41; 4 < 5; 7
3.88; 8 > 5; 4
7 – 4 = 3

Question 8.
14.6 8
-3.9 3
————
Estimate: _____

Answer:
Estimate: About 11

Explanation:
14.68; 6 > 5; 15
3.93; 9 > 5; 4
15 – 4 = 11

Use benchmarks to estimate.

Question 9.
12.4 1
-6.4 7
————
Estimate: _____

Answer:
Estimate: About 6

Explanation:
12.41 is closer to 12
6.47 is closer to 6
12 – 6 = 6

Question 10.
8.1 2
-5.5 2
————
Estimate: _____

Answer:
Estimate: About 2

Explanation:
8.12 is closer to 8
5.52 is closer to 6
8 – 6 = 2

Question 11.
9.7 5
-3.4 7
————
Estimate: _____

Answer:
Estimate: About 7

Explanation:
9.75 is closer to 10
3.47 is closer to 3
10 – 3 = 7

Practice: Copy and Solve Use rounding or benchmarks to estimate.

Question 12.
12.83 + 16.24
Estimate: _____

Answer:
Estimate: About 29

Explanation:
12.83; 8 > 5; 13
16.24; 2 <5; 16
13 + 16 = 29

Question 13.
$26.92 − $11.13
Estimate: $ _____

Answer:
Estimate: About $16

Explanation:
26.92; 9 > 5; 27
11.13; 1 < 5; 11
27 – 11 = 16

Go Math Grade 5 Lesson 3.7 Answer Key Question 14.
9.41 + 3.82
Estimate: _____

Answer:
Estimate: About 13

Explanation:
9.41; 4 < 5; 9
3.82; 8 > 5; 4
9 + 4 = 13

Use Reasoning Estimate to compare. Write < or >.

Question 15.
2.74 + 4.22 _____ 3.13 + 1.87

Answer:
2.74 + 4.22 > 3.13 + 1.87

Explanation:
2.74; 7 > 5; 3
4.22; 2 < 5 ; 4
3 + 4 = 7
3.13; 1 < 5; 3
1.87; 8 > 5; 2
3 + 2 = 5
So, 7 > 5
2.74 + 4.22 > 3.13 + 1.87

Question 16.
6.25 – 2.39 _____ 9.79 – 3.84

Answer:
6.25 – 2.39 < 9.79 – 3.84

Explanation:
6.25; 2 < 5; 6
2.39; 3 < 5; 2
6 – 2 = 4
9.79; 7 > 5; 10
3.84; 8 >5; 4
10 – 4 = 6
4 < 6
6.25 – 2.39 < 9.79 – 3.84

Problem Solving Applications – Page No. 138

Use the table to solve 17–18. Show your work.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 22

Question 17.
For the week of April 4, 1964, the Beatles had the top four songs. About how long would it take to listen to these four songs?
about _____ minutes

Answer:
about 10 minutes

Explanation:
Can’t Buy Me Love = 2.30 min
She Loves You = 2.50 min
I Want to Hold You Hand = 2.75 min
Please Please Me = 2.00 min
2.30; 3 < 5; 2
2.50; 5 = 5; 3
2.75; 7 > 5; 3
2.00; 2 < 5; 2
2 + 3 + 3 + 2 = 10 min

Question 18.
What’s the Error? Isabelle says she can listen to the first three songs in the table in 6 minutes.
Type below:
_________

Answer:
Can’t Buy Me Love = 2.30 min
She Loves You = 2.50 min
I Want to Hold You Hand = 2.75 min
2.30; 3 < 5; 2
2.50; 5 = 5; 3
2.75; 7 > 5; 3
2 + 3 + 3 = 8 minutes
About 8 minutes

Question 19.
Tracy ran a lap around the school track in 74.2 seconds. Malcolm ran a lap in 65.92 seconds. Estimate the difference in the times in which the students completed the lap.
about _____ seconds

Answer:
about 8 seconds

Explanation:
Tracy ran a lap around the school track in 74.2 seconds.
74.2; 2 < 5; 74
Malcolm ran a lap in 65.92 seconds.
65.92; 9 > 5; 66
74 – 66 = 8
about 8 seconds

Nutrition

Your body needs protein to build and repair cells. You should get a new supply of protein each day. The average 10-year-old needs 35 grams of protein daily. You can find protein in foods like meat, vegetables, and dairy products.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 23
Use estimation to solve.

Question 20.
Gina had a scrambled egg and a cup of low-fat milk for breakfast. She had an oat bran muffin for a morning snack. About how many more grams of protein did Gina have for breakfast than for a snack?
about _____ grams

Answer:
about 17 grams

Explanation:
Gina had a scrambled egg and a cup of low-fat milk for breakfast. She had an oat bran muffin for a morning snack.
1 scrambled egg = 6.75 grams
1 cup shredded whear cereal = 5.56 grams
1 oat bran muffin = 3.99 grams
1 cup low-fat milk = 8.22 grams
6.75; 7 > 5; 7
8.22; 2 < 5; 8
3.99; 9 > 5; 4
7 + 2 + 9 = 18
The average 10-year-old needs 35 grams of protein daily.
So, 35 – 18 = 17
Gina have 17 more grams of protein for breakfast than for a snack.

Question 21.
Pablo had a cup of shredded wheat cereal, a cup of low-fat milk, and one other item for breakfast. He had about 21 grams of protein. What was the third item Pablo had for breakfast?
_________

Answer:
6 grams

Explanation:
1 cup shredded wheat cereal = 5.56 grams
1 cup low-fat milk = 8.22 grams
5.56; 5 = 5; 6
8.22; 2 < 5; 9
6 + 9 = 15
15 + S = 21 grams
S = 21 – 15 = 6 grams
The third item Pablo had 6 grams for breakfast

Share and Show – Page No. 140

Estimate. Then find the sum.

Question 1.
2.5
+4.6
Estimate: _____
Sum: _____

Answer:
Estimate: 8
Sum: 7.1

Explanation:
2.5 nearest whole number is 3
4.6 nearest whole number is 5
Estimate: 3 + 5 = 8
Sum: 2.5 + 4.6 = 7.1

Question 2.
8.7 5
+6.4 3
Estimate: _____
Sum: _____

Answer:
Estimate: 15
Sum: 15.18

Explanation:
8.75 nearest whole number is 9
6.43 nearest whole number is 6
Estimate: 9 + 6 = 15
Sum: 8.75 + 6.43 = 15.18

Question 3.
2.0 3
+7.8 9
Estimate: _____
Sum: _____

Answer:
Estimate: 10
Sum: 9.92

Explanation:
2.03 nearest whole number is 2
7.89 nearest whole number is 8
Estimate: 2 + 8 = 10
Sum: 2.03 + 7.89 = 9.92

Question 4.
6.34 + 3.8 =
Estimate: _____
Sum: _____

Answer:
Estimate: 10
Sum: 10.14

Explanation:
6.34 nearest whole number is 6
3.8 nearest whole number is 4
Estimate: 6 + 4 = 10
Sum: 6.34 + 3.8 = 10.14

5th Grade Go Math Chapter 3 Practice and Homework Lesson 3.8 Question 5.
5.63 + 2.6 =
Estimate: _____
Sum: _____

Answer:
Estimate: 9
Sum: 8.23

Explanation:
5.63 nearest whole number is 6
2.6 nearest whole number is 3
Estimate: 6 + 3 = 9
Sum: 5.63 + 2.6 = 8.23

On Your Own – Page No. 141

Connect Symbols and Words Find the sum.

Question 6.
seven and twenty-five hundredths added to nine and four tenths
Type below:
________

Answer:
7.25 + 9.4 = 16.65

Explanation:
seven and twenty-five hundredths = 7.25
nine and four tenths = 9.4
7.25 + 9.4 = 16.65

Question 7.
twelve and eight hundredths added to four and thirty-five hundredths
Type below:
________

Answer:
12.08 + 4.35 = 16.43

Explanation:
twelve and eight hundredths = 12.08
four and thirty-five hundredths = 4.35
12.08 + 4.35 = 16.43

Question 8.
nineteen and seven tenths added to four and ninety-two hundredths
Type below:
________

Answer:
19.7 + 4.92 = 24.62

Explanation:
nineteen and seven tenths  = 19.7
four and ninety-two hundredths = 4.92
19.7 + 4.92 = 24.62

Question 9.
one and eighty-two hundredths added to fifteen and eight tenths
Type below:
________

Answer:
1.82 + 15.8 = 17.62

Explanation:
one and eighty-two hundredths = 1.82
fifteen and eight tenths = 15.8
1.82 + 15.8 = 17.62

Practice: Copy and Solve Find the sum.

Question 10.
7.99 + 8.34
_____

Answer:
16.33

Explanation:
7.99 + 8.34
Add hundredths; 9 + 4 = 13; regroup
Add tenths; 9 + 3 + 1 = 13; regroup
Add tens; 7 + 8  + 1 = 16
16.33

Question 11.
15.76 + 8.2
_____

Answer:
23.96

Explanation:
15.76 + 8.2
Add hundredths; 6 + 0 = 6;
Add tenths; 7 + 2 = 9;
Add tens; 5 + 8  = 13; regroup
Add hundreds; 1 + 1 = 2
23.96

Question 12.
9.6 + 5.49
_____

Answer:
15.09

Explanation:
9.6 + 5.49
Add hundredths; 0 + 9 = 9;
Add tenths; 6 + 4 = 10; regroup;
Add tens; 9 + 5 +  1 = 15; regroup
15.09

Question 13.
33.5 + 16.4
_____

Answer:
49.9

Explanation:
33.5 + 16.4
Add tenths; 5 + 4 = 9;
Add tens; 3 + 6 = 9;
Add hundreds; 3 + 1 = 4
49.9

Question 14.
9.84 + 21.52
_____

Answer:
31.36

Explanation:
9.84 + 21.52
Add hundredths; 4 + 2 = 6;
Add tenths; 8 + 5 = 13; regroup
Add tens; 9 + 1 + 1  = 11; regroup
Add hundreds; 0 + 2 + 1 = 3
31.36

Question 15.
3.89 + 4.6
_____

Answer:
8.49

Explanation:
3.89 + 4.6
Add hundredths; 9 + 0 = 9;
Add tenths; 8 + 6 = 14;
Add tens; 3 + 4 + 1 = 8;
8.49

Question 16.
42.19 + 8.8
_____

Answer:
50.99

Explanation:
42.19 + 8.8
Add hundredths; 0 + 9 = 9;
Add tenths; 1 + 8 = 9;
Add tens; 2 + 8  = 10; regroup
Add hundreds; 4 + 1 = 5
50.99

Question 17.
16.74 + 5.34
_____

Answer:
22.08

Explanation:
16.74 + 5.34
Add hundredths; 4 + 4 = 8;
Add tenths; 7 + 3 = 10; regroup
Add tens; 6 + 5 + 1 = 12; regroup
Add hundreds; 1 + 1 = 2
22.08

Question 18.
27.58 + 83.9
_____

Answer:
111.48

Explanation:
27.58 + 83.9
Add hundredths; 8 + 0 = 8;
Add tenths; 5 + 9 = 14; regroup
Add tens; 7 + 3 + 1  = 11; regroup
Add hundreds; 2 + 8 + 1 = 11
111.48

Question 19.
Tania measured the growth of her plant each week. The first week, the plant’s height measured 2.65 decimeters. During the second week, Tania’s plant grew 0.7 decimeter. How tall was Tania’s plant at the end of the second week?
Describe the steps you took to solve the problem.
_____ decimeters

Answer:
3.35 decimeters

Explanation:
Tania measured the growth of her plant each week. The first week, the plant’s height measured 2.65 decimeters. During the second week, Tania’s plant grew 0.7 decimeters.
2.65 + 0.7 = 3.35

Question 20.
Maggie had $35.13. Then her mom gave her $7.50 for watching her younger brother. She was paid $10.35 for her old roller skates. How much money does Maggie have now?
$ _____

Answer:
$52.98

Explanation:
Maggie had $35.13. Then her mom gave her $7.50 for watching her younger brother. She was paid $10.35 for her old roller skates.
35.13 + 7.50 + 10.35 = 52.98

Unlock the Problem – Page No. 142

Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 24

Question 21.
A city receives an average rainfall of 16.99 centimeters in August. One year, during the month of August, it rained 8.33 centimeters by August 15th. Then it rained another 4.65 centimeters through the end of the month. What was the total rainfall in centimeters for the month?
a. What do you need to find?
Type below:
________

Answer:
We need to find out what was the total rainfall in centimeters for the month, so we have to find the sum 8.33+ 4.65.

Explanation:
A city receives an average rainfall of 16.99 centimeters in August. One year, during the month of August, it rained 8.33 centimeters by August 15th. Then it rained another 4.65 centimeters through the end of the month. We need to find out what was the total rainfall in centimeters for the month, so we have to find the sum 8.33+ 4.65.

Question 21.
b. What information are you given?
Type below:
________

Answer:
We know that one year during the month Aug., it rained 8.33 centimeters by Aug. 15th. Then it rained another 4.65 centimeters through the end of the month.

Question 21.
c. How will you use addition to find the total number of centimeters of rain that fell?
Type below:
________

Answer:
We have to add the hundredths first, then the tenths and in the end the ones.

Question 21.
d. Show how you solved the problem.
Type below:
________

Answer:
sum 8.33+ 4.65.
Add the hundredths first. 3 hundredths + 5 hundredths = 8 hundredths.
Add the tenths. 3 tenths + 6 tenths = 9 tenths.
Add the ones. 8 + 4 = 12 tens
Therefore, the sum is 8.33+ 4.65 = 12.98.

Question 21.
e. Complete the sentence. It rained _________ centimeters for the month.
______ centimeters

Answer:
12.98 centimeters

Explanation:
It rained 12.98 centimeters for the month.

Question 22.
Horatio caught a fish that weighed 1.25 pounds. Later he caught another fish that weighed 1.92 pounds. What was the combined weight of both fish? Use the digits on the tiles to solve the problem. Digits may be used more than once or not at all.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 25
______ pounds

Answer:
3.17 pounds

Explanation:
Horatio caught a fish that weighed 1.25 pounds. Later he caught another fish that weighed 1.92 pounds.
1.25 + 1.92 = 3.17 pounds
grade 5 chapter 3 Add and Subtract Decimals 143 image 1

Share and Show – Page No. 144

Estimate. Then find the difference.

Question 1.
5.8 3
−2.1 8
———-
Estimate: ______
Difference: ______

Answer:
Estimate: 4
Difference: 3.65

Explanation:
5.83 is closer to 6
2.18 is closer to 2
6 – 2 = 4
5.83 – 2.18 = 3.65

Question 2.
4.4 5
−1.8 6
———–
Estimate: ______
Difference: ______

Answer:
Estimate: 2
Difference: 2.59

Explanation:
4.45 is closer to 4
1.86 is closer to 2
4 – 2 = 2
4.45 – 1.86 = 2.59

Question 3.
4.0 3
−2.2 5
———-
Estimate: ______
Difference: ______

Answer:
Estimate: 2
Difference: 1.78

Explanation:
4.03 is closer to 4
2.25 is closer to 2
4 – 2 = 2
4.03 – 2.25 = 1.78

Find the difference. Check your answer.

Question 4.
0.7 0
−0.4 3
———-
______

Answer:
0.27

Explanation:
0.70 − 0.43
Subtract hundredths: 0 – 3;
There are not enough hundredths. So, regroup
10 – 3 = 7
Subtract tenths: 6 – 4 = 2
Subtract ones: 0 – 0 = 0
0.27
Check: 0.70 − 0.43 = 0.27
0.27 = 0.27

Question 5.
13.2
−8.0 4
———-
______

Answer:
5.16

Explanation:
13.2 − 8.04
Subtract hundredths: 0 – 4;
There are not enough hundredths. So, regroup
10 – 4 = 6
Subtract tenths: 1 – 0 = 1
Subtract ones: 3 – 8;
There are not enough tens. So, regroup
13 – 8 = 5
Subtract hundreds: 0 – 0 = 0;
5.16
Check: 13.2 − 8.04 = 5.16
5.16 = 5.16

Go Math Grade 5 Chapter 3 Pdf Lesson 3.9 Answer Key Question 6.
15.8
−9.6 7
———-
______

Answer:
6.13

Explanation:
15.8 − 9.67
Subtract hundredths: 0 – 7;
There are not enough hundredths. So, regroup
10 – 7 = 3
Subtract tenths: 7 – 6 = 1
Subtract ones: 5 – 9;
There are not enough ones. So, regroup
15 – 9 = 6
Subtract hundreds: 0 – 0 = 0;
6.13
Check: 15.8 − 9.67 = 6.13
6.13 = 6.13

On Your Own – Page No. 145

Connect Symbols and Words Find the difference.

Question 7.
three and seventy-two hundredths subtracted from five and eighty-one hundredths
______

Answer:
three and seventy-two hundredths = 3.72
five and eighty-one hundredths = 5.81
5.81 – 3.72 = 2.09

Question 8.
one and six-hundredths subtracted from eight and thirty-two hundredths
______

Answer:
one and six-hundredths = 1.06
eight and thirty-two hundredths = 8.23
8.23 – 1.06 = 7.17

Use Reasoning Algebra Write the unknown number for n.

Question 9.
5.28 − 3.4 = n
n = ______

Answer:
n = 1.88

Explanation:
5.28 − 3.4 = 1.88

Question 10.
n − 6.47 = 4.32
n = ______

Answer:
n = 10.79

Explanation:
n − 6.47 = 4.32
n = 4.32 + 6.47
n = 10.79

Question 11.
11.57 − n = 7.51
n = ______

Answer:
n = 4.06

Explanation:
11.57 − n = 7.51
11.57 = 7.51 + n
n = 11.57 – 7.51
n = 4.06

Practice: Copy and Solve Find the difference.

Question 12.
8.42 − 5.14 = ______

Answer:
3.28

Explanation:
8.42 − 5.14
Subtract hundredths: 2 – 4;
There are not enough hundredths. So, regroup
12 – 4 = 8
Subtract tenths: 3 – 1 = 2
Subtract ones: 8 – 5 = 3
3.28

Question 13.
16.46 − 13.87 = ______

Answer:
2.59

Explanation:
16.46 − 13.87
Subtract hundredths: 6 – 7;
There are not enough hundredths. So, regroup
16 – 7 = 9
Subtract tenths: 3 – 8
There are not enough tenths. So, regroup
13 – 8 = 5
Subtract ones: 5 – 3 = 2;
Subtract hundreds: 1 – 1 = 0;
2.59

Question 14.
34.27 − 17.51 = ______

Answer:
16.76

Explanation:
34.27 − 17.51
Subtract hundredths: 7 – 1 = 6;
Subtract tenths: 2 – 5
There are not enough tenths. So, regroup
12 – 5 = 7;
Subtract ones: 3 – 7
There are not enough ones. So, regroup
13 – 7 = 6
Subtract hundreds: 2 – 1 = 1;
16.76

Question 15.
15.83 − 11.45 = ______

Answer:
4.38

Explanation:
15.83 − 11.45
Subtract hundredths: 3 – 5;
There are not enough hundredths. So, regroup
13 – 5 = 8
Subtract tenths: 7 – 4 = 3
Subtract ones: 5 – 1 = 4;
Subtract hundreds: 1 – 1 = 0;
4.38

Question 16.
12.74 − 10.54 = ______

Answer:
2.2

Explanation:
12.74 − 10.54
Subtract hundredths: 4 – 4 = 0;
Subtract tenths: 7 – 5 = 2
Subtract ones: 2 – 0 = 2;
Subtract hundreds: 1 – 1 = 0;
2.20

Question 17.
48.21 − 13.65 = ______

Answer:
34.56

Explanation:
48.21 − 13.65
Subtract hundredths: 1 – 5;
There are not enough hundredths. So, regroup
11 – 5 = 6
Subtract tenths: 1 – 6
There are not enough tenths. So, regroup
11 – 6 = 5
Subtract ones: 7 – 3 = 4;
Subtract hundreds: 4 – 1 = 3;
34.56

Question 18.
Beth finished a race in 3.35 minutes. Ana finished the race in 0.8 minute less than Beth. Fran finished the race in 1.02 minutes less than Ana. What was Fran’s time to finish the race in minutes?
______ minutes

Answer:
1.53 minutes

Explanation:
Beth finished a race in 3.35 minutes. Ana finished the race in 0.8 minute less than Beth.
3.35 – 0.8 = 2.55
Fran finished the race in 1.02 minutes less than Ana.
2.55 – 1.02 = 1.53

Question 19.
Fatima planted sunflower seeds in a flower patch. The tallest sunflower grew 2.65 meters tall. The height of the shortest sunflower was 0.34 meter less than the tallest sunflower. What was the height, in meters, of the shortest sunflower?
______ meters

Answer:
2.31 meters

Explanation:
Fatima planted sunflower seeds in a flower patch. The tallest sunflower grew 2.65 meters tall. The height of the shortest sunflower was 0.34 meter less than the tallest sunflower.
2.65 – 0.34 = 2.31

Unlock the Problem – Page No. 146

Question 20.
In peanut butter, how many more grams of protein are there than grams of carbohydrates? Use the label below.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 26
a. What do you need to know?
Type below:
_________

Answer:
We need to find how many more grams of protein are there than grams of carbohydrates.

Question 20.
b. How will you use subtraction to find how many more grams of protein there are than grams of carbohydrates?
Type below:
_________

Answer:
Grams of protein = 8.1 g
grams of carbohydrates = 6.2g
8.1 – 6.2 = 1.9 grams

Question 20.
c. Show how you solved the problem.
Type below:
_________

Answer:
8.1 – 6.2
Subtract tenths: 1 – 2
There are not enough tenths. So, regroup
11 – 2 = 9
Subtract ones:
7 – 6 = 1
1.9 grams

Question 20.
d. Complete each sentence.
The peanut butter has ______ grams of protein.
The peanut butter has ______ grams of carbohydrates.
There are ______ more grams of protein than grams of carbohydrates in the peanut butter.
Type below:
_________

Answer:
The peanut butter has 8.1 grams of protein.
The peanut butter has 6.2 grams of carbohydrates.
There are 1.9 more grams of protein than grams of carbohydrates in the peanut butter.

Question 21.
Kyle is building a block tower. Right now the tower stands 0.89 meters tall. How much higher does the tower need to be to reach a height of 1.74 meters?
______ meters

Answer:
0.85 meters

Explanation:
Kyle is building a block tower. Right now the tower stands 0.89 meters tall.
To reach a height of 1.74, 1.74 – 0.89 = 0.85

Question 22.
Dialyn scored 2.5 points higher than Gina at a gymnastics event. Select the values that could represent each student’s gymnastics score. Mark all that apply.
Options:
a. Dialyn: 18.4 points, Gina: 16.9 points
b. Dialyn: 15.4 points, Gina: 13.35 points
c. Dialyn: 16.2 points, Gina: 13.7 points
d. Dialyn: 19.25 points, Gina: 16.75 points

Answer:
c. Dialyn: 16.2 points, Gina: 13.7 points
d. Dialyn: 19.25 points, Gina: 16.75 points

Explanation:
Dialyn scored 2.5 points higher than Gina at a gymnastics event.
a. 18.4 – 16.9 = 1.5
b. 15.4 – 13.35 = 2.05
c. 16.2 – 13.7 = 2.5
d. 19.25 – 16.75 = 2.5

Share and Show – Page No. 149

Write a rule for the sequence.

Question 1.
0.5, 1.8, 3.1, 4.4, …
Think: Is the sequence increasing or decreasing?
Rule: _________

Answer:
Add 1.3 to the previous term in the sequence to get the next one.

Explanation:
Compare 0.5, 1.8; 0.5 < 1.8
The sequence is increasing as the second term is greater than the first term.
The operation will use addition.
0.5 + x = 1.8
x = 1.8 – 0.5 = 1.3
1.8 + 1.3 = 3.1
3.1 + 1.3 = 4.4
Add 1.3 to the previous term in the sequence to get the next one.

Question 2.
23.2, 22.1, 21, 19.9, …
Rule: _________

Answer:
Subtract 1.1 to the previous term in the sequence to get the next one.

Explanation:
Compare 23.2 and 22.1; 23.2 > 22.1
The sequence is decreasing as the second term is lesser than the first term.
The operation will use subtraction.
23.2 – 22.1 = 1.1
22.1 – 21 = 1.1
21 – 19.9 = 1.1
Subtract 1.1 to the previous term in the sequence to get the next one.

Write a rule for the sequence. Then find the unknown term.

Question 3.
0.3, 1.5, ____ , 3.9, 5.1
Missing value: ______
Rule: ______

Answer:
Missing value: 2.7
Rule: Add 1.2 to the previous term in the sequence to get the next one.

Explanation:
Compare 0.3 and 1.5; 0.3 < 1.5
The sequence is increasing as the second term is greater than the first term.
The operation will use addition.
1.5 – 0.3 = 1.2
0.3 + 1.2 = 1.5
1.5 + 1.2 = 2.7
2.7 + 1.2 = 3.9
3.9 + 1.2 = 5.1
Add 1.2 to the previous term in the sequence to get the next one.

Question 4.
19.5, 18.8, 18.1, 17.4, ______
Missing value: ______
Rule: ______

Answer:
Missing value: 16.7
Rule: Subtract 0.7 to the previous term in the sequence to get the next one.

Explanation:
Compare 19.5 and 18.8; 19.5 > 18.8
The sequence is decreasing as the second term is lesser than the first term.
The operation will use subtraction.
19.5 – 18.8 = 0.7
18.8 – 18.1 = 0.7
18.1 – 17.4 = 0.7
17.4 – 0.7 = 16.7
Subtract 0.7 to the previous term in the sequence to get the next one.

On Your Own

Write the first four terms of the sequence.

Question 5.
Rule: start at 10.64, subtract 1.45
______ ; ______ ; ______ ; ______

Answer:
9.19; 7.74; 6.29; 4.84

Explanation:
10.64 – 1.45 = 9.19
9.19 – 1.45 = 7.74
7.74 – 1.45 = 6.29
6.29 – 1.45 = 4.84
9.19; 7.74; 6.29; 4.84

Question 6.
Rule: start at 0.87, add 2.15
______ ; ______ ; ______ ; ______

Answer:
3.02; 5.17; 7.32; 9.47

Explanation:
0.87 + 2.15 = 3.02
3.02 + 2.15 = 5.17
5.17 + 2.15 = 7.32
7.32 + 2.15 = 9.47
3.02; 5.17; 7.32; 9.47

Question 7.
Rule: start at 19.3, add 1.8
______ ; ______ ; ______ ; ______

Answer:
21.1; 22.9; 24.7; 26.5

Explanation:
19.3 + 1.8 = 21.1
21.1 + 1.8 = 22.9
22.9 + 1.8 = 24.7
24.7 + 1.8 = 26.5
21.1; 22.9; 24.7; 26.5

Question 8.
Rule: start at 29.7, subtract 0.4
______ ; ______ ; ______ ; ______

Answer:
29.3; 28.9; 28.5; 28.1

Explanation:
29.7 – 0.4 = 29.3
29.3 – 0.4 = 28.9
28.9 – 0.4 = 28.5
28.5 – 0.4 = 28.1
29.3; 28.9; 28.5; 28.1

Question 9.
Marta put $4.87 in her coin bank. Each day she added 1 quarter, 1 nickel, and 3 pennies. How much money was in her coin bank after 6 days? Describe the pattern you used to solve.
$ ______

Answer:
$10.52
Add 1.13 to the previous term in the sequence to get the next one.

Explanation:
Marta put $4.87 in her coin bank. Each day she added 1 quarter, 1 nickel, and 3 pennies.
She added 1.13 each day.
4.87 + 1.13 = 6.00
6.00 + 1.13 = 7.13
7.13 + 1.13 = 8.26
8.26 + 1.13 = 9.39
9.39 + 1.13 = 10.52
Add 1.13 to the previous term in the sequence to get the next one.

Question 10.
Identify Relationships Look at the list below. Do the numbers show a pattern? Explain how you know.
11.23, 10.75, 10.3, 9.82, 9.37, 8.89
Type below:
_________

Answer:
Compare 11.23 and 10.75; 11.23 > 10.75
The sequence is decreasing as the second term is greater than the first term.
The operation will use subtraction.
11.23 – 10.75 = 0.48
10.75 – 10.3 = 0.45
10.3 – 9.82 = 0.48
9.82 – 9.37 = 0.45
9.37 – 8.89 = 0.48
First two terms difference is 0.48
Second and third-term difference is 0.45
third and fourth term difference is 0.48
fourth and fifth term difference is 0.45
fifth and sixth term difference is 0.48

Problem Solving Applications – Page No. 150

Pose a Problem

Question 11.
Bren has a deck of cards. As shown below, each card is labeled with a rule describing a pattern in a sequence. Select a card and decide on a starting number. Use the rule to write the first five terms in your sequence.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 27
Sequence: _____ , _____ , _____ , _____ , _____
Write a problem that relates to your sequence and requires the sequence be extended to solve.
Pose a Problem         Solve your problem.
Type below:
_________

Answer:
1.6 + 0.33 = 1.93
1.93 + 0.33 = 2.26
2.26 + 0.33 = 2.59
2.59 + 0.33 = 2.92
2.92 + 0.33 = 3.25
Start at 1.6 and write the first five terms of the sequence?
Add 0.3 to the previous term in the sequence to get the next one.

Question 12.
Colleen and Tom are playing a number pattern game. Tom wrote the following sequence.
33.5, 34.6, 35.7, ________, 37.9
What is the unknown term in the sequence?
_____

Answer:
36.8

Explanation:
33.5 < 34.6
34.6 – 33.5 = 1.1
33.5 + 1.1 = 34.6
34.6 + 1.1 = 35.7
35.7 + 1.1 = 36.8
36.8 + 1.1 = 37.9

Share and Show – Page No. 153

Question 1.
Sara wants to buy a bottle of apple juice from a vending machine. She needs exactly $2.30. She has the following bills and coins:
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 28
Make and complete a table to find all the ways Sara could pay for the juice. First, draw a table with a column for each type of bill or coin. Next, fill in your table with each row showing a different way Sara can make exactly $2.30.
Type below:
_________

Answer:
Sara wants to buy a bottle of apple juice from a vending machine. She needs exactly $2.30.
grade 5 chapter 3 Add and Subtract Decimals 153 image 1

Question 2.
What if Sara decides to buy a bottle of water that costs $1.85? What are all the different ways she can make exactly $1.85 with the bills and coins she has? Which coin must Sara use?
Type below:
_________

Answer:
If Sara decides to buy a bottle of water that costs $1.85, then
1 bill, 3 quarters, 1 dime; 1 bill, 3 quarters, 2 nickels; quarter

Go Math 5th Grade 3.11 Answer Key Question 3.
At the end of August, Mr. Diaz had a balance of $441.62. Since then, he has written two checks for $157.34 and $19.74 and made a deposit of $575.00. Mr. Diaz says his balance is $739.54. Find Mr. Diaz’s correct balance.
$ _____

Answer:
At the end of August, Mr. Diaz had a balance of $441.62.
Since then, he has written two checks for $157.34 and $19.74 and made a deposit of $575.00.
Subtract the checks from the initial amount, and add the deposit.
441.85 – (157.34 + 19.74) + 575 = 839.77
So, $839.77

On Your Own – Page No. 154

Use the following information to solve 4–6.

At Open Skate Night, admission is $3.75 with a membership card and $5.00 without a membership card. Skate rentals are $3.00.

Question 4.
Aidan paid the admission for himself and two friends at Open Skate Night. Aidan had a membership card, but his friends did not. Aidan paid with a $20 bill. How much change should Aidan receive?
$ _____

Answer:
$6.25

Explanation:
Aidan had a membership card, but his friends did not.
$3.75 + $5.00 + $5.00 = $13.75
Aidan paid with a $20 bill.
$20 – $13.75 = $6.25

Question 5.
The Moores paid $6 more for skate rentals than the Cotters did. Together, the two families paid $30 for skate rentals. How many pairs of skates did the Moores rent?
_____ pairs of skates

Answer:
6 pairs of skates

Question 6.
Analyze Jennie and 5 of her friends are going to Open Skate Night. Jennie does not have a membership card. Only some of her friends have membership cards. What is the total amount that Jennie and her friends might pay for admission?
Type below:
_________

Answer:
They will pay $27.50 if only 2 of her friends have membership cards.

Question 7.
Marisol bought 5 movie tickets for a show. Each ticket cost $6.25. Complete the table to show the price of 2, 3, 4, and 5 tickets.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 29
Type below:
_________

Answer:
grade 5 chapter 3 Add and Subtract Decimals 153 image 2

Share and Show – Page No. 156

Find the sum or difference.

Question 1.
4.19 + 0.58
_____

Answer:
4.77

Explanation:
4.19 + 0.58 = 1.38
Add hundredths 9 + 8 = 17; Regroup;
Add tenths 1 + 5 + 1 = 7;
Add ones 4 + 0 = 4
4.19 + 0.58 = 4.77

Question 2.
9.99 − 4.1
_____

Answer:
5.89

Explanation:
9.99 − 4.1
Subtract hundredths: 9 – 0 = 9;
Subtract tenths: 9 – 1 = 8
Subtract ones: 9 – 4 = 5
So, 9.99 − 4.1 = 5.89

Question 3.
5.7 + 2.25 + 1.3
_____

Answer:
9.25

Explanation:
5.7 + 2.25 + 1.3
Add hundredths 0 + 5 + 0 = 5;
Add tenths 7 + 2 + 3 = 12; Regroup
Add ones 5 + 2 + 1 + 1 = 9
5.7 + 2.25 + 1.3 = 9.25

Question 4.
28.6 − 9.84
_____

Answer:
18.76

Explanation:
28.6 − 9.84
Subtract hundredths: 0 – 4;
There are not enough hundredths. So, regroup
10 – 4 = 6.
Subtract tenths: 5 – 8;
There are not enough tenths. So, regroup
15 – 8 = 7
Subtract ones: 7 – 9;
There are not enough ones. So, regroup
17 – 9 = 8
Subtract hundreds: 1 – 0 = 1;
So, 28.6 − 9.84 = 18.76

Question 5.
$15.79 + $32.81
$ _____

Answer:
$48.6

Explanation:
$15.79 + $32.81
Add hundredths 9 + 1 = 10; Regroup
Add tenths 7 + 8 + 1 = 16; Regroup
Add ones 5 + 2 + 1  = 8
Add hundreds 1 + 3 = 4
$15.79 + $32.81 = $48.60

Question 6.
38.44 − 25.86
_____

Answer:
12.58

Explanation:
38.44 − 25.86
Subtract hundredths: 4 – 6;
There are not enough hundredths. So, regroup
14 – 6 = 8
Subtract tenths: 3 – 8;
There are not enough tenths. So, regroup
13 – 8 = 5
Subtract ones: 7 – 5 = 2;
Subtract hundreds: 3 – 2 = 1;
So, 38.44 − 25.86 = 12.58

On Your Own – Page No. 157

Find the sum or difference.

Question 7.
$ 18.39
+$7.56
————
$ _____

Answer:
$25.95

Explanation:
$ 18.39 + $7.56
Add hundredths 9 + 6 = 15; Regroup
Add tenths 5 + 3 + 1 = 9;
Add ones 8 + 7  = 15; Regroup
Add hundreds 1 + 0 + 1 = 2
$ 18.39 + $7.56 = $25.95

Question 8.
8.22 − 4.39
_____

Answer:

Explanation:
8.22 − 4.39
Subtract hundredths: 2 – 9;
There are not enough hundredths. So, regroup
12 – 9 = 3
Subtract tenths: 1 – 3;
There are not enough tenths. So, regroup
11 – 3 = 8
Subtract ones: 7 – 4 = 3;
So, 8.22 − 4.39 = 3.83

Question 9.
93.6 − 79.84
_____

Answer:
13.76

Explanation:
93.6 − 79.84
Subtract hundredths: 0 – 4;
There are not enough hundredths. So, regroup
10 – 4 = 6
Subtract tenths: 5 – 8;
There are not enough tenths. So, regroup
15 – 8 = 7
Subtract ones: 2 – 9;
There are not enough ones. So, regroup
12 – 9 = 3
Subtract hundreds: 8 – 7 = 1;
So, 93.6 − 79.84 = 13.76

Question 10.
1.82
2.28
+2.18
————
_____

Answer:
6.28

Explanation:
1.82 + 2.28 + 2.18
Add hundredths 2 + 8 + 8 = 18; Regroup
Add tenths 8 + 2 + 1 + 1 = 12;  Regroup
Add ones 1 + 2 + 2 + 1  = 6;
1.82 + 2.28 + 2.18 = 6.28

Practice: Copy and Solve Find the sum or difference.

Question 11.
6.3 + 2.98 + 7.7
_____

Answer:
16.98

Explanation:
6.3 + 2.98 + 7.7
Add hundredths 0 + 8 + 0 = 8;
Add tenths 3 + 9 + 7 = 19;  Regroup
Add ones 6 + 2 + 7 + 1  = 16;
6.3 + 2.98 + 7.7 = 16.98

Question 12.
27.96 − 16.2
_____

Answer:
11.76

Explanation:
27.96 − 16.2
Subtract hundredths: 6 – 0 = 6;
Subtract tenths: 9 – 2 = 7;
Subtract ones: 7 – 6 = 1;
Subtract hundreds: 2 – 1 = 1;
So, 27.96 − 16.2 = 11.76

Question 13.
12.63 + 15.04
_____

Answer:
27.67

Explanation:
12.63 + 15.04
Add hundredths 3 + 4 = 7;
Add tenths 6 + 0 = 6;
Add ones 2 + 5 = 7;
Add hundreds 1 + 1 = 2
12.63 + 15.04 = 27.67

Question 14.
9.24 − 2.68
_____

Answer:
6.56

Explanation:
9.24 − 2.68
Subtract hundredths: 4 – 8;
There are not enough hundredths. So, regroup
14 – 8 = 6
Subtract tenths: 1 – 6;
There are not enough tenths. So, regroup
11 – 6 = 5
Subtract ones: 8 – 2 = 6;
So, 9.24 − 2.68 = 6.56

Question 15.
$18 − $3.55
$ _____

Answer:
$14.45

Explanation:
$18 − $3.55
Subtract hundredths: 0 – 5;
There are not enough hundredths. So, regroup
10 – 5 = 5
Subtract tenths;
There are not enough tenths. So, regroup
9 – 5 = 4
Subtract ones: 7 – 3 = 4;
Subtract hundreds: 1 – 0 = 0
So, $18 − $3.55 = $14.45

Question 16.
9.73 − 2.52
_____

Answer:
7.21

Explanation:
9.73 − 2.52
Subtract hundredths: 3 – 2 = 1;
Subtract tenths; 7 – 5 = 2
Subtract ones: 9 – 2 = 7;
So, 9.73 − 2.52 = 7.21

Question 17.
$54.78 + $43.62
$ _____

Answer:
$98.4

Explanation:
$54.78 + $43.62
Add hundredths 8 + 2 = 10; Regroup
Add tenths 7 + 6 + 1 = 14;  Regroup
Add ones 4 + 3 + 1 = 8;
Add hundreds 5 + 4 = 9
$54.78 + $43.62 = $98.40

Question 18.
7.25 + 0.25 + 1.5
_____

Answer:
9

Explanation:
7.25 + 0.25 + 1.5
Add hundredths 5 + 5 + 0 = 10; Regroup
Add tenths 2 + 2 + 5 + 1 = 10;  Regroup
Add ones 7 + 0 + 1 + 1 = 9;
7.25 + 0.25 + 1.5 = 9.00

Use Reasoning Algebra Find the missing number.

Question 19.
n − 9.02 = 3.85
n = _____

Answer:
n = 12.87

Explanation:
n − 9.02 = 3.85
n = 3.85 + 9.02
n = 12.87

Question 20.
n + 31.53 = 62.4
n = _____

Answer:
n = 30.87

Explanation:
n + 31.53 = 62.4
n = 62.4 – 31.53 = 30.87
n = 30.87

Question 21.
9.2 + n + 8.4 = 20.8
n = _____

Answer:
n = 3.2

Explanation:
9.2 + n + 8.4 = 20.8
n + 17.6 = 20.8
n = 20.8 – 17.6
n = 3.2

Problem Solving Applications

Question 22.
Jake needs 7.58 meters of wood to complete a school project. He buys a 2.25-meter plank of wood and a 3.12-meter plank of wood. How many more meters of wood does Jake need to buy?
_____ meters

Answer:
2.21 meters

Explanation:
Jake needs 7.58 meters of wood to complete a school project. He buys a 2.25-meter plank of wood and a 3.12-meter plank of wood.
2.25 + 3.12 = 5.37
7.58 – 5.37 = 2.21

Question 23.
Lori needs a length of twine 8.5 meters long to mark a row in her garden. Andrew needs a length of twine 7.25 meters long for his row. They have one length of twine that measures 16.27 meters. After they each take the lengths they need, how much twine will be left?
_____ meters

Answer:
0.52 meters

Explanation:
Lori needs a length of twine 8.5 meters long to mark a row in her garden. Andrew needs a length of twine 7.25 meters long for his row. They have one length of twine that measures 16.27 meters.
8.5 + 7.25 = 15.75
16.27 – 15.75 = 0.52

Page No. 158

Use the table to solve 24–26.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals img 30

Question 24.
How much farther did the gold medal winner jump than the silver medal winner?
_____ meters

Answer:
0.1 meters

Explanation:
Gold medal = 8.34 meters
Silver medal = 8.24 meters.
8.34 – 8.24 = 0.10 meters
gold medal winner jump 0.1 meters than the silver medal winner

Question 25.
The fourth-place competitor’s jump measured 8.19 meters. If his jump had been 0.10 meter greater, what medal would he have received? Explain how you solved the problem.
_________

Answer:

Explanation:
The fourth-place competitor’s jump measured 8.19 meters. If his jump had been 0.10 meter greater
8.19 + 0.1 = 8.29
He may receive a silver medal. 8.29 is in between 8.24 and 8.34

Question 26.
In the 2004 Olympics, the gold medalist for the men’s long jump had a jump of 8.59 meters. How much farther did the 2004 gold medalist jump compared to the 2008 gold medalist?
_____ meters

Answer:
0.25 meters

Explanation:
In the 2004 Olympics, the gold medalist for the men’s long jump had a jump of 8.59 meters.
In 2008, 8.34 meters
8.59 – 8.34 = 0.25 meters

Question 27.
Alexander and Holly are solving the following word problem.
At the supermarket Carla buys 2.25 pounds of hamburger. She also buys 3.85 pounds of chicken. How many pounds of hamburger and chicken did Carla buy?
Alexander set up his problem as 2.25 + 3.85.
Holly set up her problem as 3.85 + 2.25.
Who is correct? Explain your answer and solve the problem.

Answer:
Alexander and Holly are solving the following word problem.
At the supermarket, Carla buys 2.25 pounds of hamburger. She also buys 3.85 pounds of chicken. She buys 2.25 + 3.85 = 6.10 pounds.
From the commutative property, 2.25 + 3.85 = 3.85 + 2.25
So, both answers are correct

Chapter Review/Test – Page No. 159

Question 1.
Chaz kept a record of how many gallons of gas he purchased each day last week.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals Chapter Review/Test img 31
Order the days from least amount of gas Chaz purchased to greatest amount of gas Chaz purchased.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals Chapter Review/Test img 32
Least: _____ ; _____ ; _____ ; _____ ; _____ Greatest

Answer:
grade 5 chapter 3 Add and Subtract Decimals 153 image 3
Least: 3.75; 3.9; 4.256; 4.258; 4.5 Greatest

Explanation:
Monday = 4.5 gallons
Tuesday = 3.9 gallons
Wednesday = 4.258 gallons
Thursday = 3.75 gallons
Friday = 4.256 gallons
The days from least amount of gas Chaz purchased to the greatest amount of gas Chaz purchased
4.5; 3.9; 4.258; 3.75; 4.256
3 < 4
3.9; 3.75; 4.5; 4.258; 4.256
9 > 7. So, 3.9; 3.75
5 > 2; 4.5; 4.258; 4.256
8 > 6; 4.258; 4.256
4.5; 4.258; 4.256; 3.9; 3.75
3.75; 3.9; 4.256; 4.258; 4.5

For 2a–2c, select True or False for each statement

Question 2.
2a. 16.437 rounded to the nearest whole number is 16.
i. TRUE
ii. FALSE

Answer:
i. TRUE

Explanation:
16.437; 4 < 5.
So, the nearest whole number is 16

Question 2.
2b. 16.437 rounded to the nearest tenth is 16.4.
i. TRUE
ii. FALSE

Answer:
i. TRUE

Explanation:
16.437 rounded to the nearest tenth
3 < 5
16.4

Question 2.
2c. 16.437 rounded to the nearest hundredth is 16.43.
i. TRUE
ii. FALSE

Answer:
ii. FALSE

Explanation:
16.437 rounded to the nearest hundredth is
7 > 5
16.44

Question 3.
Students are selling muffins at a school bake sale. One muffin costs $0.25, 2 muffins cost $0.37, 3 muffins cost $0.49, and 4 muffins cost $0.61. If this pattern continues, how much will 7 muffins cost? Explain how you found your answer.
$ _____

Answer:
$0.97

Explanation:
Students are selling muffins at a school bake sale. One muffin costs $0.25, 2 muffins cost $0.37, 3 muffins cost $0.49, and 4 muffins cost $0.61.
0.37 – 0.25 = 0.12
0.49 – 0.37 = 0.12
0.61 – 0.49 = 0.12
For 5 muffins 0.61 + 0.12 = 0.73
For 6 muffins 0.73 + 0.12 = 0.85
For 7 muffins 0.85 + 0.12 = 0.97
Every muffin cost increases with 0.12.

Chapter Review/Test – Page No. 160

Question 4.
What is the value of the underlined digit? Mark all that apply. 0.679
Options:
a. 0.6
b. 0.06
c. six tenths
d. six hundredths
e. 6 × \(\frac{1}{10}\)

Answer:
a. 0.6
c. six tenths
e. 6 × \(\frac{1}{10}\)

Explanation:
0.679
(0 x 1) + (6 x \(\frac{1}{10}\)) + (7 x \(\frac{1}{100}\)) + (9 x \(\frac{1}{1000}\))
6 x \(\frac{1}{10}\) = 0.6 = 6 tenths

Question 5.
Rowanda jogged 2.14 kilometers farther than Terrance. Select the values that could represent how far each student jogged. Mark all that apply.
Options:
a. Rowanda: 6.5 km, Terrance: 4.36 km
b. Rowanda: 4.8 km, Terrance: 2.76 km
c. Rowanda: 3.51 km, Terrance: 5.65 km
d. Rowanda: 7.24 km, Terrance: 5.1 km

Answer:
a. Rowanda: 6.5 km, Terrance: 4.36 km
d. Rowanda: 7.24 km, Terrance: 5.1 km

Explanation:
Rowanda jogged 2.14 kilometers farther than Terrance.
a. Rowanda: 6.5 km, Terrance: 4.36 km
6.5 – 4.36 = 2.14
b. Rowanda: 4.8 km, Terrance: 2.76 km
4.8 – 2.76 = 2.04
c. Rowanda: 3.51 km, Terrance: 5.65 km
5.65 – 3.51 = 2.14
d. Rowanda: 7.24 km, Terrance: 5.1 km
7.24 – 5.1 = 2.14
The first and fourth values can represent how far each student jogged.

Question 6.
Shade the model to show the decimal 0.542.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals Chapter Review/Test img 33
Type below:
_________

Answer:
grade 5 chapter 3 Add and Subtract Decimals 160 image 1

Explanation:
0.542 = 542/1000
5 hundredths, 4 tenths, 2 thousandths

Question 7.
Benjamin rode his bicycle 3.6 miles on Saturday and 4.85 miles on Sunday. How many miles did he ride Saturday and Sunday combined?
Use the digits on the tiles to solve the problem. Digits may be used more than once or not at all.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals Chapter Review/Test img 34
_________ miles

Answer:
8.45 miles
grade 5 chapter 3 Add and Subtract Decimals 153 image 4

Explanation:
Benjamin rode his bicycle 3.6 miles on Saturday and 4.85 miles on Sunday.
3.6 + 4.85 = 8.45

Chapter Review/Test – Page No. 161

Question 8.
The school is 3.65 miles from Tonya’s house and 1.28 miles from Jamal’s house. How much farther from school is Tonya’s house than Jamal’s house? Explain how you can use a quick picture to solve the problem.
_____ miles

Answer:
grade 5 chapter 3 Add and Subtract Decimals 161 image 2
2.37 miles

Explanation:
The school is 3.65 miles from Tonya’s house and 1.28 miles from Jamal’s house.
3.65 – 1.28 = 2.37

Question 9.
A vet measured the mass of two birds. The mass of the robin was 76.64 grams. The mass of the blue jay was 81.54 grams. Estimate the difference in the masses of the birds.
≈ _____ grams

Answer:
5 grams

Explanation:
A vet measured the mass of two birds. The mass of the robin was 76.64 grams. The mass of the blue jay was 81.54 grams.
76.64 grams is closer to 77
81.54 grams is closer to 82
82 – 77 = 5
The estimated difference in the masses of the birds is 5 grams.

Question 10.
Rick bought 5 yogurt bars at a snack shop. Each yogurt bar cost $1.75. Complete the table to show the price of 2, 3, 4, and 5 yogurt bars.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals Chapter Review/Test img 35
Type below:
_________

Answer:
grade 5 chapter 3 Add and Subtract Decimals 161 image 1

Explanation:

Question 11.
Clayton Road is 2.25 miles long. Wood Pike Road is 1.8 miles long. Kisha used a quick picture to find the combined length of Clayton Road and Wood Pike Road. Does Kisha’s work make sense? Explain why or why not
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals Chapter Review/Test img 36
i. Yes
ii. No

Answer:
i. Yes

Explanation:
Clayton Road is 2.25 miles long. Wood Pike Road is 1.8 miles long.
2.25 + 1.8 = 4.05
4 tens, 0 tenths, 5 hundredths

Chapter Review/Test – Page No. 162

Question 12.
Bob and Ling are playing a number pattern game. Bob wrote the following sequence.
28.9, 26.8, 24.7, __, 20.5
What is the unknown term in the sequence?
_____

Answer:
26.8

Explanation:
Bob and Ling are playing a number pattern game. Bob wrote the following sequence.
28.9, 26.8, 24.7, __, 20.5
28.9 – 26.8 = 2.1
26.8 – 24.7 = 2.1
Every number is increased by 2.1
So, the unknown number is 24.7 + 2.1 = 26.8

Rafael bought 2.15 pounds of potato salad and 4.2 pounds of macaroni salad to bring to a picnic. For 13a–13c, select Yes or No to indicate whether each statement is true.

Question 13.
13a. Rounded to the nearest whole number, Rafael bought 2 pounds of potato salad.
i. Yes
ii. No

Answer:
i. Yes

Explanation:
2.15 pounds of potato salad
1 < 5 ;
So, Rounded to the nearest whole number is 2

Question 13.
13b. Rounded to the nearest whole number, Rafael bought 4 pounds of macaroni salad.
i. Yes
ii. No

Answer:
i. Yes

Explanation:
4.2 pounds of macaroni salad
2 < 5
So, Rounded to the nearest whole number is 4

Question 13.
13c. Rounded to the nearest tenth, Rafael bought 2.1 pounds of potato salad.
i. Yes
ii. No

Answer:
ii. No

Explanation:
2.15 pounds of potato salad
5 = 5 ;
So, Rounded to the nearest whole number is 2.2

Question 14.
The four highest scores on the floor exercise at a gymnastics meet were 9.675, 9.25, 9.325, and 9.5 points. Choose the numbers that make the statement true.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals Chapter Review/Test img 37
The lowest: _________
The highest: _________

Answer:
The lowest: 9.25
The highest: 9.75

Explanation:
Compare ones; All ones are the same.
Compare tenths; 9.75 has the highest number of tenths and 9.25 has the lowest number of tenths.
The lowest of these four scores was 9.25 points. The highest of these four scores was 9.75 points.

Chapter Review/Test – Page No. 163

Question 15.
Michelle records the value of one euro in U.S. dollars each day for her social studies project. The table shows the data she has recorded so far.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals Chapter Review/Test img 38
On which two days was the value of 1 euro the same when rounded to the nearest hundredth of a dollar?
Options:
a. Monday
b. Tuesday
c. Wednesday
d. Thursday

Answer:
a. Monday
c. Wednesday

Explanation:
Monday = 1.448
The digit in the hundredths place is 4. 8 > 5; So, the rounded number is 1.45
Tuesday = 1.443
The digit in the hundredths place is 4. 3 < 5; So, the rounded number is 1.44
Wednesday = 1.452
The digit in the hundredths place is 5. 2 < 5; So, the rounded number is 1.45
Thursday = 1.458
The digit in the hundredths place is 5. 8 > 5; So, the rounded number is 1.46

Question 16.
Miguel has $20. He spends $7.25 on a movie ticket, $3.95 for snacks, and $1.75 for bus fare each way. How much money does Miguel have left?
$ _____

Answer:
$7.05

Explanation:
Miguel has $20. He spends $7.25 on a movie ticket, $3.95 for snacks, and $1.75 for bus fare each way.
$7.25 + $3.95 + $1.75 = $12.95
$20 – $12.95 = $7.05

Question 17.
Yolanda’s sunflower plant was 64.34 centimeters tall in July. During August, the plant grew 18.2 centimeters.
Part A
Estimate the height of Yolanda’s plant at the end of August by rounding each value to the nearest whole number. Will your estimate be less than or greater than the actual height? Explain your reasoning.
_____ cm

Answer:
First, we want to round the number 64.34 to the nearest whole number.
1. We have to round this number to the molest tenth. To round the number to the nearest tenth we need to look at the digit in the hundredths place. So, as 4 < 5, the rounded number is 64.3.
2. We now have to round this number to the nearest one. lb round the number to the nearest one we need to look at the digit in the tenths place. So, as 3 < 5, the rounded number is 64.
Now, we have to round the number 18.2 to the nearest whole number.
1. We have to round this number to the nearest one. To round the number to the nearest one we need to look at the digit in the tenths place. So, as 2 <5, the rounded number is 18.
So, we now have to find the sum of these rounded values: 64 + 18 = 82. Therefore, the estimated height of Volanda’s plant at the and of August is: 82 centimeters.
The estimate is less than the actual height because rounded values are less than the actual values.

Question 17.
Part B
What was the exact height of the plant at the end of August? Was the estimate less than or greater than the exact value?
_____ cm

Answer:
The exact height of the plant is: 64.34 + 18.2
Add the hundredths first.
4 hundre.dths + 0 hundredths = 4 hundredths
Add the tenths.
3 tenths + 2 tenths = 5 tenths Add the ones. Regroup as nee.ded
Add the tens.
6 tens + 1 ten + 1 regrouped ten = 8 tens.
Therefore, the exact height is 64.34+ 18.2 = 82.54.
The estimate is less than the actual height.

Chapter Review/Test – Page No. 164

Question 18.
Oscar ran the 100-yard dash in 12.41 seconds. Jesiah ran the 100-yard dash in 11.85 seconds. How many seconds faster was Jesiah’s time than Oscar’s time?
_____ second(s)

Answer:
0.56 seconds

Explanation:
Oscar ran the 100-yard dash in 12.41 seconds. Jesiah ran the 100-yard dash in 11.85 seconds.
12.41 – 11.85 = 0.56 seconds.
Jesiah’s time is 0.56 seconds faster than Oscar’s time.

Question 19.
Choose the value that makes the statement true.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals Chapter Review/Test img 39
Type below:
_________

Answer:
2 hundredths and 5 thousandths

Explanation:
1.025
(1 x 1) + (0 x \(\frac{1}{10}\)) + (2 x \(\frac{1}{100}\)) + (5 x \(\frac{1}{1000}\))
2 x \(\frac{1}{100}\) = 2 hundredths
5 x \(\frac{1}{1000}\) = 5 thousandths
In the number 1.025, the value of the digit 2 is 2 hundredths, and the value of the digit 5 is 5 thousandths.

Question 20.
Troy and Lazetta are solving the following word problem. Rosalie’s cat weights 9.8 pounds. Her dog weighs 25.4 pounds. What is the weight of both animals combined. Troy sets up his problem as 9.8 + 25.4. Lazetta sets up her problem as 25.4 + 9.8. Who is correct? Explain your answer and solve the problem.
_________

Answer:
Troy and Lazetta are solving the following word problem. Rosalie’s cat weighs 9.8 pounds. Her dog weighs 25.4 pounds.
9.8 + 25.4
Add tenths 8 + 4 = 12; regroup
Add ones 9 + 5 + 1 regrouped one = 15 ones; regroup
Add tens 0 + 2 + 1 regrouped ten = 3 tens.
35.2
Lazetta: 25.4 + 9.8 = 35.2
Therefore, the answer is 25.4 + 9.8 = 35.2
The weight of both animals combined is 35.2 pounds. So, both were right.

Question 21.
Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals Chapter Review/Test img 40
Type below:
_________

Answer:
0.084 and 8.4

Explanation:
0.84 is 10 times as much as
0.84 = 10S
S = 0.84/10 = 0.084
0.84 is 1/10 of
0.84 = 1/10 x S
S = 0.84 x 10 = 8.4
So, from the given answers, 0.84 is 10 times as much as 0.084 and 0.84 is 1/10 of 8.4

Conclusion:

Get the Go Math Grade 5 Answer Key Chapter 3 Add and Subtract Decimals PDF. Download Go Math Grade 5 Answer Key PDF for free. New ways of learning will make your life easier with the best practice. Quick learning and easy understanding will come with the Go Math Grade 5 Chapter 3 Solution Key. Refer to our Go math practice books and question banks for the fast way of learning. We developed the Go Math answer key to all levels of students. Every student can easily understand the math and love the math after practicing with the Go Math answer key.

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Lesson 1: Algebra • Multiplication Patterns with Decimals

Lesson 2: Investigate • Multiply Decimals and Whole Numbers

Lesson 3: Multiplication with Decimals and Whole Numbers

Lesson 4: Multiply Using Expanded Form

Lesson 5: Problem Solving • Multiply Money

Mid-Chapter Checkpoint

Lesson 6: Investigate • Decimal Multiplication

Lesson 7: Multiply Decimals

Lesson 8: Zeros in the Product

Review/Test

Share and Show – Page No. 165

Complete the pattern.

Question 1.
100 × 17.04 = 17.04
101 × 17.04 = 17.04
102 × 17.04 = 17.04
103 × 17.04 = 17.04
_____

Answer:
100 × 17.04 = 17.04
101 × 17.04 = 170.4
102 × 17.04 = 1,704
103 × 17.04 =17,040

Explanation:
As you multiply by increasing powers of 10, then the position of the decimal point moves towards the right side.
100 × 17.04 = 1 x 17.04 = 17.04
101 × 17.04 = 10 x 17.04 = 170.4
102 × 17.04 = 100 x 17.04 = 1,704
103 × 17.04 = 1000 x 17.04 = 17,040

Complete the pattern.

Question 2.
1 × 3.19 = _____
10 × 3.19 = _____
100 × 3.19 = _____
1,000 × 3.19 = _____

Answer:
1 × 3.19 = 3.19
10 × 3.19 = 31.9
100 × 3.19 = 319
1,000 × 3.19 = 3,190
As you multiply by increasing powers of 10, then the position of the decimal point moves towards the right side.

Go Math 5th Grade 4.1 Answer Key Question 3.
45.6 × 100 = _____
45.6 × 101 = _____
45.6 × 102 = _____
45.6 × 103 = _____

Answer:
45.6 × 100 = 45.6
45.6 × 101 = 456
45.6 × 102 = 4,560
45.6 × 103 = 45,600

Explanation:
As you multiply by increasing powers of 10, then the position of the decimal point moves towards the right side.
45.6 × 100 = 45.6 x 1 = 45.6
45.6 × 101 = 45.6 x 10 = 456
45.6 × 102 = 45.6 x 100 = 4,560
45.6 × 103 = 45.6 x 1000 = 45,600

Question 4.
1 × 6,391 = _____
0.1 × 6,391 = _____
0.01 × 6,391 = _____

Answer:
1 × 6,391 = 6,391
0.1 × 6,391 = 639.1
0.01 × 6,391 = 63.91
As you multiply by decreasing powers of 10, the position of the decimal point moves towards the left side

On Your Own

Complete the pattern.

Question 5.
1.06 × 1 = _____
1.06 × 10 = _____
1.06 × 100 = _____
1.06 × 1,000 = _____

Answer:
1.06 × 1 = 1.06
1.06 × 10 = 10.6
1.06 × 100 = 106
1.06 × 1,000 = 1,060
As you multiply by increasing powers of 10, then the position of the decimal point moves towards the right side.

Question 6.
1 × 90 = _____
0.1 × 90 = _____
0.01 × 90 = _____

Answer:
1 × 90 = 90
0.1 × 90 = 9.0 = 9
0.01 × 90 = 0.9

Explanation:
As you multiply by decreasing powers of 10, the position of the decimal point moves towards the left side
1 × 90 = 90
0.1 × 90 = 9.0
0.01 × 90 = 0.90

Question 7.
100 × $0.19 = $ _____
101 × $0.19 = $ _____
102 × $0.19 = $ _____
103 × $0.19 = $ _____

Answer:
100 × $0.19 = $ 0.19
101 × $0.19 = $ 1.9
102 × $0.19 = $ 19
103 × $0.19 = $ 190

Explanation:
As you multiply by increasing powers of 10, then the position of the decimal point moves towards the right side.
100 × $0.19 = $ 0.19
101 × $0.19 = $ 1.9
102 × $0.19 = $ 19
103 × $0.19 = $ 190

Go Math Lesson 4.1 5th Grade Question 8.
580 × 1 = _____
580 × 0.1 = _____
580 × 0.01 = _____

Answer:
580 × 1 = 580
580 × 0.1 = 58
580 × 0.01 = 5.8

Explanation:
As you multiply by increasing powers of 10, then the position of the decimal point moves towards the right side.
580 × 1 = 580
580 × 0.1 = 58.0 = 58
580 × 0.01 = 5.8

Question 9.
100 × 80.72 = _____
101 × 80.72 = _____
102 × 80.72 = _____
103 × 80.72 = _____

Answer:
100 × 80.72 = 80.72
101 × 80.72 = 807.2
102 × 80.72 = 8,072
103 × 80.72 = 80,720

Explanation:
As you multiply by decreasing powers of 10, the position of the decimal point moves towards the left side
100 × 80.72 = 80.72
101 × 80.72 = 807.2
102 × 80.72 = 8,072
103 × 80.72 = 80,720

Question 10.
1 × 7,230 = _____
0.1 × 7,230 = _____
0.01 × 7,230 = _____

Answer:
1 × 7,230 = 7,230
0.1 × 7,230 = 723
0.01 × 7,230 = 72.3

Explanation:
As you multiply by increasing powers of 10, then the position of the decimal point moves towards the right side.
1 × 7,230 = 7,230
0.1 × 7,230 = 723.0 = 723
0.01 × 7,230 = 72.3

Algebra Find the value

of n.

Question 11.
n × $3.25 = $325.00
n = _____

Answer:
n = 100

Explanation:
n × $3.25 = $325.00
n × $3.25 = $325.00
n x $325 x $0.01 = $325.00
n x $325 x $1/100 = $325.00
n =  $325.00/$325 x 100
n = 1 x 100 = 100

Question 12.
0.1 × n = 89.5
n = _____

Answer:
n = 895

Explanation:
0.1 × n = 89.5
1/10 x n = 895 x 0.1
n = 895 x 0.1 x 10
n = 895

Go Math Grade 5 Chapter 4 Lesson 4.3 Answer Key Question 13.
103 × n = 630
n = _____

Answer:
n = 0.63

Explanation:
103 × n = 630
1000 x n = 630
n = 630 x 1/1000
n = 630 x 0.001
n = 0.63

Problem Solving – Page No. 166

What’s the Error?

Question 14.
Kirsten is making lanyards for a convention. She needs to make 1,000 lanyards and knows that 1 lanyard uses 1.75 feet of cord. How much cord will Kirsten need?
Go Math Grade 5 Answer Key Chapter 4 Multiply Decimals img 1
Kirsten’s work is shown below.
1 × 1.75 = 1.75
10 × 1.75 = 10.75
100 × 1.75 = 100.75
1,000 × 1.75 = 1,000.75

Find and describe Kirsten’s error. Solve the problem using the correct pattern.
As you can see from the given pattern, by multiplying 1.75 by different multiplicands, she just replaced the whole number, the number before the decimal point (in our use number 1), with belonging.
But this is not the way we multiply decimal numbers with different powers of number 10.
1 x 1.75= 1.75
10 x 1.75= 17.5
100 x 1.75= 175
1,000 x 1.75= 1,750

So, Kirsten needs ______ feet of cord to make 1,000 lanyards.
Describe how Kirsten could have solved the problem without writing out the pattern needed.
Type below:
________

Answer:
Kirsten needs 1,750 feet of cord to make 1,000 lanyards.
that decimal point moves one Noce M to the right for each increasing power of 10. So, the answer is 1,750 feet.

Share and Show – Page No. 167

Use the decimal model to find the product.

Question 1.
5 × 0.06 =
Go Math Grade 5 Answer Key Chapter 4 Multiply Decimals img 2
_____

Answer:
5 × 0.06 = 0.3
Go Math Grade 5 Answer Key Chapter 4 Multiply Decimals img 2

Explanation:
The picture shows that 5 groups of 6 hundredths.
0.06 = 6 hundredths
Each square box shows 1/ 100.
So, shade 6 boxes 5 times to get the product.
Count the number of boxes shaded. There are 30 hundredths are shaded = 0.30 = 0.3
5 × 0.06 = 0.3

Question 2.
2 × 0.38 =
_____

Answer:
2 × 0.38 = 0.76
grade 5 chapter 4 Multiply Decimals 167 image 1

Explanation:
The picture shows 2 groups of 38 hundredths.
0.38 = 38 hundredths
Each square box shows 1/ 100.
So, shade 38 boxes 2 times to get the product. 38 hundredths + 38 hundredths = 76 hundredths = 0.76.

Chapter 4 Extra Practice Lesson 4.2 Answer Key Question 3.
4 × 0.24 =
_____

Answer:
4 × 0.24 = 0.96
grade 5 chapter 4 Multiply Decimals 167 image 2

Explanation:
4 groups of 24 hundredths
Each square box shows 1/ 100.
So, shade 24 boxes 4 times to get the product. 24 hundredths + 24 hundredths + 24 hundredths + 24 hundredths = 96 hundredths = 0.96.

Find the product. Draw a quick picture.

Question 4.
4 × 0.6 =
_____

Answer:
4 × 0.6 = 2.4
grade 5 chapter 4 Multiply Decimals 168 image 1

Explanation:
4 × 0.6
4 groups of 6-tenths
0.6 + 0.6 + 0.6 + 0.6 = 2.4
4 × 0.6 = 2.4

Question 5.
2 × 0.67 =
_____

Answer:
2 × 0.67 = 1.34
grade 5 chapter 4 Multiply Decimals 168 image 2

Explanation:
2 × 0.67
2 groups of 67 hundredths
0.67 + 0.67 = 1.34
2 × 0.67 = 1.34

Question 6.
3 × 0.62 =
_____

Answer:
3 × 0.62 = 1.86
grade 5 chapter 4 Multiply Decimals 168 image 3

Explanation:
3 × 0.62
3 groups of 62 hundredths
0.62 + 0.62 + 0.62 = 1.86
3 × 0.62 = 1.86

Question 7.
4 × 0.32 =
_____

Answer:
4 × 0.32 = 1.28
grade 5 chapter 4 Multiply Decimals 168 image 4

Explanation:
4 × 0.32
4 groups of 32 hundredths
0.32 + 0.32 + 0.32 + 0.32 = 1.28
4 × 0.32 = 1.28

Go Math Grade 5 Chapter 4 Review/Test Answer Key Question 8.
Describe how you solved Exercise 7 using place value and renaming.
Type below:
________

Answer:
4 × 0.32
4 groups of 32 hundredths
There are 32 hundredths.
32 hundredths there are 30 tenths and 2 hundredths.
Combine the tenths and rename.
2 + 2 + 2 + 2 = 8
Combine the tenths and rename.
There are 3-tenths.
3 + 3 + 3 + 3 = 12; 2 tenths and 1 tens
Cross out the tenths you renamed.
Combine the ones and rename them.
0 + 0 + 0 + 0 + 1 = 1
1.28
4 × 0.32 = 1.28

Problem Solving – Page No. 168

Use the table for 9–11.
Go Math Grade 5 Answer Key Chapter 4 Multiply Decimals img 3

Question 9.
Each day a bobcat drinks about 3 times as much water as a Canada goose drinks. How much water can a bobcat drink in one day?
_____ liter

Answer:
0.72 liters

Explanation:
Each day a bobcat drinks about 3 times as much water as a Canada goose drinks.
Canada goose = 0.24 liters
bobcat drinks = 3 x 0.24
3 x 0.24 = 0.72 liters

Question 10.
River otters drink about 5 times as much water as a bald eagle drinks in a day. How much water can a river otter drink in one day?
_____ liter

Answer:
0.8 liter

Explanation:
River otters drink about 5 times as much water as a bald eagle drink in a day.
Bald Eagle drinks 0.16 liters
5 times as 0.16 liters = 5 x 0.16 = 0.8 liter

Question 11.
Explain how you could use a quick picture to find the amount of water that a cat drinks in 5 days.
Type below:
________

Answer:
grade 5 chapter 4 Multiply Decimals 168 image 5

Explanation:
Cat drinks 0.15 liters of water in a day.
In 5 days, 5 x 0.15 = 0.75

Chapter 4 Review Test 5th Grade Answer Key Question 12.
Test Prep Jared has a parakeet that weighs 1.44 ounces. Susie has a Senegal parrot that weighs 3 times as much as Jared’s parakeet. How many ounces does Susie’s parrot weigh?
Options:
a. 0.32 ounce
b. 0.43 ounce
c. 4.32 ounces
d. 43.2 ounces

Answer:
c. 4.32 ounces

Explanation:
Jared has a parakeet that weighs 1.44 ounces. Susie has a Senegal parrot that weighs 3 times as much as Jared’s parakeet.
Susie’s parrot weigh 3 x 1.44 ounces = 4.32 ounces

Share and Show – Page No. 171

Place the decimal point in the product.

Question 1.
6.81
×   7
———-
4767
Think: The place value of the decimal factor is a hundredths.

Answer:
6.81 x 7 = 47.67

Explanation:
6.81 x 7 = 7 x 6.81
7 x (6 + 0.81) = (7 x 6) + (7 x 0.81) = 42 + 5.67 = 47.67

Question 2.
3.7
× 2
———-
74
_____

Answer:
7.4

Explanation:
3.7 x 2
3.7 x 10 = 37
37 x 2 = 74
37 x 0.1 = 3.7
74 x 0.1 = 7.4

Go Math 5th Grade 4.3 Answer Key Question 3.
19.34
×    5
———-
9670
_____

Answer:
96.7

Explanation:
19.34 x 100 = 1934
1934 x 5 = 9670
1934 x 0.01 = 19.34
9670 x 0.01 = 96.7

Find the product.

Question 4.
6.32
×  3
———-
_____

Answer:
18.96

Explanation:
6.32 x 100 = 632
632 x 3 = 1896
632 x 0.01 = 6.32
1896 x 0.01 = 18.96

Question 5.
4.5
× 8
———-
_____

Answer:
36

Explanation:
4.5 x 10 = 45
45 x 8 = 360
45 x 0.1 = 4.5
360 x 0.1 = 36.0

Question 6.
40.7
×  5
———-
_____

Answer:
203.5

Explanation:
40.7 x 10 = 407
407 x 5 = 2035
407 x 0.1 = 40.7
2035 x 0.1 = 203.5

On Your Own

Find the product.

Question 7.
4.93
×   7
———-
_____

Answer:
34.51

Explanation:
7 x 3 = 21 hundredths; 2 tenths and 1 hundredths
7 x 9 = 63 tenths; 63 + 2 tenths = 65 tenths; 6 ones and 5 tenths
4 x 7 = 28; 28 + 6 = 34 ones;
34.51

Question 8.
8.2
× 6
———-
_____

Answer:
49.2

Explanation:
6 x 2 = 12 tenths; 1 ones and 2 tenths
6 x 8 = 48; 48 + 1 = 49 ones
49.2

Go Math 5th Grade Lesson 4.3 Homework Answers Question 9.
0.49
×   4
———-
_____

Answer:
1.96

Explanation:
9 x 4 = 36 hundredths; 3 tenths and 6 hundredths
4 x 4 = 16 tenths; 16 + 3 tenths = 19 tenths; 1 ones and 9 tenths
4 x 0 = 0; 0 + 1 = 1ones;
1.96

Question 10.
9.08
×   9
———-
_____

Answer:
81.72

Explanation:
9 x 8 = 72 hundredths; 7 tenths and 2 hundredths
9 x 0 = 0 tenths; 0 + 7 tenths = 7 tenths; 7 tenths
9 x 9 = 81; 81
81.72

Question 11.
7.55
×  8
———-
_____

Answer:
60.4

Explanation:
8 x 5 = 40 hundredths; 4 tenths and 0 hundredths
8 x 5 = 40 tenths; 40 + 4 tenths = 44 tenths; 4 ones and 4 tenths
8 x 7 = 56 ones; 56 + 4 = 60 ones
60.40 = 60.4

Question 12.
15.37
×    5
———-
_____

Answer:
76.85

Explanation:
5 x 7 = 35 hundredths; 3 tenths and 5 hundredths
5 x 3 = 15 tenths; 15 + 3 tenths = 18 tenths; 1 ones and 8 tenths
5 x 5 = 25 ones; 25 + 1 = 26 ones; 2 hundreds and 6 ones
5 x 1 = 5 hundreds; 5 + 2 = 7 hundreds
76.85

Practice: Copy and Solve Find the product.

Question 13.
8 × 7.2 = _____

Answer:
8 × 7.2 = 57.6

Explanation:
8 × 7.2 = 8 x (7 + 0.2) = (8 x 7) + (8 x 0.2) = 56 + 1.6 = 57.6

Question 14.
3 × 1.45 = _____

Answer:
3 × 1.45 = 4.35

Explanation:
3 x 1.45 = 3 x (1 + 0.45) = (3 x 1) + (3 x 0.45) = 3 + 1.35 = 4.35

Question 15.
9 × 8.6 = _____

Answer:
9 × 8.6 = 77.4

Explanation:
9 × 8.6 = 9 x (8 + 0.6) = (9 x 8) + (9 x 0.6) = 72 + 5.4 = 77.4

Question 16.
6 × 0.79 = _____

Answer:
6 × 0.79 = 4.74

Explanation:
6 x 0.79 = 4.74

Question 17.
4 × 9.3 = _____

Answer:
4 × 9.3 = 37.2

Explanation:
4 × 9.3 = 4 x (9 + 0.3) = (4 x 9) + (4 x 0.3) = 36 + 1.2 = 37.2

Go Math Grade 5 Chapter 4 Test Pdf Question 18.
7 × 0.81 = _____

Answer:
7 × 0.81 = 5.67

Explanation:
7 × 0.81 = 5.67

Question 19.
6 × 2.08 = _____

Answer:
6 × 2.08 = 12.48

Explanation:
6 × 2.08 = 6 x (2 + 0.08) = (6 x 2) + (6 x 0.08) = 12 + 0.48 = 12.48

Question 20.
5 × 23.66 = _____

Answer:
5 × 23.66 = 118.3

Explanation:
5 × 23.66 = 5 x (23 + 0.66) = (5 x 23) + (5 x 0.66) = 115 + 3.3 = 118.3

Problem Solving – Page No. 172

Use the table for 21–23.
Go Math Grade 5 Answer Key Chapter 4 Multiply Decimals img 4

Question 21.
Sari has a bag containing 6 half dollars. What is the weight of the half dollars in Sari’s bag?
_____ grams

Answer:
68.04 grams

Explanation:
Sari has a bag containing 6 half dollars.
Half dollars = 11.34 grams
6 x 11.34 = 68.04 grams
The weight of the half dollars in Sari’s bag is 68.04 grams.

Question 22.
Felicia is running a game booth at a carnival. One of the games requires participants to guess the weight, in grams, of a bag of 9 dimes. What is the actual weight of the dimes in the bag?
_____ grams

Answer:
20.43 grams

Explanation:
Felicia is running a game booth at a carnival. One of the games requires participants to guess the weight, in grams, of a bag of 9 dimes.
9 x 2.27 grams = 20.43 grams

Question 23.
Chance has $2 in quarters. Blake has $5 in dollar coins. Whose coins have the greatest weight? Explain.
_________

Answer:
Dollar coins has the greatest weight than quarters.

Explanation:
$2 means 4 quarters = 4 x 5.67 = 22.68
$5 in dollar coins = 5 x 8.1 = 40.5
Dollar coins has the greatest weight than quarters.

Question 24.
Julie multiplies 6.27 by 7 and claims the product is 438.9. Explain without multiplying how you know Julie’s answer is not correct. Find the correct answer.
Type below:
_________

Answer:
6.27 has two decimal digits
438.9 has one decimal digit
Therefore, Julie’s answer is not correct.
6.27 x 7 = 43.89

Question 25.
Test Prep Every day on his way to and from school, Milo walks a total of 3.65 miles. If he walks to school 5 days, how many miles will Milo have walked?
_____ miles

Answer:
18.25 miles

Explanation:
Milo walks a total of 3.65 miles.
If he walks to school 5 days, 5 x 3.65 = 18.25 miles

Share and Show – Page No. 175

Draw a model to find the product.

Question 1.
19 × 0.75 =
Go Math Grade 5 Answer Key Chapter 4 Multiply Decimals img 5
_____

Answer:
grade 5 chapter 4 Multiply Decimals 175 image 1
14.25

Explanation:
19 × 0.75
19 = 10 + 9
0.75 = 0.7 + 0.05
10 x 0.7 = 7
10 x 0.05 = 0.5
9 x 0.7 = 6.3
9 x 0.05 = 0.45
7 + 0.5 + 6.3 + 0.45 = 14.25
19 × 0.75 = 14.25

Go Math Grade 5 Lesson 4 Multiply Decimals by Decimals Question 2.
27 × 8.3 =
_____

Answer:
grade 5 chapter 4 Multiply Decimals 175 image 2
224.1

Explanation:
27 × 8.3 = 224.1
27 = 20 + 7
8.3 = 8 + 0.3
20 x 8 = 160
20 x 0.3 = 6
7 x 8 = 56
7 x 0.3 = 2.1
160 + 6 + 56 + 2.1 = 224.1

Find the product.

Question 3.
18 × 8.7 = _____

Answer:
18 × 8.7 = 156.6

Explanation:
8.7 x 10 = 87
18 x 87 = 1566
87 x 0.1 = 8.7
1566 x 0.1 = 156.6

Question 4.
23 × 56.1 = _____

Answer:
1290.3

Explanation:
56.1 x 10 = 561
561 x 23 = 12,903
561 x 0.1 = 56.1
12,903 x 0.1 = 1290.3

Question 5.
47 × 5.92 = _____

Answer:
278.24

Explanation:
5.92 x 100 = 592
592 x 47 = 27,824
592 x 0.01 = 5.92
27,824 x 0.01 = 278.24

On Your Own

Draw a model to find the product.

Question 6.
71 × 8.3 =
_____

Answer:
grade 5 chapter 4 Multiply Decimals 175 image 3
589.3

Explanation:
71 = 70 + 1
8.3 = 8 + 0.3
70 x 8 = 560
70 x 0.3 = 21
1 x 8 = 8
1 x 0.3 = 0.3
560 + 21 + 8 + 0.3 = 589.3

Question 7.
28 × 0.91 =
_____

Answer:
grade 5 chapter 4 Multiply Decimals 175 image 4
25.48

Explanation:
28 = 20 + 8
0.91 = 0.90 + 0.01
20 x 0.90 = 18
20 x 0.01 = 0.2
8 x 0.90 = 7.2
8 x 0.01 = 0.08
18 + 0.2 + 7.2 + 0.08 = 25.48

Find the product.

Question 8.
19 × 0.65 = _____

Answer:
19 × 0.65 = 12.35

Explanation:
0.65 x 100 = 65
65 x 19 = 1235
65 x 0.01 = 0.65
1235 x 0.01 = 12.35

Question 9.
34 × 98.3 = _____

Answer:
34 × 98.3 = 3342.2

Explanation:
98.3 x 10 = 983
983 x 34 = 33,422
983 x 0.1 = 98.3
33,422 x 0.1 = 3342.2

Lesson 4 Homework Practice Multiply Decimals by Decimals Answer Key Question 10.
26 × 16.28 = _____

Answer:
26 × 16.28 = 423.28

Explanation:
16.28 x 100 = 1628
1628 x 26 = 42,328
1628 x 0.01 = 16.28
42,328 x 0.01 = 423.28

UNLOCK the Problem – Page No. 176

Question 11.
While researching facts on the planet Earth, Kate learned that a true Earth day is about 23.93 hours long. How many hours are in 2 weeks on Earth?
Go Math Grade 5 Answer Key Chapter 4 Multiply Decimals img 6
a. What are you being asked to find?
Type below:
_________

Answer:
We need to find How many hours are in 2 weeks on Earth? 2 weeks x 23.93 hours per day?

Question 11.
b. What information do you need to know to solve the problem?
Type below:
_________

Answer:
Number of days in a week
Hours per day

Question 11.
c. Write an expression to represent the problem to be solved.
Type below:
_________

Answer:
2 weeks = 14 days
14 x 23.93 hours

Question 11.
d. Show the steps you used to solve the problem.
Type below:
_________

Answer:
335.02 hours

Explanation:
23.93 = 23.93 x 100 = 2393
2393 x 14 = 33,502
2393 x 0.01 = 23.93
33502 x 0.01 = 335.02

Question 11.
e. Complete the sentences.
On Earth, there are about _____ hours in a day, _____ days in 1 week, and _____ days in two weeks.
Since _____ × _____ = _____, there are about _____ hours in 2 weeks on Earth.
Type below:
_________

Answer:
On Earth, there are about 23.93 hours in a day,  7 days in 1 week, and 14 days in two weeks.
Since 23.93 × 14 = 335.02, there are about 335.02 hours in 2 weeks on Earth.

Question 12.
Michael’s favorite song is 3.19 minutes long. If he listens to the song 15 times on repeat, how long will he have listened to the same song?
_____ minutes

Answer:
47.85 minutes

Explanation:
Michael’s favorite song is 3.19 minutes long.
If he listens to the song 15 times, 15 x 3.19 = 47.85 minutes

Question 13.
Test Prep A car travels 56.7 miles in an hour. If it continues at the same speed, how far will the car travel in 12 hours?
Options:
a. 68.004 miles
b. 680.04 miles
c. 680.4 miles
d. 6,804 miles

Answer:
c. 680.4 miles

Explanation:
A car travels 56.7 miles in an hour.
In 12 hours, 12 x 56.7 = 680.4 hours

Share and Show – Page No. 179

Question 1.
Manuel collects $45.18 for a fundraiser. Gerome collects $18.07 more than Manuel. Cindy collects 2 times as much as Gerome. How much money does Cindy collect for the fundraiser?
First, draw a diagram to show the amount Manuel collects.
Then, draw a diagram to show the amount Gerome collects.
Next, draw a diagram to show the amount Cindy collects.
Finally, find the amount each person collects.
Cindy collects ______ for the fundraiser.
Type below:
_________

Answer:
Manuel collects $45.18 for a fundraiser. Gerome collects $18.07 more than Manuel. Cindy collects 2 times as much as Gerome.
grade 5 chapter 4 Multiply Decimals 179 image 1
Manuel: $45.18
Gerome: $45.18 + $18.07 = $63.25
Cindy: 2 x $63.25 = $126.5

Question 2.
What if Gerome collects $9.23 more than Manuel? If Cindy still collects 2 times as much as Gerome, how much money would Cindy collect?
Type below:
_________

Answer:
Gerome collects $9.23 more than Manuel
Manuel: $45.18
Gerome: $45.18 + $9.23 = $54.41
Cindy: 2 x $54.41 = $108.82

Question 3.
It costs $5.15 to rent a kayak for 1 hour at a local state park. The price per hour stays the same for up to 5 hours of rental. After 5 hours, the cost is decreased to $3.75 per hour. How much would it cost to rent a kayak for 6 hours?
$ ______

Answer:
$29.5

Explanation:
It costs $5.15 to rent a kayak for 1 hour at a local state park. The price per hour stays the same for up to 5 hours of rental. After 5 hours, the cost is decreased to $3.75 per hour.
For first 5 hours, $5.15
Next hour after 5 hours, it decreased to $3.75
For 6 hours, 5 x $5.15 + 1 x $3.75
5 x $5.15 = $25.75
1 x $3.75 = $3.75
$25.75 + $3.75 = $29.5

Go Math 5th Grade Lesson 5 Multiply Decimals Question 4.
Jenn buys a pair of jeans for $24.99. Her friend Karen spends $3.50 more for the same pair of jeans. Vicki paid the same price as Karen for the jeans but bought 2 pairs. How much did Vicki spend?
$ ______

Answer:
$56.98

Explanation:
Jenn buys a pair of jeans for $24.99.
Karen: $24.99 + $3.50 = $28.49
Vicky: 2 x $28.49 = $56.98

On Your Own – Page No. 180

Use the sign for 5–8.
Go Math Grade 5 Answer Key Chapter 4 Multiply Decimals img 7

Question 5.
Austin shops at Surfer Joe’s Surf Shop before going to the beach. He buys 2 T-shirts, a pair of board shorts, and a towel. If he gives the cashier $60, how much change will Austin get back?
$ ______

Answer:
$2.86

Explanation:
T-Shirt = $12.75
Board Shorts = $25.99
Sandals = $8.95
Towel = $5.65
Sunglasses = $15.50
Austin shops at Surfer Joe’s Surf Shop before going to the beach. He buys 2 T-shirts, a pair of board shorts, and a towel.
(2 x $12.75) + ($25.99) + $5.65 = $25.5 + $31.64 = $57.14
$60 – $57.14 = $2.86

Question 6.
Maria buys 3 T-shirts and 2 pairs of sandals at Surfer Joe’s Surf Shop. How much does Maria spend?
$ ______

Answer:
$56.15

Explanation:
Maria buys 3 T-shirts and 2 pairs of sandals at Surfer Joe’s Surf Shop.
3 x $12.75 = $38.25
2 x $8.95 = $17.9
$38.25 + $17.9 = $56.15

Question 7.
Nathan receives a coupon in the mail for $10 off of a purchase of $100 or more. If he buys 3 pairs of board shorts, 2 towels, and a pair of sunglasses, will he spend enough to use the coupon? How much will his purchase cost?
Type below:
_________

Answer:
$94.77

Explanation:
3 pairs of board shorts, 2 towels, and a pair of sunglasses
3 x $25.99 = $77.97
2 x $5.65 = $11.3
Sunglasses = $15.50
$77.97 + $11.3 + $15.50 = $104.77
$10 off of a purchase of $100 or more
$104.77 – $10 = $94.77

Go Math Grade 4 Chapter 4 Mid Chapter Checkpoint Answer Key Question 8.
Moya spends $33.90 on 3 different items. If she did not buy board shorts, which three items did Moya buy?
Type below:
_________

Answer:
T-Shirt, Towel, and Sunglasses

Explanation:
Moya spends $33.90 on 3 different items. If she did not buy board shorts,
T-Shirt = $12.75
Towel = $5.65
Sunglasses = $15.50

Question 9.
Test Prep At a donut shop in town, each donut costs $0.79. If Mr. Thomas buys a box of 8 donuts, how much will he pay for the donuts?
Options:
a. $6.32
b. $8.79
c. $63.20
d. $87.90

Answer:
a. $6.32

Explanation:
At a donut shop in town, each donut costs $0.79. If Mr. Thomas buys a box of 8 donuts, 8 x $0.79 = $6.32

Mid-Chapter Checkpoint – Page No. 181

Concepts and Skills

Question 1.
Explain how you can use a quick picture to find 3 × 2.7.
Type below:
________

Answer:
3 × 2.7 = 8.1;
As there are 8 ones and 1 tenth, we can draw eight square boxes and 1 line to represent 1 tenth.

Complete the pattern.

Question 2.
1 × 3.6 = _______
10 × 3.6 = _______
100 × 3.6 = _______
1000 × 3.6 = _______

Answer:
1 × 3.6 = 3.6
10 × 3.6 = 36
100 × 3.6 = 360
1000 × 3.6 = 3,600

Question 3.
100 × 17.55 = _______
101 × 17.55 = _______
102 × 17.55 = _______
103 × 17.55 = _______

Answer:
100 × 17.55 = 17.55
101 × 17.55 = 175.5
102 × 17.55 = 1755
103 × 17.55 = 17,550

Explanation:
100 × 17.55 = 1 x 17.55 = 17.55
101 × 17.55 = 10 x 17.55 = 175.5
102 × 17.55 = 100 x 17.55 = 1755
103 × 17.55 = 1000 x 17.55 = 17,550

Question 4.
1 × 29 = _______
0.1 × 29 = _______
0.01 × 29 = _______

Answer:
1 × 29 = 29
0.1 × 29 = 2.9
0.01 × 29 = 0.29

Find the product.

Question 5.
3.14
×   8
———–
_____

Answer:
25.12

Explanation:
8 x (3.14) = 8 x (3 + 0.14) = (8 x 3) + (8 x 0.14) = 24 + 1.12 = 25.12

Question 6.
17 × 0.67 = _____

Answer:
11.39

Explanation:
0.67 x 100 = 67
67 x 17 = 1139
67 x 0.01 = 0.67
1139 x 0.01 = 11.39

Question 7.
29 × 7.3 = _____

Answer:
211.7

Explanation:
29 × 7.3 = 29 x (7 + 0.3) = (29 x 7) + (29 x 0.3) = 203 + 8.7 = 211.7

Draw a diagram to solve.

Question 8.
Julie spends $5.62 at the store. Micah spends 5 times as much as Julie. Jeremy spends $6.72 more than Micah. How much money does each person spend?
Julie: $ _______
Micah: $ _______
Jeremy: $ _______

Answer:
grade 5 chapter 4 Multiply Decimals 181 image 1
Julie: $ 5.62
Micah spends 5 times as much as Julie = 5 x $5.62 = $28.1
Jeremy spends $6.72 more than Micah = $28.1 + $6.72 = $34.82

Mid-Chapter Checkpoint – Page No. 182

Question 9.
Sarah is cutting ribbons for a pep rally. The length of each ribbon needs to be 3.68 inches. If she needs 1,000 ribbons, what is the length of ribbon Sarah needs?
_____ inches

Answer:
3680 inches

Explanation:
Sarah is cutting ribbons for a pep rally. The length of each ribbon needs to be 3.68 inches.
If she needs 1,000 ribbons, 3.68 x 1,000 = 3680 inches

Question 10.
Adam is carrying books to the classroom for his teacher. Each book weighs 3.85 pounds. If he carries 4 books, how many pounds is Adam carrying?
_____ pounds

Answer:
15.4 pounds

Explanation:
Adam is carrying books to the classroom for his teacher. Each book weighs 3.85 pounds. If he carries 4 books, 4 x 3.85 = 15.4 pounds.

Question 11.
A car travels 54.9 miles in an hour. If the car continues at the same speed for 12 hours, how many miles will it travel?
_____ miles

Answer:
658.8 miles

Explanation:
A car travels 54.9 miles in an hour. If the car continues at the same speed for 12 hours, 12 x 54.9 = 658.8 miles

Question 12.
Charlie saves $21.45 each month for 6 months. In the seventh month, he only saved $10.60. How much money will Charlie have saved after 7 months?
$ __________

Answer:
$139.3

Explanation:
Charlie saves $21.45 each month for 6 months. In the seventh month, he only saved $10.60.
6 x $21.45 + $10.60 = $128.7 + $10.60 = $139.3

Share and Show – Page No. 185

Multiply. Use the decimal model.

Question 1.
0.8 × 0.4 =
Go Math Grade 5 Answer Key Chapter 4 Multiply Decimals img 8

Answer:
0.8 × 0.4 = 0.32
grade 5 chapter 4 Multiply Decimals 183 image 1

Explanation:
The shaded and crossed parts represent the product.
32 hundredths = 0.32

Question 2.
0.1 × 0.7 =
Go Math Grade 5 Answer Key Chapter 4 Multiply Decimals img 9
_____

Answer:
grade 5 chapter 4 Multiply Decimals 183 image 2
0.1 × 0.7 = 0.7

Explanation:
Count the number of overlapped boxes to find the product. 7 tenths = 0.7

Chapter 4 Go Math 5th Grade Lesson 4.6 Answer Key Question 3.
0.4 × 1.6 =
Go Math Grade 5 Answer Key Chapter 4 Multiply Decimals img 10
_____

Answer:
0.4 × 1.6 = 0.64
grade 5 chapter 4 Multiply Decimals 185 image 1

Explanation:
Count the red line crossed boxes to get the product.
4 x 16 = 64
0.1 x 0.1 = 0.01
64 x 0.01 = 0.64

Question 4.
0.3 × 0.4 =
Go Math Grade 5 Answer Key Chapter 4 Multiply Decimals img 11
_____

Answer:
0.3 × 0.4 = 0.12
grade 5 chapter 4 Multiply Decimals 190 image 2

Explanation:
3 x 4 = 12
0.1 x 0.1 = 0.01
12 x 0.01 = 0.12

Question 5.
0.9 × 0.6 =
Go Math Grade 5 Answer Key Chapter 4 Multiply Decimals img 12
_____

Answer:
0.9 x 0.6 = 0.54
grade 5 chapter 4 Multiply Decimals 190 image 4

Explanation:
9 x 6 = 54
0.1 x 0.1 = 0.01
54 x 0.01 = 0.54

Question 6.
0.5 × 1.2 =
Go Math Grade 5 Answer Key Chapter 4 Multiply Decimals img 13
_____

Answer:
0.5 × 1.2 = 0.60
grade 5 chapter 4 Multiply Decimals 185 image 2

Explanation:
Count the red line crossed boxes to get the product.
5 x 12 = 60
0.1 x 0.1 = 0.01
60 x 0.01 = 0.60

Question 7.
0.8 × 0.9 =
Go Math Grade 5 Answer Key Chapter 4 Multiply Decimals img 14
_____

Answer:
0.8 × 0.9 = 0.72
grade 5 chapter 4 Multiply Decimals 190 image 3

Explanation:
8 x 9 = 72
0.1 x 0.1 = 0.01
72 x 0.01 = 0.72

Question 8.
0.5 × 0.3 =
Go Math Grade 5 Answer Key Chapter 4 Multiply Decimals img 15
_____

Answer:
0.5 × 0.3 = 0.15
grade 5 chapter 4 Multiply Decimals 190 image 1

Explanation:
5 x 3 = 15
0.1 x 0.1 = 0.01
15 x 0.01 = 0.15

Question 9.
0.5 × 1.5 =
Go Math Grade 5 Answer Key Chapter 4 Multiply Decimals img 16
_____

Answer:
0.5 × 1.5 = 0.75
grade 5 chapter 4 Multiply Decimals 185 image 3

Explanation:
Count the red line crossed boxes to get the product.
5 x 15 = 75
0.1 x 0.1 = 0.01
75 x 0.01 = 0.75

Go Math Lesson 4.6 Answer Key 5th Grade Question 10.
Explain why when you multiply and find one-tenth of one-tenth, it is equal to one hundredth.
Type below:
_________

Answer:
When you do one-tenth of one-tenth, it is one-tenth over 10 —-> (1/10) /10
So, you can consider it as (1/10) / (10/1). This is only for simplicity.
Now, you have to multiply the denominator of the fraction in the numerator with the numerator of the fraction in the denominator i.e., 10 with 10 and this comes in the denominator only.
and numerator of the fraction in the numerator with the denominator of the fraction in the denominator i.e., 1 with 1.
So, you get, (1*1) / (10*10) = 1/100
This is again the 10th part of one-tenth OR 100th part of 1 = one hundredth

Problem Solving – Page No. 186

Sense or Nonsense?

Question 11.
Randy and Stacy used models to find 0.3 of 0.5. Both Randy’s and Stacy’s models are shown below. Whose model makes sense? Whose model is nonsense? Explain your reasoning below each model. Then record the correct answer.
Randy’s Model
Go Math Grade 5 Answer Key Chapter 4 Multiply Decimals img 17

Stacy’s Model
Go Math Grade 5 Answer Key Chapter 4 Multiply Decimals img 18
0.3 × 0.5 =
• For the answer that is nonsense, describe the error the student made.
_________ model is correct

Answer:
Randy’s Model is correct. Stacy’s Model makes nonsense.
Because Stacy’s Model is showing 0.10 x 0.8 which is not equal to 0.3 x 0.5

Explanation:
Randy and Stacy used models to find 0.3 of 0.5
0.3 x 0.5 = 0.15

Share and Show – Page No. 188

Place the decimal point in the product.

Question 1.
3.62
× 1.4
———-

5068
Think: A hundredth is being multiplied by a tenth. Use the pattern 0.01 × 0.1.
___

Answer:
5.068

Explanation:
3.62 x 100 = 362 = 362 x 0.01
1.4 x 10 = 14 = 14 x 0.1
362 x 14 = 5068
0.01 x 0.1 = 0.001
5068 x 0.001 = 5.068

Question 2.
6.8
×1.2
———-
816
_____

Answer:
8.16

Explanation:
6.8 x 10 = 68 = 68 x 0.1
1.2 x 10 = 12 = 12 x 0.1
68 x 12 = 816
0.1 x 0.1 = 0.01
816 x 0.01 = 8.16

Find the product.

Question 3.
0.9
× 0.8
———-
_____

Answer:
0.72

Explanation:
0.9 x 10 = 9 = 9 x 0.1
0.8 x 10 = 8 = 8 x 0.1
9 x 8 = 72
0.1 x 0.1 = 0.01
72 x 0.01 = 0.72

Question 4.
84.5
×  5.5
———-
_____

Answer:
464.75

Explanation:
84.5 x 10 = 845 = 845 x 0.1
5.5 x 10 = 55 = 55 x 0.1
845 x 55 = 46475
0.1 x 0.1 = 0.01
46475 x 0.01 = 464.75

Lesson 4.7 Answer Key Chapter 4 Go Math 5th Grade Question 5.
2.39
×2.7
———-
_____

Answer:
6.453

Explanation:
2.39 x 100 = 239 = 239 x 0.01
2.7 x 10 = 27 = 27 x 0.1
239 x 27 = 6453
0.01 x 0.1 = 0.001
6453 x 0.001 = 6.453

On Your Own – Page No. 189

Find the product.

Question 6.
7.9
× 3.4
———-
_____

Answer:
26.86

Explanation:
7.9 x 10 = 79 = 79 x 0.1
3.4 x 10 = 34 = 34 x 0.1
79 x 34 = 2686
0.1 x 0.1 = 0.01
2686 x 0.01 = 26.86

Question 7.
9.2
×5.6
———-
_____

Answer:
51.52

Explanation:
9.2 x 10 = 92 = 92 x 0.1
5.6 x 10 = 56 = 56 x 0.1
92 x 56 = 5152
0.1 x 0.1 = 0.01
5152 x 0.01 = 51.52

Question 8.
3.45
× 9.7
———-
_____

Answer:
33.465

Explanation:
3.45 x 100 = 345 = 345 x 0.01
9.7 x 10 = 97 = 97 x 0.1
345 x 97 = 33465
0.01 x 0.1 = 0.001
33465 x 0.001 = 33.465

Question 9.
45.3
× 0.8
———-
_____

Answer:
36.24

Explanation:
45.3 x 10 = 453 = 453 x 0.1
0.8 x 10 = 8 = 8 x 0.1
453 x 8 = 3624
0.1 x 0.1 = 0.01
3624 x 0.01 = 36.24

Question 10.
6.98
× 2.5
———-
_____

Answer:
17.450

Explanation:
6.98 x 100 = 698 = 698 x 0.01
2.5 x 10 = 25 = 25 x 0.1
698 x 25 = 17,450
0.01 x 0.1 = 0.001
17450 x 0.001 = 17.450

Question 11.
7.02
×3.4
———-
_____

Answer:
23.868

Explanation:
7.02 x 100 = 702 = 702 x 0.01
3.4 x 10 = 34 = 34 x 0.1
702 x 34 = 23868
0.01 x 0.1 = 0.001
23868 x 0.001 = 23.868

Question 12.
14.9
×0.35
———-
_____

Answer:
5.215

Explanation:
14.9 x 10 = 149 = 149 x 0.1
0.35 x 100 = 35 = 35 x 0.01
149 x 35 = 5215
0.1 x 0.01 = 0.001
5215 x 0.001 = 5.215

Question 13.
50.99
×  3.7
———-
_____

Answer:
188.663

Explanation:
50.99 x 100 = 5099 = 5099 x 0.01
3.7 x 10 = 37 = 37 x 0.1
5099 x 37 = 188663
0.01 x 0.1 = 0.001
188663 x 0.001 = 188.663

Question 14.
18.43
×  1.9
———-
_____

Answer:
35.017

Explanation:
18.43 x 100 = 1843 = 1843 x 0.01
1.9 x 10 = 19 = 19 x 0.1
1843 x 19 = 35017
0.01 x 0.1 = 0.001
35017 x 0.001 = 35.017

Practice: Copy and Solve Find the product.

Question 15.
3.4 × 5.2 = _____

Answer:
17.68

Explanation:
3.4 × 5.2
34 x 52 = 1768
0.1 x 0.1 = 0.01
1768 x 0.01 = 17.68

Question 16.
0.9 × 2.46 = _____

Answer:
2.214

Explanation:
9 x 246 = 2214
0.1 x 0.01 = 0.001
2214 x 0.001 = 2.214

Question 17.
9.1 × 5.7 = ____

Answer:
51.87

Explanation:
91 x 57 = 5187
0.1 x 0.1 = 0.01
5187 x 0.01 = 51.87

Question 18.
4.8 × 6.01 = _____

Answer:
28.848

Explanation:
48 x 601 = 28848
0.1 x 0.01 = 0.001
28848 x 0.001 = 28.848

Question 20.
7.6 × 18.7 = _____

Answer:
142.12

Explanation:
76 x 187 = 14212
0.1 x 0.1 = 0.01
14212 x 0.01 = 142.12

Question 21.
0.77 × 14.9 = _____

Answer:
114.73

Explanation:
77 x 149 = 11473
0.01 x 0.1 = 0.01
11473 x 0.01 = 114.73

Question 22.
3.3 × 58.14 = _____

Answer:
191.862

Explanation:
33 x 5814 = 191862
0.1 x 0.01 = 0.001
191862 x 0.001 = 191.862

Problem Solving – Page No. 190

Go Math Grade 5 Answer Key Chapter 4 Multiply Decimals img 19

Question 23.
Charlie has an adult Netherlands dwarf rabbit that weighs 1.2 kilograms. Cliff’s adult Angora rabbit weighs 2.9 times as much as Charlie’s rabbit. How much does Cliff’s rabbit weigh?
_____ kilograms

Answer:
3.48 kilograms

Explanation:
Charlie has an adult Netherlands dwarf rabbit that weighs 1.2 kilograms. Cliff’s adult Angora rabbit weighs 2.9 times as much as Charlie’s rabbit.
1.2 x 2.9 = 3.48 kilograms

Question 24.
John has pet rabbits in an enclosure that has an area of 30.72 square feet. The enclosure Taylor is planning to build for his rabbits will be 2.2 times as large as John’s. What will be the area of the enclosure Taylor is planning to build?
_____ square feet

Answer:
67.584 square feet

Explanation:
John has pet rabbits in an enclosure that has an area of 30.72 square feet. The enclosure Taylor is planning to build for his rabbits will be 2.2 times as large as John’s.
30.72 x 2.2 = 67.584 square feet

Question 25.
A zoo is planning a new building for the penguin exhibit. First, they made a model that was 1.3 meters tall. Then, they made a more detailed model that was 1.5 times as tall as the first model. The building will be 2.5 times as tall as the height of the detailed model. What will be the height of the building?
_____ meters

Answer:
4.875 meters

Explanation:
A zoo is planning a new building for the penguin exhibit. First, they made a model that was 1.3 meters tall. Then, they made a more detailed model that was 1.5 times as tall as the first model.
1.3 x 1.5 = 1.95
The building will be 2.5 times as tall as the height of the detailed model.
2.5 x 1.95 = 4.875 meters

Question 26.
Leslie and Paul both solved the multiplication problem 5.5 x 4.6. Leslie says the answer is 25.30. Paul says the answer is 25.3. Whose answer is correct? Explain your reasoning.
Type below:
_________

Answer:
Both answers are correct. Because 25.30 = 25.3. The zeros have no value after the decimal point of a number.

Explanation:
5.5 x 4.6
55 x 46 = 2530
0.1 x 0.1 = 0.01
2530 x 0.01 = 25.30 = 25.3

Question 27.
Test Prep A vine in Mr. Jackson’s garden is 3.6 feet long. When it is measured again, it is 2.1 times as long. How long is the vine?
Options:
a. 5.7 feet
b. 6.6 feet
c. 7.5 feet
d. 7.56 feet

Answer:
a. 5.7 feet

Explanation:
A vine in Mr. Jackson’s garden is 3.6 feet long. When it is measured again, it is 2.1 times as long.
3.6 + 2.1 = 5.7 feet

Share and Show – Page No. 193

Write zeros in the product.

Question 1.
0.05
× 0.7
———-

Answer:

Explanation:

□35
Think: Hundredths are multiplied by tenths. What should be the place value of the product?
_____

Answer:
0.035

Explanation:
5 x 7 = 35
0.01 x 0.1 = 0.001
35 x 0.001 = 0.035

Question 2.
0.2
× 0.3
———-
_____

Answer:
0.06

Explanation:
2 x 3 = 6
0.1 x 0.1 = 0.01
6 x 0.01 = 0.06

Question 3.
0.02
× 0.2
———-
_____

Answer:
0.004

Explanation:
2 x 2 = 4
0.01 x 0.1 = 0.001
4 x 0.001 = 0.004

Find the product.

Question 4.
$0.05
× 0.8
———-
$ _____

Answer:
$0.04

Explanation:
5 x 8 = 40
0.01 x 0.1 = 0.001
40 x 0.001 = 0.040 = 0.04

Question 5.
0.09
× 0.7
———-
_____

Answer:
0.063

Explanation:
9 x 7 = 63
0.01 x 0.1 = 0.001
63 x 0.001 = 0.063

Question 6.
0.2
× 0.1
———-
_____

Answer:
0.02

Explanation:
2 x 1 = 2
0.1 x 0.1 = 0.01
2 x 0.01 = 0.02

On Your Own

Find the product.

Question 7.
0.3
× 0.3
———-
_____

Answer:
0.09

Explanation:
3 x 3 = 9
0.1 x 0.1 = 0.01
9 x 0.01 = 0.09

Question 8.
0.05
× 0.3
———-
_____

Answer:
0.015

Explanation:
5 x 3 = 15
0.01 x 0.1 = 0.001
15 x 0.001 = 0.015

Question 9.
0.02
× 0.4
———-
_____

Answer:
0.008

Explanation:
2 x 4 = 8
0.01 x 0.1 = 0.001
8 x 0.001 = 0.008

Question 10.
$0.40
× 0.1
———-
$ _____

Answer:
$0.04

Explanation:
40 x 1 = 40
0.10 x 0.1 = 0.010
40 x 0.010 = 0.04

Go Math Chapter 4 Test 5th Grade Answer Key Question 11.
0.09
× 0.2
———-
_____

Answer:
0.018

Explanation:
9 x 2 = 18
0.01 x 0.1 = 0.001
18 x 0.001 = 0.018

Question 12.
$ 0.05
× 0.6
———-
_____

Answer:
$0.3

Explanation:
5 x 6 = 30
0.01 x 0.1 = 0.001
30 x 0.001 = 0.30 = 0.3

Question 13.
0.04
× 0.5
———-
_____

Answer:
0.020

Explanation:
4 x 5 = 20
0.01 x 0.1 = 0.001
20 x 0.001 = 0.020

Question 14.
0.06
× 0.8
———-
_____

Answer:
0.048

Explanation:
6 x 8 = 48
0.01 x 0.1 = 0.001
48 x 0.001 = 0.048

Algebra Find the value of n.

Question 15.
0.03 × 0.6 = n
n = _____

Answer:
n = 0.018

Explanation:
0.03 × 0.6 = n
0.018 = n
n = 0.018

Question 16.
n × 0.2 = 0.08
n = _____

Answer:
n = 0.4

Explanation:
n × 0.2 = 0.08
n = 0.08/0.2
n = 0.4

Question 17.
0.09 × n = 0.063
n = _____

Answer:
n = 0.7

Explanation:
0.09 × n = 0.063
n = 0.063/0.09
n = 0.7

Page No. 194

Question 18.
On an average day, a garden snail can travel about 0.05 miles. If a snail travels 0.2 times as far as the average distance in a day, how far can it travel?
Go Math Grade 5 Answer Key Chapter 4 Multiply Decimals img 20
a. What are you being asked to find?
Type below:
_________

Answer:
We need to find how far a snail travels on 0.2 times as far as the average distance in a day.

Question 18.
b. What information will you use to solve the problem?
Type below:
_________

Answer:
On an average day, a garden snail can travel about 0.05 miles.
0.2 times as far as the average distance in a day

Question 18.
c. How will you use multiplication and place value to solve the problem?
Type below:
_________

Answer:
0.2 x 0.05

Question 18.
d. Show how you will solve the problem.
Type below:
_________

Answer:
2 x 5 = 10
0.1 x 0.01 = 0.001
10 x 0.001 = 0.010 = 0.01

Question 18.
e. Fill in the bubble for the correct answer choice above.
Options:
a. 0.7 mile
b. 0.25 mile
c. 0.1 mile
d. 0.01 mile

Answer:
d. 0.01 mile

Question 19.
In a science experiment, Tania uses 0.8 ounces of water to create a reaction. She wants the next reaction to be 0.1 times the size of the previous reaction. How much water should she use?
Options:
a. 0.08 ounce
b. 0.09 ounce
c. 0.8 ounce
d. 0.9 ounce

Answer:
a. 0.08 ounce

Explanation:
In a science experiment, Tania uses 0.8 ounces of water to create a reaction. She wants the next reaction to be 0.1 times the size of the previous reaction.
0.8 x 0.1 = 0.08 ounce

Question 20.
Michael multiplies 0.2 by a number. He records the product as 0.008. What number did Michael use?
Options:
a. 0.016
b. 0.04
c. 0.28
d. 0.4

Answer:
b. 0.04

Explanation:
Michael multiplies 0.2 by a number. He records the product as 0.008.
0.2 x n = 0.008
n = 0.008/0.2
n = 0.04
Michael use 0.04

Chapter Review/Test – Page No. 195

Check Concepts

Question 1.
Explain how estimation helps you to place the decimal point when multiplying 3.9 × 5.3.
Type below:
_________

Answer:
3.9 × 5.3
39 x 53 = 2067
0.1 x 0.1 = 0.01
2067 x 0.01 = 20.67

Complete the pattern.

Question 2.
1 × 7.45 = _______
10 × 7.45 = _______
100 × 7.45 = _______
1,000 × 7.45 = _______

Answer:
1 × 7.45 = 7.45
10 × 7.45 = 74.5
100 × 7.45 = 745
1,000 × 7.45 = 7,450

Question 3.
100 × 376.2 = _______
101 × 376.2 = _______
102 × 376.2 = _______
103 × 376.2 = _______

Answer:
100 × 376.2 = 376.2
101 × 376.2 = 3,762
102 × 376.2 = 37,620
103 × 376.2 = 376,200

Explanation:
100 × 376.2 = 1 x 376.2 = 376.2
101 × 376.2 = 10 x 376.2 = 3,762
102 × 376.2 = 100 x 376.2 =  37,620
103 × 376.2 = 1000 x 376.2 = 376,200

Question 4.
1 × 191 = _______
0.1 × 191 = _______
0.01 × 191 = _______

Answer:
1 × 191 = 191
0.1 × 191 = 19.1
0.01 × 191 = 1.91_

Find the product.

Question 5.
5 × 0.89 = _____

Answer:
4.45

Explanation:
5 × 0.89
5 x 9 = 45 hundredths; 4 tenths and 5 hundredths
5 x 8 = 40 tenths; 40 + 4 tenths = 44 tenths; 4 ones and 4 tenths
5 x 0 = 0; 0 + 4 = 4 ones
4.45

Question 6.
9 × 2.35 = _____

Answer:
21.15

Explanation:
9 × 2.35
9 x 5 = 45 hundredths; 4 tenths and 5 hundredths
9 x 3 = 27 tenths; 27 + 4 tenths = 31 tenths; 3 ones and 1 tenth
9 x 2 = 18; 18 + 3 = 21 ones
21.15

Question 7.
23 × 8.6 = _____

Answer:
197.8

Explanation:
23 x 8.6
23 x 6 = 138 tenths; 13 ones and 8 tenths
23 x 8 = 184 ones; 184 + 13 = 197 ones
197.8

Question 8.
7.3 × 0.6 = _____

Answer:
4.38

Explanation:
73 x 6 = 438
0.1 x 0.1 = 0.01
438 x 0.01 = 4.38

Question 9.
0.09 × 0.7 = _____

Answer:
0.063

Explanation:
9 x 7 = 63
0.01 x 0.1 = 0.001
63 x 0.001 = 0.063

Question 10.
0.8 × $0.40 = $ _____

Answer:
$0.32

Explanation:
8 x 4 = 32
0.1 x 0.1 = 0.01
32 x 0.01 = 0.32

Draw a diagram to solve.

Question 11.
In January, Dawn earns $9.25 allowance. She earns 3 times as much in February. If during March, she earns $5.75 more than she did in February, how much allowance does Dawn earn in March?
$ _________

Answer:
$33.5

Explanation:
In January, Dawn earns $9.25 allowance.
February: 3 x $9.25 = $27.75
March: $27.75 + $5.75 = $33.5

Chapter Review/Test – Page No. 196

Fill in the bubble completely to show your answer.

Question 12.
Janet hikes a trail at a local forest each day. The trail is 3.6 miles long, and she has hiked 5 days in the past week. How many miles has Janet hiked in the past week?
Options:
A. 18 miles
B. 15.3 miles
C. 11 miles
D. 8.6 miles

Answer:
A. 18 miles

Explanation:
Janet hikes a trail at a local forest each day. The trail is 3.6 miles long, and she has hiked 5 days in the past week.
3.6 x 5 = 18 miles

Question 13.
To earn money for his vacation, Grayson works at a local shop on weekends. His job is to cut bricks of fudge into 0.25 pound squares. If he cuts 36 equal-sized squares on Saturday, how many pounds of fudge has Grayson cut?
Options:
A. 7.25 pounds
B. 9 pounds
C. 90 pounds
D. 72.5 pounds

Answer:
B. 9 pounds

Explanation:
To earn money for his vacation, Grayson works at a local shop on weekends. His job is to cut bricks of fudge into 0.25 pound squares. If he cuts 36 equal-sized squares on Saturday,
0.25 x 36 = 9 pounds

Question 14.
James is making a scale model of his bedroom. The model is 0.6 feet wide. If the actual room is 17.5 times as wide as the model, what is the width of James’s room?
Options:
A. 18.1 feet
B. 17.11 feet
C. 16.9 feet
D. 10.5 feet

Answer:
D. 10.5 feet

Explanation:
James is making a scale model of his bedroom. The model is 0.6 feet wide. If the actual room is 17.5 times as wide as the model,
0.6 x 17.5 = 10.5 feet

Question 15.
The cost of admission to the matinee showing at a movie theater is $6.75. If 7 friends want to see the matinee showing of their favorite movie, how much will it cost?
Options:
A. $11.25
B. $14.75
C. $42.75
D. $47.25

Answer:
D. $47.25

Explanation:
The cost of admission to the matinee showing at a movie theater is $6.75. If 7 friends want to see the matinee showing of their favorite movie,
7 x $6.75 = $47.25

Chapter Review/Test – Page No. 197

Fill in the bubble completely to show your answer.

Question 16.
On Friday, Gail talked for 38.4 minutes on her cell phone. On Saturday, she uses 5.5 times as many minutes as she did on Friday. How long does Gail talk on her cell phone on Saturday?
Options:
A. 2.112 minutes
B. 21.12 minutes
C. 211.2 minutes
D. 2,112 minutes

Answer:
C. 211.2 minutes

Explanation:
On Friday, Gail talked for 38.4 minutes on her cell phone. On Saturday, she uses 5.5 times as many minutes as she did on Friday.
38.4 x 5.5 = 211.2 minutes

Question 17.
Harry walks to a produce market to buy bananas. If a pound of bananas costs $0.49, how much will Harry pay for 3 pounds of bananas?
Options:
A. $1.47
B. $3.49
C. $5.49
D. $10.47

Answer:
A. $1.47

Explanation:
Harry walks to a produce market to buy bananas. If a pound of bananas costs $0.49,
For 3 pound, 3 x $0.49 = $1.47

Question 18.
At Anne’s Fabric Emporium, a yard of chiffon fabric costs $7.85. Lee plans to purchase 0.8 yard for a craft project. How much money will Lee spend on chiffon fabric?
Options:
A. $0.63
B. $6.28
C. $7.05
D. $8.65

Answer:
B. $6.28

Explanation:
At Anne’s Fabric Emporium, a yard of chiffon fabric costs $7.85. Lee plans to purchase 0.8 yards for a craft project.
0.8 x $7.85 = $6.28

Question 19.
Mitchell has $18.79 in his savings account. Jeremy has 3 times as much as Mitchell. Maritza has $4.57 more than Jeremy. How much money does Maritza have in her savings account?
Options:
A. $13.71
B. $32.50
C. $56.37
D. $60.94

Answer:
D. $60.94

Explanation:
Mitchell: $18.79
Jeremy: 3 x $18.79 = $56.37
Maritza: $56.37 + $4.57 = $60.94

Chapter Review/Test – Page No. 198

Constructed Response

Question 20.
A river otter eats about 0.15 times its weight in food each day. At the Baytown Zoo, the male river otter weighs 5 pounds. About how much food will the otter at the zoo consume each day? Explain how you found your answer.
_____ pounds

Answer:
0.75 pounds

Explanation:
A river otter eats about 0.15 times its weight in food each day. At the Baytown Zoo, the male river otter weighs 5 pounds.
0.15 x 5 = 0.75 pounds

Performance Task

Question 21.
The cost of admission to the Baytown Zoo is shown below. Use the table to answer the questions.
Go Math Grade 5 Answer Key Chapter 4 Multiply Decimals Chapter Review/Test img 21
A. A family of 2 adults and 1 child plans to spend the day at the Baytown Zoo. How much does admission for the family cost? Explain how you found your answer.
$ _____

Answer:
$39.75

Explanation:
Senior Citizen = $10.50
Adult = $15.75
Child = $8.25
A family of 2 adults and 1 child plans to spend the day at the Baytown Zoo.
(2 x $15.75) + $8.25
$31.5 + $8.25 = $39.75

Question 21.
B. Describe another way you could solve the problem.
Type below:
________

Answer:
(2 x $15.75) + $8.25
$15.75 + $15.75 + $8.25 = $39.75

Question 21.
C. What if 2 more tickets for admission are purchased? If the two additional tickets cost $16.50, determine what type of tickets the family purchases.
Explain how you can determine the answer without calculating.
Options:
a. Senior tickets
b. Adult tickets
c. Child tickets

Answer:
c. Child tickets

Explanation:
If 2 more tickets for admission are purchased? If the two additional tickets cost $16.50,
$39.75 + $16.50 = $56.25
Two additional children’s tickets are purchased. Since senior citizen tickets cost about $10 each, then 2 tickets would cost about $20, which is too much. Adult tickets cost about $16 each, so 2 adult tickets would cost about $32, which is too much. Children’s tickets cost about $8, and 2 tickets would be about $16 which is correct.

Conclusion:

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Lesson 1: Algebra • Division Patterns with Decimals

Lesson 2: Investigate • Divide Decimals by Whole Numbers

Lesson 3: Estimate Quotients

Lesson 4: Division of Decimals by Whole Numbers

Mid-Chapter Checkpoint

Lesson 5: Investigate • Decimal Divisions

Lesson 6: Divide Decimals

Lesson 7: Write Zeros in the Dividend

Lesson 8: Problem Solving • Decimal Operations

Chapter 5 Review/Test

Share and Show – Page No. 203

Complete the pattern.

Question 1.
456 ÷ 100 = 456
456 ÷ 101 = 45.6
456 ÷ 102 = 4.56
Think: The dividend is being divided by an increasing power of 10, so the decimal point will move to the left one place for each increasing power of 10.
456 ÷ 103 = _____

Answer:
456 ÷ 103 = 0.456

Explanation:
The dividend is being divided by an increasing power of 10, so the decimal point will move to the left one place for each increasing power of 10.
456 ÷ 100 = 456
456 ÷ 101 = 45.6
456 ÷ 102 = 4.56
456 ÷ 103 = 0.456

Complete the pattern.

Question 2.
225 ÷ 100 = _____
225 ÷ 101 = _____
225 ÷ 102 = _____
225 ÷ 103 = _____

Answer:
225 ÷ 100 = 225
225 ÷ 101 = 22.5
225 ÷ 102 = 2.25
225 ÷ 103 = 0.25

Explanation:
The dividend is being divided by an increasing power of 10, so the decimal point will move to the left one place for each increasing power of 10.
225 ÷ 100 = 225/1 = 225
225 ÷ 101 = 225/10 = 22.5
225 ÷ 102 = 225/100 = 2.25
225 ÷ 103 = 225/1,000 = 0.25

Chapter 5 Math Test 5th Grade Question 3.
605 ÷ 100 = _____
605 ÷ 101 = _____
605 ÷ 102 = _____
605 ÷ 103 = _____

Answer:
605 ÷ 100 = 605
605 ÷ 101 = 60.5
605 ÷ 102 = 6.05
605 ÷ 103 = 0.605

Explanation:
The dividend is being divided by an increasing power of 10, so the decimal point will move to the left one place for each increasing power of 10.
605 ÷ 100 = 605/1 = 605
605 ÷ 101 = 605/10 = 60.5
605 ÷ 102 = 605/100 = 6.05
605 ÷ 103 = 605/1,000 = 0.605

Question 4.
74.3 ÷ 1 = _____
74.3 ÷ 10 = _____
74.3 ÷ 100 = _____

Answer:
74.3 ÷ 1 = 74.3
74.3 ÷ 10 = 7.43
74.3 ÷ 100 = 0.743

Explanation:
The dividend is being divided by an increasing power of 10, so the decimal point will move to the left one place for each increasing power of 10.
74.3 ÷ 100 = 74.3 ÷ 1 = 74.3
74.3 ÷ 101 = 74.3 ÷ 10 = 7.43
74.3 ÷ 102 = 74.3 ÷ 100 = 0.743

On Your Own

Complete the pattern.

Question 5.
156 ÷ 1 = _____
156 ÷ 10 = _____
156 ÷ 100 = _____
156 ÷ 1,000 = _____

Answer:
156 ÷ 1 = 156
156 ÷ 10 = 15.6
156 ÷ 100 = 1.56
156 ÷ 1,000 = 0.156

Explanation:
The dividend is being divided by an increasing power of 10, so the decimal point will move to the left one place for each increasing power of 10.
156 ÷ 1 = 156
156 ÷ 10 = 15.6
156 ÷ 100 = 1.56
156 ÷ 1,000 = 0.156

Question 6.
32 ÷ 1 = _____
32 ÷ 10 = _____
32 ÷ 100 = _____
32 ÷ 1,000 = _____

Answer:
32 ÷ 1 = 32
32 ÷ 10 = 3.2
32 ÷ 100 = 0.32
32 ÷ 1,000 = 0.032

Explanation:
The dividend is being divided by an increasing power of 10, so the decimal point will move to the left one place for each increasing power of 10.
32 ÷ 1 = 32
32 ÷ 10 = 3.2
32 ÷ 100 = 0.32
32 ÷ 1,000 = 0.032

Question 7.
16 ÷ 100 = _____
16 ÷ 101 = _____
16 ÷ 102 = _____
16 ÷ 103 = _____

Answer:
16 ÷ 100 = 16
16 ÷ 101 = 1.6
16 ÷ 102 = 0.16
16 ÷ 103 = 0.016

Explanation:
The dividend is being divided by an increasing power of 10, so the decimal point will move to the left one place for each increasing power of 10.
16 ÷ 100 = 16
16 ÷ 101 = 1.6
16 ÷ 102 = 0.16
16 ÷ 103 = 0.016

Question 8.
12.7 ÷ 1 = _____
12.7 ÷ 10 = _____
12.7 ÷ 100 = _____
12.7 ÷ 1,000 = _____

Answer:
12.7 ÷ 1 = 12.7
12.7 ÷ 10 = 1.27
12.7 ÷ 100 = 0.127
12.7 ÷ 1,000 = 0.0127

Explanation:
The dividend is being divided by an increasing power of 10, so the decimal point will move to the left one place for each increasing power of 10.
12.7 ÷ 1 = 12.7
12.7 ÷ 10 = 1.27
12.7 ÷ 100 = 0.127
12.7 ÷ 1,000 = 0.0127

Chapter 5 Review Test 5th Grade Answers Question 9.
92.5 ÷ 100 = _____
92.5 ÷ 101 = _____
92.5 ÷ 102 = _____
92.5 ÷ 103 = _____

Answer:
92.5 ÷ 100 = 92.5
92.5 ÷ 101 = 9.25
92.5 ÷ 102 = 0.925
92.5 ÷ 103 = 0.0925

Explanation:
The dividend is being divided by an increasing power of 10, so the decimal point will move to the left one place for each increasing power of 10.
92.5 ÷ 100 = 92.5
92.5 ÷ 101 = 9.25
92.5 ÷ 102 = 0.925
92.5 ÷ 103 = 0.0925

Question 10.
86.3 ÷ 100 = _____
86.3 ÷ 101 = _____
86.3 ÷ 102 = _____
86.3 ÷ 103 = _____

Answer:
86.3 ÷ 100 = 86.3
86.3 ÷ 101 = 8.63
86.3 ÷ 102 = 0.863
86.3 ÷ 103 = 0.0863

Explanation:
The dividend is being divided by an increasing power of 10, so the decimal point will move to the left one place for each increasing power of 10.
86.3 ÷ 100 = 86.3
86.3 ÷ 101 = 8.63
86.3 ÷ 102 = 0.863
86.3 ÷ 103 = 0.0863

Algebra Find the value of n.

Question 11.
268 ÷ n = 0.268
n = _____

Answer:
n = 1000

Explanation:
268 ÷ n = 0.268
268 = n x 0.268
n = 268 ÷ 0.268
n = 1000

Question 12.
n ÷ 102 = 0.123
n = _____

Answer:
n = 12.3

Explanation:
n ÷ 102 = 0.123
n = 0.123 x 102
n = 0.123 x 100
n = 12.3

Question 13.
n ÷ 101 = 4.6
n = _____

Answer:
n = 46

Explanation:
n ÷ 101 = 4.6
n = 4.6 x 101
n = 4.6 x 10
n = 46

Problem Solving – Page No. 204

Use the table to solve 14–16.
Go Math Grade 5 Answer Key Chapter 5 Divide Decimals img 1

Question 14.
If each muffin contains the same amount of cornmeal, how many kilograms of cornmeal are in each corn muffin?
_____ kilograms

Answer:
0.15 kilograms

Explanation:
There are 1,000 muffins. Cornmeal = 150 Kg
If each muffin contains the same amount of cornmeal, 150 ÷ 1000 = 0.15
0.15 kilograms of cornmeal is in each corn muffin

Question 15.
If each muffin contains the same amount of sugar, how many kilograms of sugar, to the nearest thousandth, are in each corn muffin?
_____ kilograms

Answer:
0.07 kilograms

Explanation:
There are 1,000 muffins. Sugar = 66.7 kilograms
If each muffin contains the same amount of sugar, 66.7 ÷ 1000 = 0.0667.
0.0667 kilograms of sugar is in each corn muffin.
The thousandth digit is 6. 6 > 5
So, 0.07

5th Grade Go Math Chapter 5 Review Test Question 16.
The bakery decided to make only 100 corn muffins on Tuesday. How many kilograms of sugar will be needed?
_____ kilograms

Answer:
0.007 kilograms

Explanation:
The bakery decided to make only 100 corn muffins on Tuesday.
As 0.07 kilograms are required for 1,000 muffins,
for 100 muffins, (100 x 0.07) ÷ 1000 = 0.007

Question 17.
Explain how you know that the quotient 47.3 ÷ 101 is equal to the product 47.3 × 0.1.
Type below:
_________

Answer:
Quotient 47.3 ÷ 101 = 47.3 ÷ 10 = 4.73. The power of 101 = 10.
47.3 × 0.1 = 4.73.
Dividing 10 to a number is equal to multiplying 0.1 by that number.

Question 18.
Test Prep Ella used 37.2 pounds of apples to make applesauce. She used one-tenth as many pounds of sugar as pounds of apples. How many pounds of sugar did Ella use?
Options:
a. 372 pounds
b. 3.72 pounds
c. 0.372 pound
d. 0.0372 pound

Answer:
b. 3.72 pounds

Explanation:
Ella used 37.2 pounds of apples to make applesauce. She used one-tenth as many pounds of sugar as pounds of apples.
37.2 ÷ 10 = 3.72 pounds

Share and Show – Page No. 207

Use the model to complete the number sentence.

Question 1.
1.6 ÷ 4 =
Go Math Grade 5 Answer Key Chapter 5 Divide Decimals img 2
_____

Answer:
1.6 ÷ 4  = 0.4

Explanation:
1.6 ÷ 4
Share your model among 4 equal groups.
Since 1 whole cannot be shared among 4 groups without regrouping, cut your model apart to show the tenths.
1 ones = 10 tenths
10 + 6 = 16 tenths
There are 16-tenths in 1.6.
Share the tenths equally among the 4 groups.
There are 0 ones and 16-tenths in each group.
Decimal for the amount in each group = 0.4
1.6 ÷ 4  = 0.4

Go Math Lesson 5.2 Answer Key 5th Grade Question 2.
3.42 ÷ 3 =
Go Math Grade 5 Answer Key Chapter 5 Divide Decimals img 3
_____

Answer:
3.42 ÷ 3 = 1.14

Explanation:
3.42 ÷ 3
Share your model among 3 equal groups.
1 whole in each group. So, 3 wholes shared equally in 3 groups. 1 ones
3 ÷ 3 = 1 ones
3 tenths shared equally in 3 groups. 1 tenth has remained. 1 tenth
3 ÷ 3 = 1 tenths
1 tenth = 10 hundredths.
10 + 2 = 12 hundredths.
Share 12 hundredths equally among the 3 groups.
12 hundredths ÷ 3 = 4 hundredths.
Decimal for the amount in each group = 1.14
3.42 ÷ 3 = 1.14

Divide. Use base-ten blocks.

Question 3.
1.8 ÷ 3 = _____

Answer:
1.8 ÷ 3 = 0.6

Explanation:
1.8 ÷ 3
Share your model among 3 equal groups.
Since 1 whole cannot be shared among 3 groups without regrouping, cut your model apart to show the tenths. 0 ones
1 ones = 10 tenths
10 + 8 = 18 tenths
There are 18 tenths in 1.8.
Share the 18 tenths equally among the 3 groups.
18 ÷ 3 = 6
There are 0 ones and 18 tenths in each group.
Decimal for the amount in each group = 0.6
1.8 ÷ 3 = 0.6

Question 4.
3.6 ÷ 4 = _____

Answer:
3.6 ÷ 4 = 0.9

Explanation:
3.6 ÷ 4
Share your model among 4 equal groups.
Since 3 whole cannot be shared among 4 groups without regrouping, cut your model apart to show the tenths. 0 ones
1 ones = 10 tenths
30 + 6 = 36 tenths
There are 36 tenths in 3.6.
Share the 36 tenths equally among the 4 groups.
There are 0 ones and 36 tenths in each group.
36 ÷ 4 = 9
Decimal for the amount in each group = 0.9
3.6 ÷ 4 = 0.9

Question 5.
2.5 ÷ 5 = _____

Answer:
2.5 ÷ 5 = 0.5

Explanation:
2.5 ÷ 5
Share your model among 5 equal groups.
Since 2 whole cannot be shared among 5 groups without regrouping, cut your model apart to show the tenths. 0 ones
1 ones = 10 tenths
20 + 5 = 25 tenths
There are 25 tenths in 2.5.
Share the 25 tenths equally among the 5 groups.
There are 0 ones and 25 tenths in each group.
25 ÷ 5 = 5
Decimal for the amount in each group = 0.5
2.5 ÷ 5 = 0.5

Go Math Grade 5 Lesson 5.2 Answer Key Question 6.
2.4 ÷ 8 = _____

Answer:
2.4 ÷ 8 = 0.3

Explanation:
2.4 ÷ 8
Share your model among 8 equal groups.
Since 2 whole cannot be shared among 8 groups without regrouping, cut your model apart to show the tenths. 0 ones
1 ones = 10 tenths
20 + 4 = 24 tenths
There are 24-tenths in 2.4.
Share the 24-tenths equally among the 8 groups.
There are 0 ones and 24-tenths in each group.
24 ÷ 8 = 3
Decimal for the amount in each group = 0.3
2.4 ÷ 8 = 0.3

Question 7.
3.78 ÷ 3 = _____

Answer:
3.78 ÷ 3 = 1.26

Explanation:
3.78 ÷ 3
Share your model among 3 equal groups.
1 whole in each group. So, 3 wholes are shared equally in 3 groups.
3 ÷ 3 = 1 ones
6 tenths are shared equally in 3 groups. 1 tenth has remained.
6 ÷ 3 = 2 tenths
1 tenth = 10 hundredths.
10 + 8 = 18 hundredths.
Share 18 hundredths equally among the 3 groups.
18 hundredths ÷ 3 = 6 hundredths.
Decimal for the amount in each group = 1.26
3.78 ÷ 3 = 1.26

Question 8.
1.33 ÷ 7 = _____

Answer:
1.33 ÷ 7 = 0.19

Explanation:
1.33 ÷ 7
Share your model among 7 equal groups.
Since 1 whole cannot be shared among 7 groups without regrouping, cut your model apart to show the tenths. 0 ones
1 ones = 10 tenths
10 + 3 = 13 tenths
There are 13 tenths in 1.3.
Share the 13 tenths equally among the 7 groups.
Share 7 tenths equally among the 3 groups. 6 tenths remained.
7 ÷ 7 = 1 tenths
Since 6 tenths cannot be shared among 7 groups without regrouping, cut your model apart to show the tenths.
1 tenths = 10 hundredths
60 + 3 = 63 hundredths
Share 63 hundredths equally among the 7 groups.
63 ÷ 7 = 9 hundredths
Decimal for the amount in each group = 0.19
1.33 ÷ 7 = 0.19

Question 9.
4.72 ÷ 4 = _____

Answer:
4.72 ÷ 4 = 1.18

Explanation:
4.72 ÷ 4
Share your model among 4 equal groups.
1 whole in each group. So, 4 wholes shared equally in 4 groups. 1 ones
4 ÷ 4 = 1 ones
4 tenths shared equally in 4 groups. 3 tenths have remained.
4 ÷ 4 = 1 tenths
1 tenth = 10 hundredths.
30 + 2 = 32 hundredths.
Share 32 hundredths equally among the 4 groups.
32 hundredths ÷ 4 = 8 hundredths.
Decimal for the amount in each group = 1.18
4.72 ÷ 4 = 1.18

Go Math Lesson 5.2 5th Grade Question 10.
2.52 ÷ 9 = _____

Answer:
2.52 ÷ 9 = 0.28

Explanation:
2.52 ÷ 9
Share your model among 9 equal groups.
Since 2 whole cannot be shared among 9 groups without regrouping, cut your model apart to show the tenths.
9 ÷ 9 = 1 ones
1 ones = 10 tenths
20 + 5 = 25 tenths
There are 25 tenths in 2.5.
Share the 18 tenths equally among the 9 groups. 7 tenths remained.
18 ÷ 9 = 2 tenths
1 tenth = 10 hundredths.
70 + 2 hundredths = 72 hundredths
Share the 72 hundredths equally among the 9 groups.
72 ÷ 9 = 8
Decimal for the amount in each group = 0.28
2.52 ÷ 9 = 0.28

Question 11.
6.25 ÷ 5 = _____

Answer:
6.25 ÷ 5 = 1.25

Explanation:
6.25 ÷ 5
Share your model among 5 equal groups.
1 whole in each group. So, 5 wholes shared equally in 5 groups. 1 whole remained.
5 ÷ 5 = 1 ones 
1 ones = 10 tenths
10 + 2 = 12 tenths
10 tenths shared equally in 5 groups. 2 tenths have remained.
10 ÷ 5 = 2 tenths
1 tenth = 10 hundredths.
20 + 5 = 25 hundredths.
Share 25 hundredths equally among the 5 groups.
25 hundredths ÷ 5 = 5 hundredths.
Decimal for the amount in each group = 1.25
6.25 ÷ 5 = 1.25

Problem Solving – Page No. 208

What’s the Error?

Question 12.
Aida is making banners from a roll of paper that is 4.05 meters long. She will cut the paper into 3 equal lengths. How long will each banner be?
Go Math Grade 5 Answer Key Chapter 5 Divide Decimals img 4
Look how Aida solved the problem.      Solve the problem and correct
Find the error.                                            the error.
Go Math Grade 5 Answer Key Chapter 5 Divide Decimals img 5
So, Aida said that each banner would be _________ meters long, but each banner should be _________ meters long.
Type below:
_________

Answer:
So, Aida said that each banner would be 4.05 meters long, but each banner should be 1.35 meters long.
So, 1 ones, 3 tenths, and 5 hundredths are shared among 3 groups.
But Aida draws only one whole and 5 hundredths among 3 groups.

Explanation:
Aida is making banners from a roll of paper that is 4.05 meters long. She will cut the paper into 3 equal lengths.
4.05 ÷ 3