Rama

Go Math Grade 4 Chapter 9 Answer Key Pdf: Are you looking for the best Practice Books and Answer Keys for 4th-grade students? Follow Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals. Students love to solve more problems using Go Math Grade 4 Chapter 9 Relate Fractions and Decimals Answer Key. Different types of questions with explained answers (images, text, easy steps) help the students to show interest in math. Every student love to do maths if they refer HMH 4th Grade Go Math Answer Key.

Grab practical knowledge by practicing questions on Go Math Grade 4 Chapter 9 Solution Key. Get the pdf formatted Go math Grade 4 Chapter 9 Relate Fractions and Decimals answer key and solve every problem as per your convenience. Download HMH Go math Grade 4 Answer Key for Free. It is easy to download and comfortable to use to crack top grades.

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

The best practice comes to your fingertips with Go Math Grade 4 Solutions Key. Utilize the opportunity of easy solving with the help of HMH Go Math Grade 4 Chapter 9 Answer Key. Various kinds of questions are provided with the best method of solving. Question, answers, and explanation all come together if you use Go Math Grade 4 answer key. Simply, click on the links below and go to the lesson you want to solve. You can instantly get a PDF of Go Math Grade 4 Chapter 9 Answer Key and start your practice.

Lesson 1: Relate Tenths and Decimals

• Relate Tenths and Decimals – Page No. 499
• Relate Tenths and Decimals Lesson Check – Page No. 500

Lesson 2: Relate Hundredths and Decimals

• Relate Hundredths and Decimals – Page No. 503
• Relate Hundredths and Decimals Lesson Check – Page No. 504
• Relate Hundredths and Decimals Lesson Check 1 – Page No. 505
• Relate Hundredths and Decimals Lesson Check 2 – Page No. 506

Lesson 3: Equivalent Fractions and Decimals

• Equivalent Fractions and Decimals – Page No. 509
• Equivalent Fractions and Decimals Lesson Check – Page No. 510
• Equivalent Fractions and Decimals Lesson Check 1 – Page No. 511
• Equivalent Fractions and Decimals Lesson Check 2 – Page No. 512

Lesson 4: Relate Fractions, Decimals, and Money

• Relate Fractions, Decimals, and Money – Page No. 515
• Relate Fractions, Decimals, and Money Lesson Check – Page No. 516
• Relate Fractions, Decimals, and Money Lesson Check 1 – Page No. 517
• Relate Fractions, Decimals, and Money Lesson Check 2 – Page No. 518

Lesson 5: Problem Solving • Money

• Money – Page No. 521
• Money Lesson Check – Page No. 522
• Money Lesson Check 1 – Page No. 523
• Money Lesson Check 2 – Page No. 524

Mid-Chapter Checkpoint

• Mid-Chapter Checkpoint – Page No. 525
• Mid-Chapter Checkpoint Lesson Check – Page No. 526

Lesson 6: Add Fraction Parts of 10 and 100

• Add Fraction Parts of 10 and 100 – Page No. 529
• Add Fraction Parts of 10 and 100 Lesson Check – Page No. 530
• Add Fraction Parts of 10 and 100 Lesson Check 1 – Page No. 531
• Add Fraction Parts of 10 and 100 Lesson Check 2 – Page No. 532

Lesson 7: Compare Decimals

• Compare Decimals – Page No. 535
• Compare Decimals Lesson Check – Page No. 536
• Compare Decimals Lesson Check 1 – Page No. 537
• Compare Decimals Lesson Check 2 – Page No. 538

Review/Test

• Review/Test – Page No. 539
• Review/Test – Page No. 540
• Review/Test – Page No. 541
• Review/Test – Page No. 542
• Review/Test – Page No. 543
• Review/Test – Page No. 544
• Review/Test – Page No. 551
• Review/Test – Page No. 552

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

Answer:

Question 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.

Type below:
________

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

Explanation:

Question 4.

Type below:
________

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

Explanation:

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?

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?

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.
b.
c.
d.

Answer:
c.

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.

_____

Answer:

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

Question 2.

Type below:
_________

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

Explanation:
68 boxes are shaded out of 100 boxes.

Question 3.

Type below:
_________

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

Explanation:
8 boxes are shaded out of 100 boxes.

Question 4.

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.

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.

Type below:
_________

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

Explanation:
75 boxes are shaded out of 100 boxes.

Question 7.

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.

Type below:
_________

Answer:

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.

_____

Answer:

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.

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.

Answer:

Question 2.

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.

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.

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?

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 \(\frac{9}{10}-\frac{6}{10}\)?

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.

Type below:
_________

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

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

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

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:
\(\frac{30}{100}\)

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:

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:
\(\frac{8}{10}\)

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

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:
\(\frac{80}{100}\)

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

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

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:
\(\frac{6}{10}\)

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:
\(\frac{9}{10}\)

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:
\(\frac{7}{10}\)

0.7

Explanation:

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:

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:

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:

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:

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.

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:

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

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.
\(\frac{5}{10}\) \(\frac{5}{10}\) = \(\frac{5 \times 10}{10 \times 10}\) = \(\frac{50}{100}\)

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.

\(\frac{2}{10}\) = \(\frac{2 x 10}{10 x 10}\) = \(\frac{20}{100}\)

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.

\(\frac{8}{10}\) = \(\frac{8 x 10}{10 x 10}\) = \(\frac{80}{100}\)

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.
\(\frac{6}{10}\) = \(\frac{6 x 10}{10 x 10}\) = \(\frac{60}{100}\)

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.

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.

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.

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.

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.

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:

$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:

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:

$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:

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.

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:

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.

Type below:
_________

Answer:

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.

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

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

Question 2.

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:

$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:

$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:

$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:

$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:

$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?

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?

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.

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

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.

Answer:

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.

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.

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.

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:
\(\frac{80}{100}\)

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

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?

$ _____

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.

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.

\(\frac{□}{□}\) 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: \(\frac{2 \times 10}{10 \times 10}=\frac{20}{100}\)

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

Explanation:
Think: Write \(\frac{2}{10}\) as a fraction with a denominator of 100: \(\frac{2 \times 10}{10 \times 10}=\frac{20}{100}\)

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.

0.39 ____ 0.42

Answer:

0.39 < 0.42

Compare. Write <, >, or =.

Question 2.

0.26 ____ 0.23

Answer:
0.26 > 0.23

Explanation:

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.

0.7 ____ 0.54

Answer:
0.7 > 0.54

Explanation:

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.

1.15 ____ 1.3

Answer:
1.15 < 1.3

Explanation:

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.

4.5 ____ 2.89

Answer:
4.5 > 2.89

Explanation:

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

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.

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.

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.

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.

Harrison rode his bike _______ mile to the park.
_____

Answer:

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.

_____

Answer:

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.

Answer:

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.

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.

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?

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.

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.

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:

\(\overline{A B}\) is a line segment.

Draw and label an example of the figure.

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

Answer:

\(\underset { XY }{ \longleftrightarrow } \) is a line

Question 3.
obtuse ∠K
Type below:
__________

Answer:

Angle K is greater than a right angle and less than a straight angle.

Question 4.
∠CDE
Type below:
__________

Answer:

angle CDE

Use Figure M for 5 and 6.

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:

\(\overrightarrow{P Q}\) is a ray.

Question 8.
acute ∠RST
Type below:
__________

Answer:

Angle RST

Question 9.
straight ∠WXZ
Type below:
__________

Answer:

Use Figure F for 10–15.

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.

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.

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.

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.


\(\overline{B G}\) _________
\(\underset { CD }{ \longleftrightarrow } \) _________
∠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:

Achieve excellent grades with the help of Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals PDF. Follow every method and step-by-step process included in HMH Go Math Grade 4 Chapter 9 Answer Key. Students can easily catch up on the way of solving math problems and they learn their own way to solve any difficult math problem by using Go Math Answer Key Grade 4 Chapter 9. Get flexible learning using Go Math Grade 4 Answer Key Chapter 9 Relate Fractions and Decimals.

Go Math Grade 4 Chapter 8 Answer Key Pdf: Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers will help the students to enhance math skills. Improve logical thinking with the best practice of 4th Grade HMH Go Math problems. The 4th Grade Go Math Answer Key is provided with solved questions that make the students show interest in doing maths. Also, the Go Math Grade 4 Answer Key Chapter 8 will reach the student’s expectations. It is totally developed on user standards. Every candidate can easily understand and solve every math problem using HMH Go Math Answer Key.

1, 2, 3, 4….. counting the number of advantages with Go Math Grade 4 Solution Key is an infinite process. From a very basic level to standard level, all problems are solved in an easy manner. By referring step by step process involved in Go Math Grade 4 Chapter Answer Key, students can learn all the concepts included in their math book. The learning way of math is simplified and explained with the best examples. So, quickly interact with Go Math Solution Key and improve your math skills.

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

Use the provided handy solutions of all questions included in our HMH Go Math Grade 4 Answer Key. Learn quick math with the best approach. You can implement these math practices into your real-time life and solve daily life math calculations within a fraction of seconds. Get the best and do the best with the help of Go Math Grade 4 Chapter 8 Answer Key.

Lesson 1: Multiples of Unit Fractions

• Multiples of Unit Fractions – Page No. 459
• Multiples of Unit Fractions Lesson Check – Page No. 460

Lesson 2: Multiples of Fractions

• Multiples of Fractions – Page No. 463
• Multiples of Fractions Lesson Check – Page No. 464
• Multiples of Fractions Lesson Check 1 – Page No. 465
• Multiples of Fractions Lesson Check 2 – Page No. 466

Mid-Chapter Checkpoint

• Mid-Chapter Checkpoint – Page No. 467
• Mid-Chapter Checkpoint Lesson Check – Page No. 468

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

• Multiply a Fraction by a Whole Number Using Models – Page No. 471
• Multiply a Fraction by a Whole Number Using Models Lesson Check – Page No. 472
• Multiply a Fraction by a Whole Number Using Models Lesson Check 1 – Page No. 473
• Multiply a Fraction by a Whole Number Using Models Lesson Check 2 – Page No. 474

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

• Multiply a Fraction or Mixed Number by a Whole Number – Page No. 477
• Multiply a Fraction or Mixed Number by a Whole Number Lesson Check – Page No. 478
• Multiply a Fraction or Mixed Number by a Whole Number Lesson Check 1 – Page No. 479
• Multiply a Fraction or Mixed Number by a Whole Number Lesson Check 2- Page No. 480

Lesson 5: Problem Solving • Comparison Problems with Fractions

• Comparison Problems with Fractions – Page No. 483
• Comparison Problems with Fractions Lesson Check – Page No. 484
• Comparison Problems with Fractions Lesson Check 1 – Page No. 485
• Comparison Problems with Fractions Lesson Check 2 – Page No. 486

Review/Test

• • Review/Test – Page No. 487
  • Review/Test – Page No. 488
  • Review/Test – Page No. 489
  • Review/Test – Page No. 490
  • Review/Test – Page No. 491
  • Review/Test – Page No. 492
  • Review/Test – Page No. 497
  • Review/Test – Page No. 498

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.

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:

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:

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 \(\frac{3}{8}\).

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.

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.

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.

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.

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?

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:

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.

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.

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.

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.

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.

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.

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.

Answer:

Question 2.
3 × \(\frac{2}{5}\) = \(\frac{□}{□}\)

Answer:

3 x 2/5 = 6/5

Question 3.
7 × \(\frac{3}{10}\) = \(\frac{□}{□}\)

Answer:

7 x 3/10 = 21/10

Question 4.
3 × \(\frac{5}{12}\) = \(\frac{□}{□}\)

Answer:

3 x 5/12 = 15/12

Question 5.
6 × \(\frac{3}{4}\) = \(\frac{□}{□}\)

Answer:

6 x 3/4 = 18/4

Question 6.
4 × \(\frac{2}{8}\) = \(\frac{□}{□}\)

Answer:

4 x 2/8 = 8/8

Question 7.
5 × \(\frac{2}{3}\) = \(\frac{□}{□}\)

Answer:

5 x 2/3 = 10/3

Question 8.
2 × \(\frac{7}{8}\) = \(\frac{□}{□}\)

Answer:

2 x 7/8 = 14/8

Question 9.
6 × \(\frac{4}{5}\) = \(\frac{□}{□}\)

Answer:

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.

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.

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:

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.

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.

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?

Answer:
5 feet

Explanation:

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.

Marta must measure \(\frac{1}{8}\) _________ cup times.
_________

Answer:

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.

A blue shark is ____ feet long.
_____

Answer:

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 \(\frac{3}{5}\).

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.

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.


Type below:
_________

Answer:

Page No. 490

Question 12.
Asta made a fraction number line to help her find 3 × \(\frac{4}{5}\).

Select a way to write 3 × \(\frac{4}{5}\) as the product of a whole number and a unit fraction.

Type below:
_________

Answer:

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.

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.

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:

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.

Fraction: __________ Decimal: __________
Type below:
_________

Answer:

5/10 = 0.5

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

Question 2.

Type below:
_________

Answer:
3\(\frac{2}{10}\)
three and two-tenths

Question 3.

Type below:
_________

Answer:
\(\frac{8}{10}\)

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

Question 4.

Type below:
_________

Answer:
4/10 = 0.4

Explanation:
4 boxes are shaded out of 10 boxes. So, the fraction is 4/10.

Question 5.

Type below:
_________

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

Question 6.

Type below:
_________

Answer:
2\(\frac{9}{10}\)

Question 7.

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.

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.

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.

Go Math Grade 4 Chapter 6 Answer Key Pdf: Get access to Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison for free. Don’t look for the resource of Go Math Grade 4 Answer Key. Just check out here for the Go Math Grade 4 Chapter 6 Fraction Equivalence and Comparison Solution Key for all the questions, answers, and also explanations for every question. The top-rated Go Math Grade 4 Answer Key and Practice Books are provided for all the students for free.

Fraction Equivalence and Comparison Go Math Grade 4 Chapter 6 Answer Key Pdf

Join in the list of the top-ranking students by taking the help of Go Math 4th Grade Solution key. HMH Go Math Grade 4 Answer Key PDF also provided for free. Download it now and start solving every question to gain knowledge. Online and also offline practice will easy with the Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison. The HMH Grade 4 Answer Key is designed with easy problem-solving.

Lesson 1: Investigate • Equivalent Fractions

• Equivalent Fractions – Page No. 331
• Equivalent Fractions Lesson Check – Page No. 332

Lesson 2: Generate Equivalent Fractions

• Generate Equivalent Fractions – Page No. 335
• Generate Equivalent Fractions Lesson Check – Page No. 336
• Generate Equivalent Fractions Lesson Check 1 – Page No. 337
• Generate Equivalent Fractions Lesson Check 2 – Page No. 338

Lesson 3: Simplest Form

• Simplest Form – Page No. 341
• Simplest Form Lesson Check – Page No. 342
• Simplest Form Lesson Check 1 – Page No. 343
• Simplest Form Lesson Check 2 – Page No. 344

Lesson 4: Common Denominators

• Common Denominators – Page No. 347
• Common Denominators Lesson Check – Page No. 348
• Common Denominators Lesson Check 1 – Page No. 349
• Common Denominators Lesson Check 2 – Page No. 350
• Common Denominators Lesson Check 3 – Page No. 353
• Common Denominators Lesson Check 4 – Page No. 354

Lesson 5: Problem Solving • Find Equivalent Fractions

• Find Equivalent Fractions – Page No. 355
• Find Equivalent Fractions Lesson Check – Page No. 356

Mid-Chapter Checkpoint

• Mid-Chapter Checkpoint – Page No. 357
• Mid-Chapter Checkpoint Lesson Check – Page No. 358

Lesson 6: Compare Fractions Using Benchmarks

• Compare Fractions Using Benchmarks – Page No. 361
• Compare Fractions Using Benchmarks Lesson Check – Page No. 362
• Compare Fractions Using Benchmarks Lesson Check 1 – Page No. 363
• Compare Fractions Using Benchmarks Lesson Check 2 – Page No. 364

Lesson 7: Compare Fractions

• Compare Fractions – Page No. 367
• Compare Fractions Lesson Check – Page No. 368
• Compare Fractions Lesson Check 1 – Page No. 369
• Compare Fractions Lesson Check 2 – Page No. 370

Lesson 8: Compare and Order Fractions

• Compare and Order Fractions – Page No. 373
• Compare and Order Fractions Lesson Check – Page No. 374
• Compare and Order Fractions Lesson Check 1 – Page No. 375
• Compare and Order Fractions Lesson Check 2- Page No. 376

Review/Test

• Review/Test – Page No. 377
• Review/Test – Page No. 378
• Review/Test – Page No. 379
• Review/Test – Page No. 380
• Review/Test – Page No. 381
• Review/Test – Page No. 382
• Review/Test – Page No. 387
• Review/Test – Page No. 388

Common Core – Equivalent Fractions – Page No. 331

Equivalent Fractions
Use the model to write an equivalent fraction.

Question 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.

\(\frac{3}{4}\) = \(\frac{□}{□}\)

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.

Type below:
___________

Answer:

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.

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.

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.

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.

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.

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.

______

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.

______ parts

Answer:

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.
\(\frac{2}{3} \text { and } \frac{3}{4}\)

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.

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.

_____ 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.

\(\frac{□}{□}\)

Answer:

\(\frac{2}{3}\), \(\frac{8}{12}\), \(\frac{40}{60}\)

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?

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.

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.

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 >.

\(\frac{2}{5}\) _____ \(\frac{1}{8}\)

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.

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.

Answer:
\(\frac{1}{8}\) < \(\frac{6}{10}\)

Explanation:

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?

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 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 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?

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.

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.

Answer:
\(\frac{1}{5}\) < \(\frac{2}{10}\)

Explanation:

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.

Type below:
___________

Answer:

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?

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.
\(\frac{5}{8}, \frac{2}{12}, \frac{8}{10}\)

Answer:
\(\frac{2}{12}, \frac{5}{8}, \frac{8}{10}\)

Explanation:

Question 2.
\(\frac{1}{5}, \frac{2}{3}, \frac{5}{8}\)
Type below:
_________

Answer:
\(\frac{1}{5}, \frac{5}{8}, \frac{2}{3}\)

Explanation:

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:

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:

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:

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:

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:

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:

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.

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.
\(\frac{7}{8} in. \frac{3}{16} in. \frac{1}{4} in. \frac{3}{8} in. \frac{4}{8} in. \frac{11}{16} in.\)

Type below:
_________

Answer:

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.

Answer:

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.

Type below:
_________

Answer:

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.

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.

Type below:
_________

Answer:

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.

Type below:
_________

Answer:

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.

Type below:
_________

Answer:

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.

_____ parts

Answer:

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.

Type below:
_________

Answer:
\(\frac{3}{5}\) + \(\frac{1}{5}\) = \(\frac{4}{5}\)

Question 2.

Type below:
_________

Answer:
\(\frac{2}{3}\) – \(\frac{1}{3}\) = \(\frac{1}{3}\)

Question 3.

Type below:
_________

Answer:
\(\frac{1}{4}\) + \(\frac{1}{4}\) = \(\frac{2}{4}\)

Question 4.

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.

\(\frac{3}{4}-\frac{1}{4}\) = \(\frac{□}{□}\)

Answer:
\(\frac{2}{4}\)

Question 6.

\(\frac{5}{6}+\frac{1}{6}\) = \(\frac{□}{□}\)

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.

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:

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.


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.