# Go Math Grade 5 Answer Key Chapter 1 Place Value, Multiplication, and Expressions

## Go Math Grade 5 Answer Key Chapter 1 Place Value, Multiplication, and Expressions

It is really terrible to deal with the students and give an explanation for their questions. Now, you will no more face such difficulties. We are providing Go Math Grade 5 Answer Key Chapter 1 PDF questions, answers, and also explanations for every question. So, just check the question and find out the complete answers and explanations for every problem. Download Go Math Grade 5 Chapter 1 Place Value, Multiplication, and Expressions Solution Key PDF.

Lesson 1: Investigate • Place Value and Patterns

Lesson 2: Place Value of Whole Numbers

Lesson 3: Algebra • Properties

Lesson 4: Algebra • Powers of 10 and Exponents

Lesson 5: Algebra • Multiplication Patterns

Mid-Chapter Checkpoint

Lesson 6: Multiply by 1-Digit Numbers

Lesson 7: Multiply by Multi-Digit Numbers

Lesson 8: Relate Multiplication to Division

Lesson 9: Problem Solving • Multiplication and Division

Lesson 10: Algebra • Numerical Expressions

Lesson 11: Algebra • Evaluate Numerical Expressions

Lesson 12: Algebra • Grouping Symbols

Review/Test

### Place Value and Patterns – Share and Show – Page No. 7

Complete the sentence.

Question 1.
500 is 10 times as much as ______

50

Explanation:
Let the unknown number is S.
500 = 10S
S = 500/10 = 50.
500 is 10 times as much as 50.

Question 2.
20,000 is $$\frac{1}{10}$$ of ______

2,00,000

Explanation:
Let the unknown number is S.
20,000 = $$\frac{1}{10}$$ S
S = 20,000 X 10 = 2,00,000

Question 3.
900 is $$\frac{1}{10}$$ of ______

9,000

Explanation:
Let the unknown number is S.
900 = $$\frac{1}{10}$$ S
S = 900 X 10 = 9,000

Question 4.
600 is 10 times as much as ______

60

Explanation:
Let the unknown number is S.
600 = 10S
S = 600/10 = 60.

Use place-value patterns to complete the table

Question 5.

 Numbers 10 times as much as $$\frac{1}{10}$$ of 10 ______ ______ 3,000 ______ ______ 800 ______ ______ 50 ______ ______

 Numbers 10 times as much as $$\frac{1}{10}$$ of 10 ___1___ ___100___ 3,000 ___300___ ___30,000___ 800 ___80___ ___8,000___ 50 ___5___ ___500___

Explanation:
1. 10 is 10 times as much as ______
Let the unknown number is S.
10 = 10S
S = 10/10 = 1.
10 is 10 times as much as 1.
10 is $$\frac{1}{10}$$ of ______
Let the unknown number is S.
10 = $$\frac{1}{10}$$ S
S = 10 X 10 = 100.
2. 3,000 is 10 times as much as ______
Let the unknown number is S.
3,000 = 10S
S = 3,000/10 = 300.
3,000 is 10 times as much as 300.
3,000 is $$\frac{1}{10}$$ of ______
Let the unknown number is S.
3,000 = $$\frac{1}{10}$$ S
S = 3,000 X 10 = 30,000.
3. 800 is 10 times as much as ______
Let the unknown number is S.
800 = 10S
S = 800/10 = 80.
800 is 10 times as much as 80.
800 is $$\frac{1}{10}$$ of ______
Let the unknown number is S.
800 = $$\frac{1}{10}$$ S
S = 800 X 10 = 8,000.
4. 50 is 10 times as much as ______
Let the unknown number is S.
50 = 10S
S = 50/10 = 5.
50 is 10 times as much as 5.
50 is $$\frac{1}{10}$$ of ______
Let the unknown number is S.
50 = $$\frac{1}{10}$$ S
S = 50 X 10 = 500.

Question 6.

 Numbers 10 times as much as $$\frac{1}{10}$$ of 400 ______ ______ 90 ______ ______ 6,000 ______ ______ 200 ______ ______

 Numbers 10 times as much as $$\frac{1}{10}$$ of 400 __40____ ___4,000___ 90 ___9___ ___900___ 6,000 __600____ __60,000____ 200 ___20___ ___2,000___

Explanation:
1. 400 is 10 times as much as ______
Let the unknown number is S.
400 = 10S
S = 400/10 = 40.
400 is 10 times as much as 40.
400 is $$\frac{1}{10}$$ of ______
Let the unknown number is S.
400 = $$\frac{1}{10}$$ S
S = 400 X 10 = 4,000.
2. 90 is 10 times as much as ______
Let the unknown number is S.
90 = 10S
S = 90/10 = 9.
90 is 10 times as much as 9.
90 is $$\frac{1}{10}$$ of ______
Let the unknown number is S.
90 = $$\frac{1}{10}$$ S
S = 90 X 10 = 900.
3. 6,000 is 10 times as much as ______
Let the unknown number is S.
6,000 = 10S
S = 6,000/10 = 600.
6,000 is 10 times as much as 600.
6,000 is $$\frac{1}{10}$$ of ______
Let the unknown number is S.
6,000 = $$\frac{1}{10}$$ S
S = 6,000 X 10 = 60,000.
4. 200 is 10 times as much as ______
Let the unknown number is S.
200 = 10S
S = 200/10 = 20.
200 is 10 times as much as 20.
200 is $$\frac{1}{10}$$ of ______
Let the unknown number is S.
200 = $$\frac{1}{10}$$ S
S = 200 X 10 = 2,000.

Complete the sentence with 100 or 1,000.

Question 13.
200 is ______ times as much as 2

200 is 100 times as much as 2

Explanation:
Let the unknown number is S.
200 = 2S
S = 200/2 = 100

Question 14.
4,000 is ______ times as much as 4

4,000 is 1000 times as much as 4

Explanation:
Let the unknown number is S.
4,000 = 2S
S = 4,000/2 = 1,000

Question 15.
700,000 is ______ times as much as 700

700,000 is 1,000 times as much as 700

Explanation:
Let the unknown number is S.
700,000 = 700S
S = 700,000/700 = 1,000

Question 16.
600 is ______ times as much as 6

600 is 100 times as much as 6

Explanation:
Let the unknown number is S.
600 = 6S
S = 600/6= 100

Question 17.
50,000 is ______ times as much as 500

50,000 is 100_ times as much as 500

Explanation:
Let the unknown number is S.
50,000 = 500S
S = 50,000/500= 100

Question 18.
30,000 is ______ times as much as 30

30,000 is 1,000 times as much as 30

Explanation:
Let the unknown number is S.
30,000 = 30S
S = 30,000/30 = 1,000

Question 19.
Explain how you can use place-value patterns to describe how 50 and 5,000 compare.
Type below:
__________

5,000 is 100 times as much as 50

Explanation:
5,000/50 = 100

### Place Value and Patterns – Problem Solving – Page No. 8

Sense or Nonsense?

Question 20.
Mark and Robyn used base-ten blocks to show that 300 is 100 times as much as 3. Whose model makes sense? Whose model is nonsense? Explain your reasoning.

Type below:
__________

Robyn’s model makes sense. Because the given data 300 is 100 times as much as 3. It clearly states that there are 100 model-blocks and one model blocks should take to solve the problem.

Question 20.
Explain how you would help Mark understand why he should have used small cubes instead of longs.
Type below:
__________

Mark’s drew 100 model-blocks and 10 model-blocks which. To get 300 is 100 times as much as 3, he needs to do 300/3 = 100 model blocks.

### Place Value of Whole Numbers – Share and Show – Page No. 11

Complete the place-value chart to find the value of each digit.

Question 1.

Type below:
__________

7,333,820

Explanation:
7 x 1,000,000 = 7,000,000
3 x 100,000 = 300,000
3 x 1,000 = 3000
8 x 100 = 800
2 x 10 = 20

Write the value of the underlined digit.

Question 2.
1,574,833
__________

4,000

Explanation:
(1 x 1,000,000) + (5 x 1,00,000) + (7 x 10,000) + (4 x 1,000) + (8 x 100) + (3 x 10) + (3 x 1)
4 x 1,000 = 4 thousands = 4,000

Question 3.
598,102
__________

100

Explanation:
(5 x 1,00,000) + (9 x 10,000) + (8 x 1,000) + (1 x 100) + (0 x 10) + (2 x 1)
1 x 100 = 4 hundreds = 100

Question 4.
7,093,455
__________

90,000

Explanation:
(7 x 1,000,000) + (0 x 1,00,000) + (9 x 10,000) + (3 x 1,000) + (4 x 100) + (5 x 10) + (5 x 1)
9 x 10,000 = 9 ten-thousands = 90,000

Question 5.
301,256,878
__________

3,00,000,000

Explanation:
(3 x 1,00,000,000) + (0 x 10,000,000) + (1 x 1,000,000) + (2 x 1,00,000) + (5 x 10,000) + (6 x 1,000) + (8 x 100) + (7 x 10) + (8 x 1)
3 x 1,00,000,000 = 3 hundred- millions = 3,00,000,000

Write the number in two other forms.

Question 6.
(8 × 100,000) + (4 × 1,000) + (6 × 1) =
__________

80,4006
Eight Hundred Four Thousand Six

Explanation:
(8 × 100,000) + (4 × 1,000) + (6 × 1) = 800,000 + 4,000 + 6 = 80,4006

Question 7.
seven million, twenty thousand, thirty-two
__________

7,020,032
Seven Million Twenty Thousand Thirty-Two

Explanation:
seven million = 7,000,000
twenty thousand = 20,000
thirty-two = 32

Write the value of the underlined digit.

Question 8.
849,567,043
__________

40,000,000

Explanation:
(8 x 1,00,000,000) + (4 x 10,000,000) + (9 x 1,000,000) + (5 x 1,00,000) + (6 x 10,000) + (7 x 1,000) + (0 x 100) + (4 x 10) + (3 x 1)
4 x 10,000,000 = 4 ten- millions = 40,000,000

Question 9.
9,422,850
__________

4,00,000

Explanation:
(9 x 1,000,000) + (4 x 1,00,000) + (2 x 10,000) + (2 x 1,000) + (8 x 100) + (5 x 10) + (0 x 1)
4 x 1,00,000 = 4 Hundred Thousand = 4,00,000

Question 10.
96,283
__________

90,000

Explanation:
(9 x 10,000) + (6 x 1,000) + (2 x 100) + (8 x 10) + (3 x 1)
9 x 10,000 = 9 ten-thousands = 90,000

Question 11.
498,354,021
__________

4,00,000,000

Explanation:
(4 x 1,00,000,000) + (9 x 10,000,000) + (8 x 1,000,000) + (3 x 1,00,000) + (5 x 10,000) + (4 x 1,000) + (0 x 100) + (2 x 10) + (1 x 1)
4 x 1,00,000,000 = Four Hundred Million = 4,00,000,000

Question 12.
791,350
__________

300

Explanation:
(7 x 1,00,000) + (9 x 10,000) + (1 x 1,000) + (3 x 100) + (5 x 10) + (0 x 1)
3 x 100 = 3 hundred = 300

Question 13.
27,911,534
__________

7,000,000

Explanation:
(2 x 10,000,000) + (7 x 1,000,000) + (9 x 1,00,000) + (1 x 10,000) + (1 x 1,000) + (5 x 100) + (3 x 10) + (4 x 1)
7 x 1,000,000 = Seven Million = 7,000,000

Question 14.
105,980,774
__________

80,000

Explanation:
(1 x 1,00,000,000) + (0 x 10,000,000) + (5 x 1,000,000) + (9 x 1,00,000) + (8 x 10,000) + (0 x 1,000) + (7 x 100) + (7 x 10) + (4 x 1)
8 x 10,000 = 8 ten-thousand = 80,000

Question 15.
8,265,178
__________

5,000

Explanation:
(8 x 1,000,000) + (2 x 1,00,000) + (6 x 10,000) + (5 x 1,000) + (1 x 100) + (7 x 10) + (8 x 1)
5 x 1,000 = 5 one-thousand = 5,000

Write the number in two other forms.

Question 16.
345,000
Type below:
__________

Three Hundred Forty-Five Thousand
(3 x 1,00,000) + (4 x 10,000) + (5 x 1,000) + (0 x 100) + (0 x 10) + (0 x 1)

Question 17.
119,000,003
Type below:
__________

One Hundred Nineteen Million Three
(1 x 100,000,000) + (1 x 10,000,000) + (9 x 1,000,000) + (0 x 1,00,000) + (0 x 10,000) + (0 x 1,000) + (0 x 100) + (0 x 10) + (3 x 1)

### Place Value of Whole Numbers – Problem Solving – Page No. 12

Use the table for 18–19.

Question 18.
Which planet is about 10 times as far as Earth is from the Sun?

__________

Saturn

Explanation:
Saturn = 1,427,000/10 = 142,700 which is 10 times as far as Earth

Question 19.
Which planet is about $$\frac{1}{10}$$ of the distance Uranus is from the Sun?
__________

Mars

Explanation:
Mars = 227,900
$$\frac{1}{10}$$ x 2,871,000 = 287,100
Which planet is about $$\frac{1}{10}$$ of the distance Uranus is from the Sun

Question 20.
What’s the Error? Matt wrote the number four million, three hundred five thousand, seven hundred sixty-two as 4,350,762. Describe and correct his error.
Type below:
__________

Matt switched 2 digits in the thousands period: 4,305,762

Question 21.
Explain how you know that the values of the digit 5 in the numbers 150,000 and 100,500 are not the same.
Type below:
__________

In 150,000, the digit 5 is in the ten-thousands place, So, its value is 50,000; in 100,500, the digit 5 is in the hundreds place. So, its value is 500.

Question 22.
Test Prep In the number 869,653,214, which describes how the digit 6 in the ten-millions place compares to the digit 6 in the hundred-thousands place?
Options:
A. 10 times as much as
B. 100 times as much as
C. 1,000 times as much as
D.$$\frac{1}{10}$$ of

B. 100 times as much as

Explanation:
869,653,214
(8 x 100,000,000) + (6 x 10,000,000) + (9 x 1,000,000) + (6 x 1,00,000) + (5 x 10,000) + (3 x 1,000) + (2 x 100) + (1 x 10) + (4 x 1)
6 x 10,000,000 = 60,000,000
6 x 1,00,000 = 6,00,000
60,000,000/6,00,000 = 100

### Properties – Share and Show – Page No. 15

Use properties to find 4 × 23 × 25.

Question 1.
23 × × 25 ________ Property of Multiplication
23 × ( × ) ________ Property of Multiplication
23 ×
__________
____

23 x 4 x 25; Commutative Property of Multiplication
23 x (4 x 25); Associative Property of Multiplication
23 x 100
2,300

Use properties to find the sum or product.

Question 2.
89 + 27 + 11 = ____

89 + (27 + 11); Associative Property of Addition
89 + 38
127

Question 3.
9 × 52 = ____

468

Explanation:
9 x 52
Write 52 = (50 + 2)
9 x (50 + 2)
(9 x 50) + (9 x 2); Distributive Property of Multiplication
450 + 18
468

Question 4.
107 + 0 + 39 + 13 = ____

107 + 0 + 39 + 13
(107 + 0) + (39 + 13); Associative Property of Addition
107 + 0 = 107; Identity Property of Addition
107 + 52 = 159

Complete the equation, and tell which property you used.

Question 5.
9 × (30 + 7) = (9 × ____) + (9 × 7)

9 × (30 + 7) = (9 ×30) + (9 × 7)
Distributive Property of Multiplication

Explanation:
9 x (30 + 7)
(9 x 30) + (9 x 7); Distributive Property of Multiplication
270 + 63 = 333

Question 6.
0 + ____ = 47

Explanation:
0 + 47 = 47; Identity Property of Addition

Question 6.
Describe how you can use properties to solve problems more easily.
Type below:
__________

Using Properties of Addition and Properties of Multiplication, we can solve problems more easily. Simplifying problems is easy with the properties.

Practice: Copy and Solve Use properties to find the sum or product.

Question 7.
3 × 78 = ____

234, Associative Property of Multiplication

Explanation:
Write 78 as 6 x 13
3 x 6 x 13
(3 x 6) x 13; Associative Property of Multiplication
18 x 13 = 234

Question 8.
4 × 60 × 5 = ____

1,200; Associative Property of Multiplication

Explanation:
4 x 60 x 5
4 x (60 x 5); Associative Property of Multiplication
4 x 300 = 1,200

Question 9.
21 + 25 + 39 + 5 = ____

Explanation:
(21 + 25) + (39 + 5); Associative Property of Addition
46 + 44 = 90

Complete the equation, and tell which property you used.

Question 10.
11 + (19 + 6) = (11 + ____) + 6

11 + (19 + 6) = (11 + 19) + 6; Associative Property of Addition

Question 11.
25 + 14 = ____ + 25

25 + 14 = 14 + 25; Commutative Property of Addition

Question 12.
Show how you can use the Distributive Property to rewrite and find (32 × 6) + (32 × 4).
____

(32 × 6) + (32 × 4) = 32 x (6 + 4); Distributive Property

### Properties – Problem Solving – Page No. 16

Question 13.
Three friends’ meals at a restaurant cost $13,$14, and $11. Use parentheses to write two different expressions to show how much the friends spent in all. Which property does your pair of expressions demonstrate?$ ____

$38; Associative Law of Addition Explanation: Three friends’ meals at a restaurant cost$13, $14, and$11.
Friends spent in all = $13 +$14 + $11$13 + ($14 +$11) = ($13 +$14) + $11 Associative Law of Addition Question 14. Jacob is designing an aquarium for a doctor’s office. He plans to buy 6 red blond guppies, 1 blue neon guppy, and 1 yellow guppy. The table shows the price list for the guppies. How much will the guppies for the aquarium cost?$ ____

$162 Explanation: Jacob is designing an aquarium for a doctor’s office. He plans to buy 6 red blond guppies, 1 blue neon guppy, and 1 yellow guppy. (6 x$22) + (1 x $11) + (1 x$19) = $132 +$11 + $19 =$162

Question 15.
Sylvia bought 8 tickets to a concert. Each ticket costs $18. To find the total cost in dollars, she added the product 8 × 10 to the product 8 × 8, for a total of 144. Which property did Sylvia use? i. Distributive Property ii. Associative Property Answer: i. Distributive Property Explanation: Sylvia bought 8 tickets to a concert. Each ticket costs$18.
To find the total cost in dollars = 8 x $18 Using Distributive Property (8 × 10) + (8 × 8) = 8 x (10 + 8) = 144. Question 16. Sense or Nonsense? Julie wrote (15 – 6) – 3 = 15 – (6 – 3). Is Julie’s equation sense or nonsense? Do you think the Associative Property works for subtraction? Explain. __________ Answer: Nonsense; (15 – 6) – 3 = 9 – 3 = 6. 15 – (6 – 3) = 15 – 3 = 12 6 not equal to 12. So, Associative Property does not work for subtraction Question 17. Test Prep Canoes rent for$29 per day. Which expression can be used to find the cost in dollars of renting 6 canoes for a day?
Options:
A. (6 + 20) + (6 + 9)
B. (6 × 20) + (6 × 9)
C. (6 + 20) × (6 + 9)
D. (6 × 20) × (6 × 9)

B. (6 × 20) + (6 × 9)

Explanation:
Canoes rent for $29 per day. For renting 6 canoes for a day, 6 x$29
6 x $(20 + 9) = (6 x 20) + (6 x 9) ### Powers of 10 and Exponents – Share and Show – Page No. 18 Write in exponent form and word form. Question 1. 10 × 10 Exponent form: Word form: Type below: __________ Answer: Exponent form: 102 Word form: the second power of ten Explanation: 10 × 10 Base = 10; Exponent = 2; Exponent Form: 102 Word Form: the second power of ten Question 2. 10 × 10 × 10 × 10 Exponent form: Word form: Type below: __________ Answer: Exponent Form: 104 Word Form: the fourth power of ten Explanation: 10 × 10 × 10 × 10 Base = 10; Exponent = 4; Exponent Form: 104 Word Form: the fourth power of ten Find the value. Question 3. 102 = ____ Answer: 100 Explanation: 100 = 1; 101 = 1 x 10 = 10; 102 = 10 x 10 = 100; Question 4. 4 × 102 = ____ Answer: 400 Explanation: 4 × 102 = 100 = 1; 101 = 1 x 10 = 10; 102 = 10 x 10 = 100; 4 x 100 = 400 Question 5. 7 × 102 = ____ Answer: 700 Explanation: 7 × 102 = 100 = 1; 101 = 1 x 10 = 10; 102 = 10 x 10 = 100; 7 x 100 = 700 ### Powers of 10 and Exponents – On Your Own – Page No. 19 Write in exponent form and word form. Question 6. 10 × 10 × 10 exponent form: word form: Type below: __________ Answer: Exponent form: 103 Word form: the third power of ten Explanation: 10 × 10 × 10 Base = 10; Exponent = 3; Exponent Form: 103 Word Form: the third power of ten Question 7. 10 × 10 × 10 × 10 × 10 exponent form: word form: Type below: __________ Answer: Exponent form: 105 Word form: the fifth power of ten Explanation: 10 × 10 × 10 × 10 × 10 Base = 10; Exponent = 5; Exponent Form: 105 Word Form: the fifth power of ten Find the value. Question 8. 104 = ____ Answer: 10,000 Explanation: 100 = 1; 101 = 1 x 10 = 10; 102 = 10 x 10 = 100; 103 = 10 x 10 x 10 = 1,000; 104 = 10 x 10 x 10 x 10 = 10,000; Question 9. 2 × 103 = ____ Answer: 2,000 Explanation: 2 × 103 = 100 = 1; 101 = 1 x 10 = 10; 102 = 10 x 10 = 100; 103 = 10 x 10 x 10 = 1,000; 2 x 1,000 = 2,000 Question 10. 6 × 104 = ____ Answer: 60,000 Explanation: 6 × 104 100 = 1; 101 = 1 x 10 = 10; 102 = 10 x 10 = 100; 103 = 10 x 10 x 10 = 1,000; 104 = 10 x 10 x 10 x 10 = 10,000; 6 x 10,000 = 60,000 Complete the pattern. Question 11. 7 × 100 = 7 × 1 = _______ 7 × 101 = 7 × 10 = _______ 7 × 102 = 7 × 10 × 10 = _______ 7 × 103 = 7 × 10 × 10 × 10 = _______ 7 × 104 = 7 × 10 × 10 × 10 × 10 = _______ Answer: 7 × 100 = 7 × 1 = 7 7 × 101 = 7 × 10 = 70 7 × 102 = 7 × 10 × 10 = 7 x 100 = 700 7 × 103 = 7 × 10 × 10 × 10 = 7 x 1,000 = 7,000 7 × 104 = 7 × 10 × 10 × 10 × 10 = 7 x 10,000 = 70,000 Explanation: 100 = 1; 101 = 1 x 10 = 10; 102 = 10 x 10 = 100; 103 = 10 x 10 x 10 = 1,000; 104 = 10 x 10 x 10 x 10 = 10,000; Question 12. 9 × 100 = _______ = 9 9 × 101 = _______ = 90 9 × 102 = _______ = 900 9 × 103 = _______ = 9,000 9 × 104 = _______ = 90,000 Answer: 9 × 100 = 9 x 1 = 9 9 × 101 = 9 x 10 = 90 9 × 102 = 9 x 10 x 10 = 900 9 × 103 = 9 x 10 x 10 x 10= 9,000 9 × 104 = 9 x 10 x 10 x 10 x 10 = 90,000 Explanation: 100 = 1; 101 = 1 x 10 = 10; 102 = 10 x 10 = 100; 103 = 10 x 10 x 10 = 1,000; 104 = 10 x 10 x 10 x 10 = 10,000; Question 13. 12 × 100 = 12 × 1 = _______ 12 × 101 = 12 × 10 = _______ 12 × 102 = 12 × 10 × 10 = _______ 12 × 103 = 12 × 10 × 10 × 10 _______ 12 × 104 = 12 × 10 × 10 × 10 × 10 _______ Answer: 12 × 100 = 12 × 1 = 12 12 × 101 = 12 × 10 = 120 12 × 102 = 12 × 10 × 10 = 1,200 12 × 103 = 12 × 10 × 10 × 10 = 12,000 12 × 104 = 12 × 10 × 10 × 10 × 10 = 120,000 Explanation: 100 = 1; 101 = 1 x 10 = 10; 102 = 10 x 10 = 100; 103 = 10 x 10 x 10 = 1,000; 104 = 10 x 10 x 10 x 10 = 10,000; Question 14. 103 = 10 × 10n What is the value of n? Think: 103 = 10 × () × (), or 10 × () The value of n is …….. n = ______ Answer: 2 Explanation: 103 = 10 × 10n 103 = 10 x 10 x 10 = 10 x 102 The value of n is 2 Question 15. Explain how to write 50,000 using exponents. Type below: __________ Answer: 5 x 104 Explanation: 5 x 10,000 100 = 1; 101 = 1 x 10 = 10; 102 = 10 x 10 = 100; 103 = 10 x 10 x 10 = 1,000; 104 = 10 x 10 x 10 x 10 = 10,000; 10,000 = 10 x 10 x 10 x 10 = 104 5 x 104 ### Powers of 10 and Exponents – UNLOCK the Problem – Page No. 20 Question 16. Lake Superior is the largest of the Great Lakes. It covers a surface area of about 30,000 square miles. How can you show the estimated area of Lake Superior as a whole number multiplied by a power of ten? a. What are you asked to find? Options: A. 3 × 102 sq mi B. 3 × 103 sq mi C. 3 × 104 sq mi D. 3 × 105 sq mi Answer: C. 3 × 104 sq mi Explanation: Lake Superior is the largest of the Great Lakes. It covers a surface area of about 30,000 square miles. 3 x 10,000 100 = 1; 101 = 1 x 10 = 10; 102 = 10 x 10 = 100; 103 = 10 x 10 x 10 = 1,000; 104 = 10 x 10 x 10 x 10 = 10,000; 10,000 = 10 x 10 x 10 x 10 = 104 3 x 104 Question 16. b. How can you use a pattern to find the answer? Type below: __________ Answer: 3 x 10,000 100 = 1; 101 = 1 x 10 = 10; 102 = 10 x 10 = 100; 103 = 10 x 10 x 10 = 1,000; 104 = 10 x 10 x 10 x 10 = 10,000; 10,000 = 10 x 10 x 10 x 10 = 104 3 x 104 Question 16. c. Write a pattern using the whole number 3 and powers of ten. 3 × 101 = 3 × 10 = 3 × 102 = = 3 × 103 = = 3 × 104 = = Type below: __________ Answer: 3 × 101 = 3 × 10 = 3 × 102 = 3 x 10 x 10 = 300 3 × 103 = 3 x 10 x 10 x 10 = 3,000 3 × 104 = 3 x 10 x 10 x 10 x 10 = 30,000 Question 16. d. Fill in the correct answer choice above. Type below: __________ Answer: 3 × 104 = 3 x 10 x 10 x 10 x 10 = 30,000 Question 17. The Earth’s diameter through the equator is about 8,000 miles. What is the Earth’s estimated diameter written as a whole number multiplied by a power of ten? Options: A. 8 × 101 miles B. 8 × 102 miles C. 8 × 103 miles D. 8 × 104 miles Answer: C. 8 × 103 miles Explanation: The Earth’s diameter through the equator is about 8,000 miles. 8 x 1,000 100 = 1; 101 = 1 x 10 = 10; 102 = 10 x 10 = 100; 103 = 10 x 10 x 10 = 1,000; 1,000 = 10 x 10 x 10 8 x 1,000 = 8 x 103 Question 18. The Earth’s circumference around the equator is about 25 × 103 miles. What is the Earth’s estimated circumference written as a whole number? Options: A. 250,000 miles B. 25,000 miles C. 2,500 miles D. 250 miles Answer: B. 25,000 miles Explanation: The Earth’s circumference around the equator is about 25 × 103 miles. 25 × 103 miles; 100 = 1; 101 = 1 x 10 = 10; 102 = 10 x 10 = 100; 103 = 10 x 10 x 10 = 1,000; 25 x 1,000 = 25,000 miles ### Multiplication Patterns – Share and Show – Page No. 22 Use mental math and a pattern to find the product. Question 1. • What basic fact can you use to help you find 30×4,000? 30 × 4,000 = ____ Answer: 3 x 4 = 12 Explanation: 30 × 4,000 The basic fact is 3 x 4 = 12 Use mental math to complete the pattern. Question 2. 1 × 1 = 1 1 × 101 = _______ 1 × 102 = _______ 1 × 103 = _______ Answer: 1 × 1 = 1 1 × 101 = 10 1 × 102 = 100 1 × 103 = 1,000 Explanation: 1 × 1 = 1 1 × 101 = 1 x 10 = 10 1 × 102 = 1 x 10 x 10 = 100 1 × 103 = 1 x 10 x 10 x 10 = 1,000 Question 3. 7 × 8 = 56 (7 × 8) × 101 = _______ (7 × 8) × 102 = _______ (7 × 8) × 106 = _______ Answer: 7 × 8 = 56 (7 × 8) × 101 = 560 (7 × 8) × 102 = 5,600 (7 × 8) × 106 = 56,000,000 Explanation: 7 × 8 = 56 (7 × 8) × 101 = 56 x 10 = 560 (7 × 8) × 102 = 56 x 10 x 10 = 5,600 (7 × 8) × 106 = 56 x 10 x 10 x 10 x 10 x 10 x 10 = 56,000,000 Question 4. 6 × 5 = _______ 6 × 5 × _______ = 300 6 × 5 × _______ = 3000 6 × 5 × _______ = 30,000 Answer: 6 × 5 = 30 6 × 5 × 101 = 300 6 × 5 × 103 = 3000 6 × 5 × 104 = 30,000 Explanation: 6 × 5 = 30 6 × 5 × 10 = 300 6 × 5 × 10 x 10 x 10 = 3000 6 × 5 × 10 x 10 x 10 x 10 = 30,000 On Your Own Use mental math to complete the pattern. Question 5. 9 × 5 = 45 (9 × 5) × 101 = _______ (9 × 5) × 102 = _______ (9 × 5) × 103 = _______ Answer: 9 × 5 = 45 (9 × 5) × 101 = 450 (9 × 5) × 102 = 4,500 (9 × 5) × 103 = 45,000 Explanation: 9 × 5 = 45 (9 × 5) × 101 = 45 x 10 = 450 (9 × 5) × 102 = 45 x 10 x 10 = 4,500 (9 × 5) × 103 = 45 x 10 x 10 x 10 = 45,000 Question 6. 3 × 7 = 21 (3 × 7) × 101 = _______ (3 × 7) × 102 = _______ (3 × 7) × 103 = _______ Answer: 3 × 7 = 21 (3 × 7) × 101 = 210 (3 × 7) × 102 = 2,100 (3 × 7) × 103 = 21,000 Explanation: 3 × 7 = 21 (3 × 7) × 101 = 21 x 10 = 210 (3 × 7) × 102 = 21 x 10 x 10 = 2,100 (3 × 7) × 103 = 21 x 10 x 10 x 10 = 21,000 Question 7. 5 × 4 = _______ (5 × 4) × _______ = 200 (5 × 4) × _______ = 2,000 (5 × 4) × _______ = 20,000 Answer: 5 × 4 = 20 (5 × 4) × 101 = 200 (5 × 4) × 102 = 2,000 (5 × 4) × 103 = 20,000 Explanation: 5 × 4 = 20 (5 × 4) × 10 = 200 (5 × 4) × 10 x 10 = 2,000 (5 × 4) × 10 x 10 x 10 = 20,000 Question 8. 5 × 7 = _______ (5 × 7) × _______ = 350 (5 × 7) × _______ = 3,500 (5 × 7) × _______ = 35,000 Answer: 5 × 7 = 35 (5 × 7) × 101 = 350 (5 × 7) × 102 = 3,500 (5 × 7) × 103 = 35,000 Explanation: 5 × 7 = 35 (5 × 7) × 10 = 350 (5 × 7) × 10 x 10 = 3,500 (5 × 7) × 10 x 10 x 10 = 35,000 Question 9. 4 × 2 = 8 (4 × 2) × 101 = _______ (4 × 2) × 102 = _______ (4 × 2) × 103 = _______ Answer: 4 × 2 = 8 (4 × 2) × 101 = 80 (4 × 2) × 102 = 800 (4 × 2) × 103 = 8,000 Explanation: 4 × 2 = 8 (4 × 2) × 101 = 8 x 10 = 80 (4 × 2) × 102 = 8 x 10 x 10 = 800 (4 × 2) × 103 = 8 x 10 x 10 x 10 = 8,000 Question 10. 6 × 7 = 42 (6 × 7) × 101 = _______ (6 × 7) × 102 = _______ (6 × 7) × 103 = _______ Answer: 6 × 7 = 42 (6 × 7) × 101 = 420 (6 × 7) × 102 = 4,200 (6 × 7) × 103 = 42,000 Explanation: 6 × 7 = 42 (6 × 7) × 101 = 42 x 10 = 420 (6 × 7) × 102 = 42 x 10 x 10 = 4,200 (6 × 7) × 103 = 42 x 10 x 10 x 10 = 42,000 Use mental math and a pattern to find the product. Question 11. (6 × 6) × 101 = ____ Answer: (6 × 6) × 101 = 360 Explanation: 6 x 6 =36 (6 × 6) × 101 = 36 x 10 = 360 Question 12. (7 × 4) × 103 = ____ Answer: 28,000 Explanation: 7 x 4 = 28 (7 × 4) × 101 = 28 x 10 = 280 (7 × 4) × 102 = 28 x 10 x 10 = 2,800 (7 × 4) × 103 = 28 x 10 x 10 x 10 = 28,000 Question 13. (9 × 8) × 102 = ____ Answer: 7,200 Explanation: (9 × 8) = 72 (9 × 8) × 101 = 72 x 10 = 720 (9 × 8) × 102 = 72 x 10 x 10 = 7,200 Question 14. (4 × 3) × 102 = ____ Answer: 1,200 Explanation: (4 × 3) = 12 (4 × 3) × 101 = 12 x 10 = 120 (4 × 3) × 102 = 12 x 10 x 10 = 1,200 Question 15. (2 × 5) × 103 = ____ Answer: 10,000 Explanation: (2 × 5) = 10 (2 × 5) × 101 = 10 x 10 = 100 (2 × 5) × 102 = 10 x 10 x 10 = 1,000 (2 × 5) × 103 = 10 x 10 x 10 x 10 = 10,000 Question 16. (2 × 8) × 102 = ____ Answer: 1,600 Explanation: (2 × 8) = 16 (2 × 8) × 101 = 16 x 10 = 160 (2 × 8) × 102 = 16 x 10 x 10 = 1,600 Question 17. (6 × 5) × 103 = ____ Answer: 30,000 Explanation: (6 × 5) = 30 (6 × 5) × 101 = 30 x 10 = 300 (6 × 5) × 102 = 30 x 10 x 10 = 3,000 (6 × 5) × 103 = 30 x 10 x 10 x 10 = 30,000 Question 18. (8 × 8) × 104 = ____ Answer: 640,000 Explanation: (8 × 8) = 64 (8 × 8) × 101 = 64 x 10 = 640 (8 × 8) × 102 = 64 x 10 x 10 = 6,400 (8 × 8) × 103 = 64 x 10 x 10 x 10 = 64,000 (8 × 8) × 104 = 64 x 10 x 10 x 10 x 10 = 640,000 Question 19. (7 × 8) × 104 = ____ Answer: 560,000 Explanation: (7 × 8) = 56 (7 × 8) × 101 = 56 x 10 = 560 (7 × 8) × 102 = 56 x 10 x 10 = 5,600 (7 × 8) × 103 = 56 x 10 x 10 x 10 = 56,000 (7 × 8) × 104 = 56 x 10 x 10 x 10 x 10 = 560,000 ### Multiplication Patterns – Share and Show – Page No. 23 Use mental math to complete the table. Question 20. 1 roll = 50 dimes ; Think:50 dimes per roll × 20 rolls =(5 × 2) × (10 × 10) Type below: __________ Answer: Explanation: 1 roll = 50 dimes ; Think:50 dimes per roll × 20 rolls =(5 × 2) × (10 × 10) = 10 x 102 50 dimes per roll × 30 rolls = (5 x 3) x (10 × 10) = 15 x 102 50 dimes per roll × 40 rolls = (5 x 4) x (20 × 10) = 20 x 102 50 dimes per roll × 50 rolls = (5 x 5) x (10 × 10) = 25 x 102 50 dimes per roll × 60 rolls = (5 x 6) x (10 × 10) = 30 x 102 50 dimes per roll × 70 rolls = (5 x 7) x (10 × 10) = 35 x 102 50 dimes per roll × 80 rolls = (5 x 8) x (10 × 10) = 40 x 102 50 dimes per roll × 90 rolls = (5 x 9) x (10 × 10) = 45 x 102 50 dimes per roll × 100 rolls = (5 x 10) x (10 × 10) = 50 x 102 Question 21. 1 roll = 40 quarters ; Think:40 quarters per roll × 20 rolls =(4 × 2) × (10 × 10) Type below: __________ Answer: Explanation: 1 roll = 40 quarters ; Think:40 quarters per roll × 20 rolls =(4 × 2) × (10 × 10) = 8 x 102 40 quarters per roll × 30 rolls =(4 × 3) × (10 × 10) = 12 x 102 40 quarters per roll × 40 rolls =(4 × 4) × (10 × 10) = 16 x 102 40 quarters per roll × 50 rolls =(4 × 5) × (10 × 10) = 20 x 102 40 quarters per roll × 60 rolls =(4 × 6) × (10 × 10) = 24 x 102 40 quarters per roll × 70 rolls =(4 × 7) × (10 × 10) = 28 x 102 40 quarters per roll × 80 rolls =(4 × 8) × (10 × 10) = 32 x 102 40 quarters per roll × 90 rolls =(4 × 9) × (10 × 10) = 36 x 102 40 quarters per roll × 100 rolls =(4 × 10) × (10 × 10) = 40 x 102 Question 22. Type below: __________ Answer: Explanation: 80 x 800 = 64 x 103 80 x 6 = (8 x 6) x 10 = 48 x 101 80 x 70 = (8 x 7) x (10 x 10) = 56 x 102 80 x 9,000 = (8 x 9) x (10 x 10 x 10 x 10) = 64 x 104 Question 23. Type below: __________ Answer: Explanation: Given that 90 x 9,000 = (9 x 9) x 10 x 10 x 10 x 10 = 81 x 104 90 x 6 = (9 x 6) x 10 = 54 x 101 90 x 70 = (9 x 7) x (10 x 10) = 63 x 102 90 x 800 = (9 x 8) x (10 x 10 x 10) = 72 x 103 Problem Solving Use the table for 24–26. Question 24. What if you magnified the image of a cluster fly by 9 × 103 ? What would the length appear to be? ____ mm Answer: 9,000 mm Explanation: 9 × 103 = 9 x 10 x 10 x 10 = 9,000 Question 25. If you magnified the image of a fire ant by 4 × 103 and a tree hopper by 3 × 103 , which insect would appear longer? How much longer? ____ mm Answer: 103 mm Explanation: fire ant: 4 × 103 = 4 x 10 x 10 x 10 = 4,000 mm tree hopper: 3 × 103 = 3 x 10 x 10 x 10 = 3,000 mm 4,000 > 3,000. So, fire ant appears to be longer. 4,000 – 3,000 = 1,000 = 103 Question 26. John wants to magnify the image of a fire ant and a crab spider so they appear to be the same length. How many times their actual sizes would he need to magnify each image? Fire ant by _______ times Crab spider by ______ times Answer: Fire ant by 5 times Crab spider by 4 times Explanation: Given that Fire ant = 4 mm crab spider = 5 mm So, to make them have the same lengths, multiply fire ant by 5 mm and multiply Crab spider by 4 mm ### Multiplication Patterns – Share and Show – Page No. 24 Question 27. What does the product of any whole-number factor multiplied by 100 always have? Explain. Type below: __________ Answer: The product of any whole number factor multiplied by 100 has two digits which are 0 in ones and tens place. Example: 2 x 100 = 200 Question 28. Test Prep How many zeros are in the product (5 × 4) × 104? Options: A. 3 B. 4 C. 5 D. 6 Answer: C. 5 Explanation: (5 × 4) × 104 = 20 x 104 = 2 x 105 5 zeroes Use patterns and mental math to solve. Question 29. A human body has about 30 times as many platelets as white blood cells. A small sample of blood has 8×103 white blood cells. About how many platelets are in the sample? ______ platelets Answer: 24 x 104 platelets Explanation: Let the number of platelets = s. s = 30 x 8×103 s = 30 x 8 x 10 x 10 x 10 = (3 x 8) x (10 x 10 x 10 x 10) = 24 x 104 Question 30. Basophils and monocytes are types of white blood cells. A blood sample has about 5 times as many monocytes as basophils. If there are 60 basophils in the sample, about how many monocytes are there? ______ monocytes Answer: 3 x 102 monocytes Explanation: Let the number of monocytes = S S = 5 x 60 = 300 = 3 x 100 S = 3 x 102 Question 31. Lymphocytes and eosinophils are types of white blood cells. A blood sample has about 10 times as many lymphocytes as eosinophils. If there are 2 × 102 eosinophils in the sample, about how many lymphocytes are there? ______ lymphocytes Answer: 2 × 103 lymphocytes Explanation: Lymphocytes and eosinophils are types of white blood cells. A blood sample has about 10 times as many lymphocytes as eosinophils. There are 2 × 102 eosinophils in the sample Then, Lymphocytes = 10 x 2 × 102 eosinophils = 2 × 103 Question 32. An average person has 6 × 102 times as many red bloods cells as white blood cells. A small sample of blood has 7 × 103 white blood cells. About how many red blood cells are in the sample? ______ red blood cells Answer: 42 x 10 red blood cells Explanation: Let the red blood cells = S S = 7 × 103 x 6 × 102 S = 42 x 10 ### Mid-Chapter Checkpoint – Vocabulary – Page No. 25 Choose the best term for the box. Question 1. A group of three digits separated by commas in a multidigit number is a __ ________ Answer: Period Question 2. An __ is the number that tells how many times a base is used as a factor ________ Answer: exponent Concepts and Skills Complete the sentence. Question 3. 7 is $$\frac{1}{10}$$ of ______ Answer: 70 Explanation: Let the unknown number is S. 7 = $$\frac{1}{10}$$ S S = 7 X 10 = 70 Question 4. 800 is 10 times as much as ______ Answer: 80 Explanation: Let the unknown number is S. 800 = 10S S = 800/10 = 80. Write the value of the underlined digit. Question 5. 6,581,678 ________ Answer: 80,000 Explanation: (6 x 1,000,000) + (5 x 1,00,000) + (8 x 10,000) + (1 x 1,000) + (6 x 100) + (7 x 10) + (8 x 1) 8 x 10,000 = 80,000 Question 6. 25,634 ________ Answer: 600 Explanation: (2 x 10,000) + (5 x 1,000) + (6 x 100) + (3 x 10) + (4 x 1) 6 x 100 = 600 Question 7. 34,634,803 ________ Answer: 4,000,000 Explanation: (3 x 10,000,000) + (4 x 1,000,000) + (6 x 1,00,000) + (3 x 10,000) + (4 x 1,000) + (8 x 100) + (0 x 10) + (3 x 1) 4 x 1,000,000 = 4,000,000 Question 8. 2,764,835 ________ Answer: 700,000 Explanation: (2 x 1,000,000) + (7 x 1,00,000) + (6 x 10,000) + (4 x 1,000) + (8 x 100) + (3 x 10) + (5 x 1) 7 x 1,00,000 = 700,000 Complete the equation, and tell which property you used. Question 9. 8 × (14 + 7) = ________ + (8 × 7) Answer: 8 × (14 + 7) = (8 x 14) + (8 × 7); Distributive Property of Multiplication Explanation: 8 × (14 + 7) (8 x 14) + (8 × 7); Distributive Property of Multiplication Question 10. 7 + (8 + 12) = ________ + 12 Answer: 7 + (8 + 12) = (7 + 8) + 12 Associative Property of Addition Find the value. Question 11. 103 = ______ Answer: 1,000 Explanation: 100 = 1; 101 = 1 x 10 = 10; 102 = 10 x 10 = 100; 103 = 10 x 10 x 10 = 1,000; Question 12. 6 × 102 = ______ Answer: 600 Explanation: 6 × 102 100 = 1; 101 = 1 x 10 = 10; 102 = 10 x 10 = 100; 6 x 100 = 600 Question 13. 4 × 104 = ______ Answer: 40,000 Explanation: 4 × 104 100 = 1; 101 = 1 x 10 = 10; 102 = 10 x 10 = 100; 103 = 10 x 10 x 10 = 1,000; 104 = 10 x 10 x 10 x 10 = 10,000; 4 x 10,000 = 40,000 Use mental math and a pattern to find the product. Question 14. 70 × 300 = ______ Answer: 21,000 Explanation: 70 × 300 = (7 x 3) x (10 x 10 x 10) = 21 x 1,000 = 21,000 Question 15. (3 × 4) × 103 = ______ Answer: 12,000 Explanation: (3 × 4) × 103 100 = 1; 101 = 1 x 10 = 10; 102 = 10 x 10 = 100; 103 = 10 x 10 x 10 = 1,000; 12 x 1,000 = 12,000 ### Mid-Chapter Checkpoint – Page No. 26 Fill in the bubble completely to show your answer. Question 16. DVDs are on sale for$24 each. Which expression can be used to find the cost in dollars of buying 4 DVDs?
Options:
A. (4 + 20) + (4 + 4)
B. (4 × 20) + (4 × 4)
C (4 + 20) × (4 + 4)
D. (4 × 20) × (4 × 4)

B. (4 × 20) + (4 × 4)

Explanation:
24 can be written as 25 – 1
4 x 24 = 4 x (20 + 4) = (4 x 20) + (4 x 4)

Question 17.
The Muffin Shop chain of bakeries sold 745,305 muffins last year. Which choice shows that number in expanded form?
Options:
A. (7 × 100,000) + (45 × 10,000) + (3 × 100) + (5 × 10)
B. (7 × 100,000) + (4 × 10,000) + (5 × 1,000) + (5 × 10)
C. (7 × 100,000) + (4 × 10,000) + (5 × 1,000) + (3 × 100) + (5 × 1)
D. (7 × 100,000) + (4 × 10,000) + (3 × 100) + (5 × 1)

C. (7 × 100,000) + (4 × 10,000) + (5 × 1,000) + (3 × 100) + (5 × 1)

Explanation:
First, we can write 745,305 as:
700,000 + 40, 000 + 5,000 + 300 + 5
(7 x 100,000) + (4 x 10,000) + (5 x 1,000) + (3 x 100) + 5

Question 18.
The soccer field at Mario’s school has an area of 6,000 square meters. How can Mario show the area as a whole number multiplied by a power of ten?
Options:
A. 6 × 104 sq m
B. 6 × 103 sq m
C. 6 × 102 sq m
D. 6 × 101 sq m

B. 6 × 103 sq m

Explanation:
6,000 square meters = 6 x 1,000 = 6 x 10 x 10 x 10 = 6 × 103 sq m

Question 19.
Ms. Alonzo ordered 4,000 markers for her store. Only $$\frac{1}{10}$$ of them arrived. How many markers did she receive?
Options:
A. 4
B. 40
C. 400
D. 1,400

C. 400

Explanation:
Ms. Alonzo ordered 4,000 markers for her store. Only $$\frac{1}{10}$$ of them arrived.
4,000 x $$\frac{1}{10}$$ = 400

Question 20.
Mark wrote the highest score he made on his new video game as the product of 70 × 6,000. What was his score?
Options:
A. 420
B. 4,200
C. 42,000
D. 420,000

D. 420,000

Explanation:
Mark wrote the highest score he made on his new video game as the product of 70 × 6,000.
(7 x 6) x (10 x 10 x 10 x 10) = 42 x 10,000 = 420,000

### Multiply by 1-digit numbers – Share and Show – Page No. 29

Complete to find the product.

Question 1.
6 × 796           Estimate: 6 × ___ = ___

______

4,776

Explanation:

Estimate. Then find the product.

Question 2.
Estimate: ___
6 0 8
×   8
———-
Estimate: ________
Product: 608 × 8 = ________

Estimate: 6,000
Product: 608 × 8 = 4,864

Explanation:
Estimate: 608 is close to 600; 8 is close to 10
600 x 10 = 6,000
608 x 8
Multiply the ones; 8 x 8 = 64. 4 ones and 6 tens. Write the ones and the
regrouped tens.
Multiply the tens; 0 x 8 = 0 + 6 = 6
Multiply the hundreds; 6 x 8 = 48.
So, 4,864 is the product of 608 × 8
Product: 4,864

Question 3.
Estimate: __
5 5 6
×   4
———–
Estimate: ________
Product: 556 × 4 = ________

Estimate: 2,780
Product: 556 × 4 = 2,224

Explanation:
Estimate: 556 is close to 550; 4 is close to 5
556 x 5 = 2,780
556 × 4
Multiply the ones; 6 x 4 = 24. 4 ones and 2 tens. Write the ones and the
regrouped tens.
Multiply the tens; 5 x 4 = 20 + 2 = 22; 2 tens and 2 hundreds. Write the tens and regrouped hundreds.
Multiply the hundreds; 5 x 4 = 20; 20 + 2 = 22.
So, 2,224 is the product of 556 × 4
Product: 2,224

Question 4.
Estimate:
1,925
×    7
———–
Estimate: ________
Product: 1,925 × 7 = ________

Estimate: 10,000
Product: 1,925 × 7 = 13,475

Explanation:
Estimate: 1,925 is close to 2000; 7 is close to 5
2,000 x 5 = 10,000
1,925 × 7
Multiply the ones; 7 x 5 = 35. 5 ones and 3 tens. Write the ones and the
regrouped tens.
Multiply the tens; 7 x 2 = 14; 14 + 3 = 17; 7 tens and 1 hundreds. Write the tens and regrouped hundreds.
Multiply the hundreds; 7 x 9 = 63; 63 + 1 = 64. 4 hundred and 6 thousand Write the hundreds and regrouped thousands.
Multiply the thousands; 7 x 1 = 7; 7 + 6 = 13
So, 13,475 is the product of 1,925 × 7
Product: 13,475

Estimate. Then find the product.

Question 5.
Estimate:__
7 9 4
×   3
———-
Estimate: ________
Product:794 × 3 = ________

Estimate: 800
Product:794 × 3 = 2,382

Explanation:
Estimate: 794 is close to 800 and 3 is close to 1
800 x 1 = 800
794 x 3 = (700 + 90 + 4) x 3 = (700 x 3) + (90 x 3) + (4 x 3) = 2100 + 270 + 12 = 2,382

Question 6.
Estimate:___
8 2 2
×   6
———-
Estimate: ________
822 × 6 = ________

Estimate: 4,000
822 × 6 = 4,932

Explanation:
Estimate: 822 is close to 800 and 6 is close to 5
800 x 5 = 4,000
822 × 6 = (800 + 20 + 2) x 6 = (800 x 6) + (20 x 6) + (2 x 6) = 4800 + 120 + 12 = 4,932

Question 7.
Estimate:
3,102
×    5
———–
Estimate: ________
Product: 3,102 × 5 = ________

Estimate: 15,500
Product: 3,102 × 5 = 15,510

Explanation:
Estimate: 3,102 is close to 3,100 and 5 is close to 5
3,100 x 5 = 15,500
3,102 x 5 = (3,000 + 100 + 0 + 2) x 5 = (3000 x 5) + (100 x 5) + 0 + (2 x 5) = 15,000 + 500 + 0 + 10 = 15,510

Algebra Solve for the unknown number.

Question 8.
3 9 6
×   6
———
2, 3 6
396 × 6 = 23 ______ 6

7

Explanation:
396 x 6 = (300 + 90 + 6) x 6 = (300 x 6) + (90 x 6) + (6 x 6) = 1800 + 540 + 36 = 2376. So, the unknown number is 7

Question 9.
5,1 2
×   8
——–
16
Type below:
__________

5127 x 8 = 41,016.
Unknown numbers = 7 and 410

Explanation:
5,127 x 8 = (5000 + 100 + 20 + 7) x 8 = (5000 x 8) + (100 x 8) + (20 x 8) + (7 x 8) = 40000 + 800 + 160 + 56 = 41,016

Question 10.
8, 5 6
×    7
———
60,03
Type below:
__________

8,576 x 7 = 60,032

Explanation:
8,576 x 7 = (8000 + 500 + 70 + 6) x 7 = (8000 x 7) + (500 x 7) + (70 x 7) + (6 x 7) = 56000 + 3500 + 490 + 42 = 60,032

Practice: Copy and Solve Estimate. Then find the product.

Question 11.
116 × 3 = _______
Estimate: _______

Estimate: 300
116 × 3 = 348

Explanation:
Estimate: 116 is close to 100;
100 x 3 = 300
116 x 3
6 x 3 =18; add ones and regroup tens
3 x 1 = 3; 3 + 1 = 4
3 x 1 = 3
So, 348 is the product

Question 12.
338 × 4 = _______
Estimate: _______

338 × 4 = 1,352
Estimate: 1,200

Explanation:
Estimate: 338 is close to 300;
300 x 4 = 1,200
338 × 4
8 x 4 =32; add ones and regroup tens
3 x 4 = 12; 12 + 3 = 15; add tens and regroup hundreds
3 x 4 = 12; 12 + 1 = 13
So, 1352 is the product

Question 13.
6 × 219 = _______
Estimate: _______

6 × 219 = 1,314
Estimate: 1200

Explanation:
Estimate: 219 is close to 200
200 x 6 = 1200
6 × 219
6 x 9 = 54; add ones and regroup tens
6 x 1 = 6; 6 + 5 = 11; add tens and regroup hundreds
6 x 2 = 12; 12 + 1 = 13
So, 1,314

Question 14.
7 × 456 = _______
Estimate: _______

7 × 456 = 3192
Estimate: 3500

Explanation:
Estimate: 456 is close to 500
500 x 7 = 3500
7 x 456
7 x 6 = 42; add ones and regroup tens
7 x 5 = 35; 35 + 4 = 39; add tens and regroup hundreds
7 x 4 = 28; 28 + 3 = 31
So, 3192

Question 15.
5 × 1,012 = _______
Estimate: _______

5 × 1,012 = 5,060
Estimate: 5,000

Explanation:
Estimate: 1,012 is close to 1,000
1,000 x 5 = 5,000
5 × 1,012
5 x 2 = 10; add ones and regroup tens
5 x 1 = 5; 5 + 1 = 6; add tens and regroup hundreds
5 x 0 = 0
5 x 1 = 5
So, 5,060

Question 16.
2,921 × 3 = _______
Estimate: _______

2,921 × 3 = 8,763
Estimate: 9,000

Explanation:
Estimate: 2,921 is close to 3,000
3,000 x 3 = 9,000
2,921 × 3
3 x 1 = 3;
3 x 2 = 6;
3 x 9 = 27; add hundreds and regroup thousands
3 x 2 = 6; 6 + 2 = 8
So, 8,763

Question 17.
8,813 × 4 = _______
Estimate: _______

8,813 × 4 = 35,252
Estimate: 3,600

Explanation:
Estimate: 8,813 is close to 9,000
9,000 x 4 = 3,600
8,813 × 4
4 x 3 = 12; add ones and regroup tens
4 x 1 = 4; 4 + 1 = 5;
4 x 8 = 32; add hundreds and regroup thousands
4 x 8 = 32; 32 + 3 = 35
So, 35,252

Question 18.
9 × 3,033 = _______
Estimate: _______

Explanation:
Estimate: 3,033 is close to 3,000
3,000 x 9 = 27,000
9 × 3,033
9 x 3 = 27; add ones and regroup tens
9 x 3 = 27; 27 +  = 11; add tens and regroup hundreds
6 x 2 = 12; 12 + 1 = 13
So, 1,314

### Multiply by 1-digit numbers – Problem Solving – Page No. 30

What’s the Error?

Question 19.
The Plattsville Glee Club is sending 8 of its members to a singing contest in Cincinnati, Ohio. The cost will be $588 per person. How much will it cost for the entire group of 8 students to attend? Both Brian and Jermaine solve the problem. Brian says the answer is$40,074. Jermaine’s answer is $4,604. Estimate the cost. A reasonable estimate is _$ ______

$4,800 Explanation: The Plattsville Glee Club is sending 8 of its members to a singing contest in Cincinnati, Ohio. The cost will be$588 per person.
So, for entire group 8 x $588 =$4,704
Jermaine’s answer is correct. Because the $4,604 is close to$4,704
588 is close to 600. So, 600 x 8 = $4,800 Question 19. Although Jermaine’s answer seems reasonable, neither Brian nor Jermaine solved the problem correctly. Find the errors in Brian’s and Jermaine’s work. Then, solve the problem correctly. What error did Brian make? Explain. Type below: __________ Answer: When Brian multiplied the tens, he wrote the total number of tens in the product instead of regrouping, so the place values of his product are incorrect. Question 19. What error did Jermaine make? Explain. Type below: __________ Answer: Jermaine regrouped the wrong amount of hundreds. He regrouped the tens as 6 hundred instead of 7 hundred.$588 x 8 = $4,704 Question 19. How could you predict that Jermaine’s answer might be incorrect using your estimate? Type below: __________ Answer: I used 600 × 8 to estimate the product; 588 is 12 less than 600. Since 12 × 8 = 96, and 4,604 is almost 200 less than the estimate of 4,800, the answer is probably too low. ### Multiply by 2-digit numbers – Share and Show – Page No. 33 Complete to find the product Question 1. Type below: __________ Answer: 2,752 Explanation: 64 x 3 = 192 64 x 40 = 2,560 2,560 + 192 = 2,752 Question 2. Type below: __________ Answer: 21,698 Explanation: 571 x 8 = 4,568 571 x 30 = 17,130 17,130 + 4,568 = 21,698 Estimate. Then find the product. Question 3. Estimate:____ 2 4 × 1 5 ———- Estimate: ________ Product: ________ Answer: Estimate: 300 Product: 360 Explanation: 2 4 x 15 Estimate: 20 x 15 = 300 24 x 5 = 120 24 x 10 = 240 Product:: 240 + 120 = 360 Question 4. Estimate:____ 3 7 × 6 3 ———- Estimate: ________ Product: ________ Answer: Estimate: 2,400 Product: 2,331 Explanation: 37 x 63 Estimate: 40 x 60 = 2,400 37 x 3 = 111 37 x 60 = 2220 Product:: 2220 + 111 = 2,331 Question 5. Estimate:____ 3 8 4 × 4 5 ———- Estimate: ________ Product: ________ Answer: Estimate: 20,000 Product: 17,280 Explanation: 384 x 45 Estimate: 400 x 50 = 20,000 384 x 5 = 1920 384 x 40 = 15,360 Product:: 15,360 + 1920 = 17,280 On Your Own Estimate. Then find the product. Question 6. Estimate:____ 2 8 × 2 2 ———- Estimate: ________ Product: ________ Answer: Estimate: 600 Product: 616 Explanation: 28 x 22 Estimate: 30 x 20 = 600 28 x 2 = 56 28 x 20 = 560 Product:: 56 + 560 = 616 Question 7. Estimate:____ 9 3 × 7 6 ———- Estimate: ________ Product: ________ Answer: Estimate: 7200 Product: 7,068 Explanation: 93 x 76 Estimate: 90 x 80 = 7200 93 x 6 = 558 93 x 70 = 6,510 Product:: 558 + 6,510 = 7,068 Question 8. Estimate:____ 2 9 5 × 5 1 ———- Estimate: ________ Product: ________ Answer: Estimate: 15,000 Product: 15,045 Explanation: 295 x 51 Estimate: 300 x 50 = 15,000 295 x 1 = 295 295 x 50 = 14,750 Product:: 295 + 14,750 = 15,045 Practice: Copy and Solve Estimate. Then find the product. Question 9. Estimate: ________ 54 × 31 = ________ Answer: Estimate: 1,500 Product: 1,674 Explanation: 54 x 31 Estimate: 50 x 30 = 1,500 54 x 1 = 54 54 x 30 = 1,620 Product:: 54 + 1,620 = 1,674 Question 10. Estimate: ________ 42 × 26 = ________ Answer: Estimate: 1,200 Product: 1,092 Explanation: 42 x 26 Estimate: 40 x 30 = 1,200 42 x 6 = 252 42 x 20 = 840 Product:: 252 + 840 = 1,092 Question 11. Estimate: ________ 38 × 64 = ________ Answer: Estimate: 2,400 Product: 2,432 Explanation: 38 × 64 Estimate: 40 x 60 = 2,400 38 x 4 = 152 38 x 60 = 2,280 Product:: 152 + 2,280 = 2,432 Question 12. Estimate: ________ 63 × 16 = ________ Answer: Estimate: 1,200 Product: 1,008 Explanation: 63 x 16 Estimate: 60 x 20 = 1,200 63 x 6 = 378 63 x 10 = 630 Product:: 378 + 630 = 1,008 Question 13. Estimate: ________ 204 × 41 = ________ Answer: Estimate: 8,000 Product: 8,364 Explanation: 204 × 41 Estimate: 200 x 40 = 8,000 204 x 1 = 204 204 x 40 = 8,160 Product:: 204 + 8,160 = 8,364 Question 14. Estimate: ________ 534 × 25 = ________ Answer: Estimate: 15,000 Product: 13,350 Explanation: 534 x 25 Estimate: 500 x 30 = 15,000 534 x 5 = 2,670 534 x 20 = 10,680 Product:: 2,670 + 10,680 = 13,350 Question 15. Estimate: ________ 722 × 39 = ________ Answer: Estimate: 28,000 Product: 28,158 Explanation: 722 × 39 Estimate: 700 x 40 = 28,000 722 x 9 = 6,498 722 x 30 = 21,660 Product:: 6,498 + 21,660 = 28,158 Question 16. Estimate: ________ 957 × 43 = ________ Answer: Estimate: 40,000 Product: 44,022 Explanation: 957 × 43 Estimate: 1,000 x 40 = 40,000 957 x 3 = 2,871 957 x 40 = 41,151 Product:: 2,871 + 41,151 = 44,022 ### Multiply by 2-digit numbers – Problem Solving – Page No. 34 Use the table for 17–20. Question 17. How much sleep does a jaguar get in 1 year? _____ hours Answer: 4,004 hours Explanation: 52 weeks x 77 = 4,004 hours Question 18. In 1 year, how many more hours of sleep does a giant armadillo get than a platypus? _____ hours Answer: 1,508 hours Explanation: giant armadillo: 52 x 127 = 6,604 platypus: 52 x 98 = 5,096 6,604 – 5,096 = 1,508 Question 19. Owl monkeys sleep during the day, waking about 15 minutes after sundown to find food. At midnight, they rest for an hour or two, then continue to feed until sunrise. They live about 27 years. How many hours of sleep does an owl monkey that lives 27 years get in its lifetime? _____ Answer: 4927.5 days Explanation: Given that the time of Owl monkeys sleeps during the day walking about 15 minutes after sundown. Then, at midnight they rest for an hour or two then continue to feed until sunrise. Notice that the above description doesn’t say that they sleep in after sundown. They either eat or rest. Day time is usually considered from 6 am to 6 pm which is total of 12 hours. As per the given information, owl monkey sleeps in that period. Given that owl, monkeys live for 27 years. So the time for sleeping in their lifetime = 12 hours * 27 years = (12/24 days) * 27 years = (1/2 days) * 27 years = (1/2 days) * (27*365 days) = (1/2 days) * (9855 days) = 4927.5 days Hence final answer is 4927.5 days. Question 20. Three-toed sloths move very slowly, using as little energy as possible. They sleep, eat, and even give birth upside down. A baby sloth may cling to its mother for as much as 36 weeks after being born. How much of that time is the sloth asleep? _____ hours Answer: 3,636 hours Explanation: 101 x 36 = 3,636 Question 21. Test Prep A sloth’s maximum speed on the ground is 15 feet in 1 minute. Even though it would be unlikely for a sloth to stay in motion for more than a few moments, how far would a sloth travel in 45 minutes at that speed? Options: A. 60 feet B. 270 feet C. 675 feet D. 6,750 feet Answer: C. 675 feet Explanation: sloth’s maximum speed on the ground is 15 feet in 1 minute. For 45 minutes, 45 x 15 = 675 feet ### Relate Multiplication to Division – Share and Show – Page No. 37 Question 1. Brad has 72 toy cars that he puts into 4 equal groups. How many cars does Brad have in each group? Use the array to show your answer. 4 × = 72 72 ÷ 4 = 4 × ________ = 72 72 ÷ 4 = ________ Answer: Explanation: Brad has 18 toy cars in each group. Because 72÷4 =18 4 × 18 = 72 4 x (9 + 9) = (4 x 9) + (4 x 9) Use multiplication and the Distributive Property to find the quotient. Question 2. 108 ÷ 6 = _____ Answer: 18 Explanation: 108 ÷ 6 6 x 18 = 6 x (9 + 9) = (6 x 9) + (6 x 9) = 54 + 54 = 108 (36 + 72) ÷ 6 = (36 ÷ 6) + (72÷ 6) = 6 + 12 = 18 Question 3. 84 ÷ 6 = _____ Answer: 14 Explanation: 84 ÷ 6 (42 + 42) ÷ 6 = (42÷ 6) + (42÷ 6) = 7 + 7 = 14 6 x 14 = 6 x (7 + 7) = (6 x 7) + (6 x 7) = 42 + 42 = 84 Question 4. 184 ÷ 8 = _____ Answer: 23 Explanation: 184 ÷ 8 (92 + 92) ÷ 8 = (92÷ 8) + (92÷ 8) = 11.5 + 11.5 = 23 8 x 23 = 8 x (11 + 12) = (8 x 11) + (8 x 12) = 88 + 96 = 184 On Your Own Use multiplication and the Distributive Property to find the quotient. Question 5. 60 ÷ 4 = _____ Answer: 15 Explanation: 60 ÷ 4 (20 + 40) ÷ 4 = (20 ÷ 4) + (40 ÷ 4) = 5 + 10 = 15 4 x 15 = 4 x (7+ 8) = (4 x 7) + (4 x 8) = 28 + 32 = 60 Question 6. 144 ÷ 6 = _____ Answer: 24 Explanation: 144 ÷ 6 (72 + 72) ÷ 6 = (72 ÷ 6) + (72 ÷ 6) = 12 + 12 = 24 6 x 24 = 6 x ( 12 + 12) = (6 x 12) + (6 x 12) = 72 + 72 = 144 Question 7. 252 ÷ 9 = _____ Answer: 28 Explanation: 252 ÷ 9 (126 + 126) ÷ 9 = (126 ÷ 9) + (126 ÷ 9) = 14 + 14 = 28 6 x 28 = 6 x ( 14 + 14) = (6 x 14) + (6 x 14) = 126 + 126 = 252 Find each quotient. Then compare. Write <, > or =. Question 8. 51 ÷ 3 _____ 68 ÷ 4 Answer: 51 ÷ 3 = 68 ÷ 4 Explanation: 51 ÷ 3 = 17 68 ÷ 4 = 17 17 = 17. Question 9. 252 ÷ 6 _____ 135 ÷ 3 Answer: 252 ÷ 6 < 135 ÷ 3 Explanation: 252 ÷ 6 = 42 135 ÷ 3 = 45 42 < 45 Question 10. 110 ÷ 5 _____ 133 ÷ 7 Answer: 110 ÷ 5 > 133 ÷ 7 Explanation: 110 ÷ 5 = 22 133 ÷ 7 = 19 22 > 19 ### Relate Multiplication to Division – Problem Solving – Page No. 38 Use the table to solve 11–13. Question 11. A group of 6 friends share a bag of the 45-millimeter bouncy balls equally among them. How many does each friend get? ____ balls Answer: 7 balls Explanation: A group of 6 friends shares a bag of the 45-millimeter bouncy balls equally among them. 45/6 = 7 balls and 3 balls remained Question 12. Mr. Henderson has 2 bouncy-ball vending machines. He buys one bag of the 27-millimeter balls and one bag of the 40-millimeter balls. He puts an equal number of each in the 2 machines. How many bouncy balls does he put in each machine? ________ balls of the 27-millimeter . ________ balls of the 40-millimeter . ________ total balls Answer: 51 balls of the 27-millimeter 29 balls of the 40-millimeter 80 total balls Explanation: There’s 51 27 mm, 29 40 mm Question 13. Lindsey buys a bag of each size of bouncy ball. She wants to put the same number of each size of bouncy ball into 5 party-favor bags. How many of each size of bouncy ball will she put in a bag? ________ balls of the 27-millimeter ________ balls of the 40-millimeter ________ balls of the 45-millimeter Answer: 34 balls of the 27-millimeter 12 balls of the 40-millimeter 34 balls of the 45-millimeter Explanation: There’s 34 27 mm, 12 40 mm, and 34 45 mm bouncy balls Question 14. What’s the Error? Sandy writes (4 × 30) + (4 × 2) and says the quotient for 128 ÷ 4 is 8. Is she correct? Explain. 128 ÷ 4 = ____ Answer: Sandy’s answer is incorrect. 128 ÷ 4 = 32 Explanation: (4 × 30) + (4 × 2) = 120 + 8 = 128 128 ÷ 4 = 32. (4 × 30) + (4 × 2) = 4 x (30 + 2) = 4 x 32 = 128. 128 ÷ 4 = 32 Question 15. Test Prep Which of the following can be used to find 150 ÷ 6? Options: A. (6 × 20) + (6 × 5) B. (6 × 10) + (6 × 5) C. (2 × 75) + (2 × 3) D. (6 × 15) + (6 × 5) Answer: A. (6 × 20) + (6 × 5) Explanation: 150 ÷ 6 = 25 25 x 6 = 150 6 x 25 = 6 x (20 + 5) = (6 × 20) + (6 × 5) ### Problem Solving Multiplication and Division – Share and Show – Page No. 41 Question 1. To make concrete mix, Monica pours 34 pounds of cement, 68 pounds of sand, 14 pounds of small pebbles, and 19 pounds of large pebbles into a large wheelbarrow. If she pours the mixture into 9 equalsize bags, how much will each bag weigh? First, find the total weight of the mixture. ____ pounds Answer: 135 pounds Explanation: 34 + 68 + 14 + 19 = 135 Question 1. Then, divide the total by the number of bags. Break the total into two simpler numbers to make the division easier, if necessary. Finally, find the quotient and solve the problem. So, each bag will weigh _ pounds. ____ pounds Answer: 15 pounds Explanation: now, calculate 135/9 = 15 pounds. Question 2. What if Monica pours the mixture into 5 equal-size bags? How much will each bag weigh? ____ pounds Answer: 27 pounds Explanation: 135/5 = 27 Question 3. Taylor is building doghouses to sell. Each doghouse requires 3 full sheets of plywood which Taylor cuts into new shapes. The plywood is shipped in bundles of 14 full sheets. How many doghouses can Taylor make from 12 bundles of plywood? ____ Answer: 56 doghouses Explanation: Taylor is building doghouses to sell. Each doghouse requires 3 full sheets of plywood which Taylor cuts into new shapes. The plywood is shipped in bundles of 14 full sheets. (12 x 14)/3 = 168/3 = 56 doghouses Question 4. Eileen is planting a garden. She has seeds for 60 tomato plants, 55 sweet corn plants, and 21 cucumber plants. She plants them in 8 rows, with the same number of plants in each row. How many seeds are planted in each row? ____ seeds / row Answer: 17 seeds Explanation: Eileen is planting a garden. She has seeds for 60 tomato plants, 55 sweet corn plants, and 21 cucumber plants. She plants them in 8 rows, with the same number of plants in each row. 60 + 55 + 21 = 136 136/8 = 17 ### Problem Solving Multiplication and Division – On Your Own – Page No. 42 Question 5. Starting on day 1 with 1 jumping jack, Keith doubles the number of jumping jacks he does every day. How many jumping jacks will Keith do on day 10? ____ jumping jack Answer: 512 jumping jacks Explanation: She doubled the number so you’re supposed to multiply by 2. On day 1, 1 jumping pack; On day 2, 2 jumping packs; On day 3, 2 x 2 = 4 jumping packs; On day 4, 2 x 2 x 2 = 8 jumping packs; On day 5, 2 x 2 x 2 x 2 = 16 jumping packs; On day 6, 2 x 2 x 2 x 2 x 2 = 32 jumping packs; On day 7, 2 x 2 x 2 x 2 x 2 x 2 = 64 jumping packs; On day 8, 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128 jumping packs; On day 9, 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256 jumping packs; On day 10, 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 512 jumping packs; 512 jumping jacks Question 6. Starting in the blue square, in how many different ways can you draw a line that passes through every square without picking up your pencil or crossing a line you’ve already drawn? Show the ways. ____ ways Answer: 8 ways Explanation: 8 ways Question 7. On April 11, Millie bought a lawn mower with a 50-day guarantee. If the guarantee begins on the date of purchase, what is the first day on which the mower will no longer be guaranteed? __________ Answer: May 31 Explanation: The guarantee begins on April 11. April has 30 days. So, we have 20 days of the guarantee in April. May has 31 days. So, we have 30 days of the guarantee in May. Therefore, the last day of the guarantee is May 31. Question 8. A classroom bulletin board is 7 feet by 4 feet. If there is a picture of a student every 6 inches along the edge, including one in each corner, how many pictures are on the bulletin board? ____ pictures Answer: 40 pictures Explanation: 2 pictures per foot, so that’s 14 pics along the top and bottom (counting the corners), and 6 pictures along each side (not counting the corners) 14+14+6+6 = 40 Question 9. Dave wants to make a stone walkway. The rectangular walkway is 4 feet wide and 12 feet long. Each 2 foot by 2 foot stone covers an area of 4 square feet. How many stones will Dave need to make his walkway? ____ stones Answer: 12 stones Explanation: Area of walkway = 4 x 12 = 48 square feet Area of 1 stone = 2 x 2 = 4 square feet 48/4 = 12 stones. Question 10. Test Prep Dee has 112 minutes of recording time. How many 4-minute songs can she record? Options: A. 28 B. 27 C. 18 D. 17 Answer: A. 28 Explanation: Dee has 112 minutes of recording time. 112/4 = 28 ### Numerical Expressions – Share and Show – Page No. 45 Circle the expression that matches the words. Question 1. Teri had 18 worms. She gave 4 worms to Susie and 3 worms to Jamie. (18 – 4) + 3 18 – (4 + 3) __________ Answer: 18 – (4 + 3) Explanation: Teri had 18 worms. She gave 4 worms. 18 – 4 = 14. 3 worms to Jamie 14 – 3 = 11. (18 – 4) + 3 = 14 + 3 = 17 not equal to 11; 18 – (4 + 3) = 18 – 7 = 11 = 11 Question 2. Rick had$8. He then worked 4 hours for $5 each hour.$8 + (4 × $5) ($8 + 4) × $5 __________ Answer:$8 + (4 × $5) Explanation: Rick had$8. He then worked 4 hours for $5 each hour = 4 x$5 = $20;$20 +$8 =$28.
$8 + (4 ×$5) = 8 + 20 = $28 =$28.

Write an expression to match the words.

Question 3.
Greg drives 26 miles on Monday and 90 miles on Tuesday.
Type below:
__________

26 + 90 = 116 miles

Explanation:
Greg drives 26 miles on Monday and 90 miles on Tuesday. 26 + 90 = 116 miles

Question 4.
Lynda has 27 fewer fish than Jack. Jack has 80 fish.
Type below:
__________

80 – 27 = 53

Explanation:
Lynda has 27 fewer fish than Jack. Jack has 80 fish. 80 – 27 = 53

Write words to match the expression.

Question 5.
34 – 17
Type below:
__________

Anna has 17 fewer apples than Jack. Jack has 34 apples.

Explanation:
34 – 17 = 17.
Anna has 17 fewer apples than Jack. Jack has 34 apples.

Question 6.
6 × (12 – 4)
Type below:
__________

Teri had 12 worms. She gave 4 worms to Susie. She sell remaining worms for $6 each. Explanation: Teri had 12 worms. She gave 4 worms to Susie. She sell remaining worms for$6 each.

Write an expression to match the words.

Question 7.
José shared 12 party favors equally among 6 friends.
Type below:
__________

12/6 = 2

Explanation:
José shared 12 party favors equally among 6 friends. 12/6 = 2

Question 8.
Braden has 14 baseball cards. He finds 5 more baseball cards.
Type below:
__________

14 + 5 = 19

Explanation:
Braden has 14 baseball cards. He finds 5 more baseball cards. 14 + 5 = 19

Question 9.
Isabelle bought 12 bottles of water at $2 each. Type below: __________ Answer: 12 x$2 = $24 Explanation: Isabelle bought 12 bottles of water at$2 each. 12 x $2 =$24

Question 10.
Monique had $20. She spent$5 on lunch and $10 at the bookstore. Type below: __________ Answer: 20 – (5 + 10) Explanation: Monique had$20. She spent $5 on lunch and$10 at the bookstore. 20 – (5 + 10)

Write words to match the expression.

Question 11.
36 ÷ 9
Type below:
__________

Anna shared 36 apples to 9 friends.

Question 12.
35 – (16 + 11)
Type below:
__________

Monique had 35 balls. She gave 16 to her one frined and 11 to other friend.

Draw a line to match the expression with the words.

Question 13.
Fred catches 25 fish. Then he
releases 10 fish and catches 8 more.     •        •3 × (15 – 6)

Nick has 25 pens. He gives 10 pens to
one friend and 8 pens to another friend.  •     •15 – 6

Jan catches 15 fish and lets 6 fish go.       •     •25 – (10 + 8)

Libby catches 15 fish and lets 6 fish go
for three days in a row.                             •     •(25 – 10) + 8
Type below:
__________

Fred catches 25 fish. Then he releases 10 fish and catches 8 more = (25 – 10) + 8
Nick has 25 pens. He gives 10 pens to one friend and 8 pens to another friend = 25 – (10 + 8)
Jan catches 15 fish and lets 6 fish go = 15 – 6
Libby catches 15 fish and lets 6 fish go for three days in a row = 3 × (15 – 6)

### Numerical Expressions – Problem Solving – Page No. 46

Use the rule and the table for 14.

Question 14.
Write a numerical expression to represent the total number of lemon tetras that could be in a 20-gallon aquarium.
_____ lemon tetras

2 lemon tetras

Explanation:
From the given data, increase each inch of lenth, 1 gallon of water increases.
2 + 3 + 5 + 3 + 5 = 18 inches. So, 18 gallon of water available in aquarium. Add 1 lemon tetra to get the 20 gallon of water. So, in total there are 2 lemon tetra available.

Question 15.
Write a word problem for an expression that is three times as great as (15 + 7). Then write the expression.
Type below:
__________

3 x (15 + 7)

Explanation:
Given that that is three times as great as (15 + 7)

Question 16.
What’s the Question? Lu has 3 swordtails in her aquarium. She buys 2 more swordtails.
Type below:
__________

3 + 2 = 5

Explanation:
Lu has 3 swordtails in her aquarium. She buys 2 more swordtails. So, 3 + 2 = 5 swordtails

Question 17.
Tammy gives 45 stamps to her 9 friends. She shares them equally among her friends. Write an expression to match the words. How many stamps does each friend get?
_____ stamps

45/9 = 5 stamps

Explanation:
Tammy gives 45 stamps to her 9 friends. 45/9 = 5.

Question 18.
Test Prep Josh has 3 fish in each of 5 buckets. Then he releases 4 fish. Which expression matches the words?
Options:
a. (3 × 4) – 5
b. (5 × 4) – 3
c. (5 × 3) – 4
d. (5 – 3) × 4

c. (5 × 3) – 4

Explanation:
Josh has 3 fish in each of 5 buckets. 3 x 5.
Then he releases 4 fish. (3 x 5) – 4

### Evaluate Numerical Expressions – Share and Show – Page No. 49

Evaluate the numerical expression.

Question 1.
10 + 36 ÷ 9
_____

14

Explanation:
10 + 36 ÷ 9 = 10 + (36 ÷ 9) = 10 + 4 = 14

Question 2.
10 + (25 – 10) ÷ 5
_____

13

Explanation:
10 + (25 – 10) ÷ 5 = 10 + 15 ÷ 5 = 10 + (15 ÷ 5) = 10 + 3 = 13

Question 3.
9 – (3 × 2) + 8
_____

11

Explanation:
9 – (3 × 2) + 8 = 9 – 6 + 8 = 3 + 8 = 11

Evaluate the numerical expression.

Question 4.
(4 + 49) – 4 × 10
_____

13

Explanation:
(4 + 49) – 4 × 10 = 53 – 4 x 10 = 53 – (4 x 10) = 53 – 40 = 13

Question 5.
5 + 17 – 100 ÷ 5
_____

Explanation:
5 + 17 – 100 ÷ 5 = (5 + 17) – (100 ÷ 5) = 22 – 20 = 2

Question 6.
36 – (8 + 5)
_____

23

Explanation:
36 – (8 + 5) = 36 – 13 = 23

Question 7.
125 – (68 + 7)
_____

50

Explanation:
125 – (68 + 7) = 125 – 75 = 50

Question 8.
(4 × 6) – 12
_____

12

Explanation:
(4 × 6) – 12 = 24 – 12 = 12

Question 9.
3 × (22 – 2)
_____

60

Explanation:
3 × (22 – 2) = 3 x 20 = 60

Question 10.
23 + (16 – 7)
_____

32

Explanation:
23 + (16 – 7) = 23 + 9 = 32

Question 11.
(25 – 4) ÷ 3
_____

7

Explanation:
(25 – 4) ÷ 3 = 21 ÷ 3 = 7

Rewrite the expression with parentheses to equal the given value.

Question 12.
100 – 30 ÷ 5
value: 14
Type below:
__________

(100 – 30) ÷ 5 = 14

Explanation:
100 – 30 ÷ 5 = (100 – 30) ÷ 5 = 70 ÷ 5 = 14

Question 13.
12 + 17 – 3 × 2
value: 23
Type below:
__________

23

Explanation:
(12 + 17) – (3 × 2) = 29 – 6 = 23

Question 14.
9 + 5 ÷ 5 + 2
value: 12
Type below:
__________

12

Explanation:
9 + (5 ÷ 5) + 2 = 9 + 1 + 2 = 12

### Evaluate Numerical Expressions – UNLOCK the Problem – Page No. 50

Question 15.
A movie theater has 4 groups of seats. The largest group of seats, in the middle, has 20 rows, with 20 seats in each row. There are 2 smaller groups of seats on the sides, each with 20 rows and 6 seats in each row. A group of seats in the back has 5 rows, with 30 seats in each row. How many seats are in the movie theater?

a. What do you need to know?
Type below:
__________

We have to know the number of seats in each row to calculate the total number of seats.

Question 15.
b. What operation can you use to find the number of seats in the back group of seats? Write the expression.
Type below:
__________

A group of seats in the back has 5 rows with 30 seats in each row. So, to calculate the number of seats, we can use multiplication.

Question 15.
c. What operation can you use to find the number of seats in both groups of side seats? Write the expression.
Type below:
__________

2 x (20 x 6) = 2 x 120 = 240

Question 15.
d. What operation can you use to find the number of seats in the middle group? Write the expression.
Type below:
__________

20 x 20 = (2 x 2) x (10 x 10) = 4 x 100 = 400

Question 15.
e. Write an expression to represent the total number of seats in the theater.
Type below:
__________

(20 x 20) + (2 x 20 x 6) + (5 x 30)

Question 15.
f. How many seats are in the theater? Show the steps you use to solve the problem.
_____ seats

(20 x 20) + (2 x 20 x 6) + (5 x 30) = 400 + 240 + 150 = 640 + 150 = 790

Question 16.
Test Prep In the wild, an adult giant panda eats about 30 pounds of food each day. Which expression shows how many pounds of food 6 pandas eat in 3 days?
Options:
a. 3 + (30 × 6)
b. 3 × (30 × 6)
c. (30 × 6) ÷ 3
d. (30 × 6) – 3

b. 3 × (30 × 6)

Explanation:
1 panda eats 30 pounds of food each day.
for 3 days, 3 x 30 = 90
1 panda eats 90 pounds of food in 3 days.
6 pandas can eat 90 x 6 = 540 pounds.
3 + (180) = 183 not equal to 540 pounds.
3 x (30 x 6) = 3 x (180) = 540

Question 17.
Test Prep Which expression has a value of 6?
Options:
a. (6 ÷ 3) × 4 + 8
b. 27 – 9 ÷ 3 × ( 4 + 1)
c. (18 + 12) × 6 – 4
d. 71 – 5 × (9 + 4)

d. 71 – 5 × (9 + 4)

Explanation:
(6 ÷ 3) × 4 + 8 = 2 x 4 + 8 = 8 + 8 = 16
27 – 9 ÷ 3 × ( 4 + 1) = 27 – (9 ÷ 3) × 5 = 27 – 3 x 5 = 27 – 15 = 12
(18 + 12) × 6 – 4 = 180 – 4 = 176
71 – 5 × (9 + 4) = 71 – (5 x 13) = 71 – 65 = 6

### Grouping Symbols – Share and Show – Page No. 53

Evaluate the numerical expression.

Question 1.
12 + [(15 – 5) + (9 – 3)]
12 + [10 + ____]
12 +____
____

12 + [(15 – 5) + (9 – 3)]
12 + [10 + 6]
12 + 16
28

Question 2.
5 × [(26 – 4) – (4 + 6)]
____

5 × [(26 – 4) – (4 + 6)]
5 x [22 – 10]
5 x 12 = 60

Question 3.
36 ÷ [(18 – 10) – (8 – 6)]
____

36 ÷ [(18 – 10) – (8 – 6)]
36 ÷ [8 – 2]
36 ÷ 6 = 6

Evaluate the numerical expression.

Question 4.
4 + [(16 – 4) + (12 – 9)]
____

4 + [(16 – 4) + (12 – 9)]
4 + [12 + 3]
4 + 15 = 19

Question 5.
24 – [(10 – 7) + (16 – 9)]
____

24 – [(10 – 7) + (16 – 9)]
24 – [3 + 7] = 24 – 10 = 14

Question 6.
16 ÷ [(13 + 7) – (12 + 4)]
____

16 ÷ [(13 + 7) – (12 + 4)]
16 ÷ [20 – 16]
16 ÷ 4 = 4

Question 7.
5 × [(7 – 2) + (10 – 8)]
____

5 × [(7 – 2) + (10 – 8)]
5 x [5 + 2]
5 x 7 = 35

Question 8.
[(17 + 8) + (29 – 12)] ÷ 6
____

[(17 + 8) + (29 – 12)] ÷ 6
[25 + 17] ÷ 6
42 ÷ 6 = 7

Question 9.
[(6 × 7) + (3 × 4)] – 28
____

[(6 × 7) + (3 × 4)] – 28
[42 + 12] – 28
54 – 28 = 26

Question 10.
3 × {[(12 – 8) × 2] + [(11 – 9) × 3]}
____

3 × {[(12 – 8) × 2] + [(11 – 9) × 3]}
3 x {[4 x 2] + [2 x 3]}
3 x {8 + 6}
3 x 14 = 42

Question 11.
{[(3 × 4) + 18] + [(6 × 7) – 27]} ÷ 5
____

{[(3 × 4) + 18] + [(6 × 7) – 27]} ÷ 5
{[12 + 18] + [42 – 27]} ÷ 5
{30 + 15} ÷ 5
45 ÷ 5 = 9

### Grouping Symbols – UNLOCK the Problem – Page No. 54

Question 12.
Dan has a flower shop. Each day he displays 24 roses. He gives away 10 and sells the rest. Each day he displays 36 carnations. He gives away 12 and sells the
rest. What expression can you use to find out how many roses and carnations Dan sells in a week?

a. What information are you given?
Type below:
__________

Each day, Dan displays 24 roses (gives away 10 and sells the rest), and he displays 36 carnations (gives away 12 and selles the rest).

Question 12.
b. What are you being asked to do?
Type below:
__________

We have to find out how many roses and carnations Dan sells in a week.

Question 12.
c. What expression shows how many roses Dan sells in one day?
Type below:
__________

24 – 10 = 14 roses

Question 12.
d. What expression shows how many carnations Dan sells in one day?
Type below:
__________

36 – 12 = 24 carnation

Question 12.
e. Write an expression to represent the total number of roses and carnations Dan sells in one day.
Type below:
__________

(24 – 10) + (36 – 12) = 14 + 24 = 38 roses and carnations

Question 12.
f. Write the expression that shows how many roses and carnations Dan sells in a week.
Type below:
__________

7 x ((24 – 10) + (36 – 12)) = 7 x (14 + 24) = 7 x 38 = 266 roses and carnations

Question 13.
Evaluate the expression to find out how many roses and carnations Dan sells in a week.
____ flowers

7 x ((24 – 10) + (36 – 12))
7 x (14 + 24)
7 x 38 = 266 roses and carnations

Explanation:

Question 14.
Test Prep Which expression has a value of 4?
Options:
a. [(4 × 5) + (9 + 7)] + 9
b. [(4 × 5) + (9 + 7)] ÷ 9
c. [(4 × 5) – (9 + 7)] × 9
d. [(4 + 5) + (9 + 7)] – 9

b. [(4 × 5) + (9 + 7)] ÷ 9

Explanation:
[(4 × 5) + (9 + 7)] + 9 = [20 + 16] + 9 = 36 + 9 = 45
[(4 × 5) + (9 + 7)] ÷ 9 = [20 + 16] ÷ 9 = 36 ÷ 9 = 4

### Chapter Review/Test – Vocabulary – Page No. 55

Question 1.
The ____ states that multiplying a sum by a number is the same as multiplying each addend in the sum by the number and then adding the products.
__________

Distributive Property

Concepts and Skills

Complete the sentence.

Question 2.
7,000 is 10 times as much as _____

700

Explanation:
Let the unknown number is S.
7,000 = 10S
S = 7,000/10 = 700.
7,000 is 10 times as much as 700.

Question 3.
50 is $$\frac{1}{10}$$ of _____

500

Explanation:
Let the unknown number is S.
50 = $$\frac{1}{10}$$ S
S = 50 X 10 = 500

Complete the equation, and tell which property you used.

Question 4.
4 × (12 + 14) =
Type below:
________

104; Distributive Property of Multiplication

Explanation:
4 × (12 + 14) = (4 x 12) + (4 x 14) = 48 + 56 = 104; Distributive Property of Multiplication

Question 5.
45 + 16 =__ + 45
Type below:
Type below:
________

45 + 16 = 16 + 45; Commutative Property of Addition

Explanation:
45 + 16 = 16 + 45; Commutative Property of Addition

Find the value.

Question 6.
102 = _____

100

Explanation:
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;

Question 7.
3 × 104 = _____

30,000

Explanation:
3 × 104
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;
104 = 10 x 10 x 10 x 10 = 10,000;
3 x 10,000 = 30,000

Question 8.
8 × 103 = _____

8,000

Explanation:
8 × 103
100 = 1;
101 = 1 x 10 = 10;
102 = 10 x 10 = 100;
103 = 10 x 10 x 10 = 1,000;
8 x 1,000 = 8,000

Estimate. Then find the product.

Question 9.
Estimate:
5 7 9
×   6
———-
Estimate: _____ Product: _____

Estimate: 3,600
Product: 3,474

Explanation:
Estimate: 579 is close to 600;
600 x 6 = 3,600
579 x 6
6 x 9 =54; add ones and regroup tens
6 x 7 = 42; 42 + 5 = 47; add tens and regroup hundreds
6 x 5 = 30; 30 + 4 = 34
So, 3,474 is the product

Question 10.
Estimate:
7,316
×    6
———-
Estimate: _____ Product: _____

Estimate: 42,000
Product: 43,986

Explanation:
Estimate: 7,316 is close to 7,000;
7,000 x 6 = 42,000
7,316 x 6
6 x 6 = 36; add ones and regroup tens
6 x 1 = 6; 6 + 3 = 18; add tens and regroup hundreds
6 x 3 = 18; 18 + 1 = 19; add hundreds and regroup thousads
6 x 7 = 42; 42 + 1 = 43
So, 43,986 is the product

Question 11.
Estimate:
4 3 6
× 3 2
———-
Estimate: _____ Product: _____

Estimate: 12,000
Product: 13,952

Explanation:
Estimate: 436 is close to 400; 32 is close to 30
400 x 30 = 12,000
436 x 32;
436 x 2 = 872
436 x 30 = 13,080
13,080 + 872 = 13,952

Use multiplication and the Distributive Property to find the quotient.

Question 12.
54 ÷ 3 = _____

18

Explanation:
54 ÷ 3
(27 + 27) ÷ 3 = (27 ÷ 3) + (27 ÷ 3) = 9 + 9 = 18
3 x 18 = 3 x (9+ 9) = (3 x 9) + (3 x 9) = 27 + 27 = 54

Question 13.
90 ÷ 5 = _____

18

Explanation:
90 ÷ 5
(45 + 45) ÷ 5 = (45 ÷ 5) + (45 ÷ 5) = 9 + 9 = 18
5 x 18 = 5 x (9+ 9) = (5 x 9) + (5 x 9) = 45 + 45 = 90

Question 14.
96 ÷ 6 = _____

Explanation:
96 ÷ 6
(48 + 48) ÷ 6 = (48 ÷ 6) + (48 ÷ 6) = 8 + 8 = 16
6 x 16 = 6 x (8 + 8) = (6 x 8) + (6 x 8) = 48 + 48 = 96

Evaluate the numerical expression.

Question 15.
42 − (9 + 6) = _____

42 − (9 + 6)
42 – 15
27

Question 16.
15 + (22 − 4) ÷ 6 = _____

15 + (22 − 4) ÷ 6
15 + (18 ÷ 6)
15 + 3
18

Question 17.
6 × [(5 × 7) − (7 + 8)] = _____

6 × [(5 × 7) − (7 + 8)]
6 x [35 – 15]
6 x [20]
120

### Chapter Review/Test – Page No. 56

Question 18.
Erica’s high score on her new video game is 30,000 points. Maria’s high score is $$\frac{1}{10}$$ of Erica’s. How many points did Maria score?
Options:
A. 30
B. 300
C. 3,000
D. 30,000

C. 3,000

Explanation:
Erica’s high score on her new video game is 30,000 points. Maria’s high score is $$\frac{1}{10}$$ of Erica’s.
30,000 x $$\frac{1}{10}$$ = 3,000

Question 19.
Rich makes $35 a week mowing lawns in his neighborhood. Which expression can be used to show how much money he makes in 8 weeks? Options: A. (8 × 30) + (8 × 5) B. (8 × 30) + (8 × 5) C. (8 + 30) × (8 + 5) D. (8 × 30) × (8 × 5) Answer: B. (8 × 30) + (8 × 5) Explanation: Rich makes$35 a week mowing lawns in his neighborhood.
_____ weeks