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

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**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**

- Powers of 10 and Exponents – Page No. 18
- Powers of 10 and Exponents Lesson Check – Page No. 19
- UNLOCK the Problem – Page No. 20

**Lesson 5: Algebra • Multiplication Patterns**

- Multiplication Patterns – Page No. 22
- Multiplication Patterns Lesson Check – Page No. 23
- Multiplication Patterns Lesson Check 1 – Page No. 24

**Mid-Chapter Checkpoint**

**Lesson 6: Multiply by 1-Digit Numbers**

**Lesson 7: Multiply by Multi-Digit Numbers**

- Multiply by Multi-Digit Numbers – Page No. 33
- Multiply by Multi-Digit Numbers Lesson Check – Page No. 34

**Lesson 8: Relate Multiplication to Division**

- Relate Multiplication to Division – Page No. 37
- Relate Multiplication to Division Lesson Check – Page No. 38

**Lesson 9: Problem Solving • Multiplication and Division**

**Lesson 10: Algebra • Numerical Expressions**

**Lesson 11: Algebra • Evaluate Numerical Expressions**

- Evaluate Numerical Expressions – Page No. 49
- Evaluate Numerical Expressions Lesson Check – Page No. 50

**Lesson 12: Algebra • Grouping Symbols**

**Review/Test**

- Review/Test – Page No. 55
- Review/Test – Page No. 56
- Review/Test – Page No. 57
- Review/Test – Page No. 58

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

**Complete the sentence.**

Question 1.

500 is 10 times as much as ______

Answer:

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 ______

Answer:

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 ______

Answer:

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 ______

Answer:

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 | ______ | ______ |

Answer:

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 | ______ | ______ |

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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:

__________

Answer:

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:

__________

Answer:

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:

__________

Answer:

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:

__________

Answer:

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

__________

Answer:

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

__________

Answer:

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

__________

Answer:

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

__________

Answer:

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) =

__________

Answer:

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

__________

Answer:

7,020,032

Seven Million Twenty Thousand Thirty-Two

Explanation:

seven million = 7,000,000

twenty thousand = 20,000

thirty-two = 32

**On Your Own**

**Write the value of the underlined digit.**

Question 8.

849,567,043

__________

Answer:

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

__________

Answer:

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

__________

Answer:

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

__________

Answer:

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

__________

Answer:

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

__________

Answer:

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

__________

Answer:

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

__________

Answer:

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:

__________

Answer:

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:

__________

Answer:

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?

__________

Answer:

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?

__________

Answer:

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:

__________

Answer:

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:

__________

Answer:

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

Answer:

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 ×

__________

____

Answer:

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 = ____

Answer:

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

89 + 38

127

Question 3.

9 × 52 = ____

Answer:

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 = ____

Answer:

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)

Answer:

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

Answer:

47; Identity Property of Addition

Explanation:

0 + 47 = 47; Identity Property of Addition

Question 6.

Describe how you can use properties to solve problems more easily.

Type below:

__________

Answer:

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

**On Your Own**

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

Question 7.

3 × 78 = ____

Answer:

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 = ____

Answer:

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 = ____

Answer:

90; Associative Property of Addition

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

Answer:

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

Question 11.

25 + 14 = ____ + 25

Answer:

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).

____

Answer:

(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?

$ ____

Answer:

$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?

$ ____

Answer:

$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)

Answer:

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: 10^{2}

Word form: the second power of ten

Explanation:

10 × 10

Base = 10;

Exponent = 2;

Exponent Form: 10^{2}

Word Form: the second power of ten

Question 2.

10 × 10 × 10 × 10

Exponent form:

Word form:

Type below:

__________

Answer:

Exponent Form: 10^{4}

Word Form: the fourth power of ten

Explanation:

10 × 10 × 10 × 10

Base = 10;

Exponent = 4;

Exponent Form: 10^{4}

Word Form: the fourth power of ten

**Find the value.**

Question 3.

10^{2} = ____

Answer:

100

Explanation:

10^{0} = 1;

10^{1} = 1 x 10 = 10;

10^{2} = 10 x 10 = 100;

Question 4.

4 × 10^{2} = ____

Answer:

400

Explanation:

4 × 10^{2} =

10^{0} = 1;

10^{1} = 1 x 10 = 10;

10^{2} = 10 x 10 = 100;

4 x 100 = 400

Question 5.

7 × 10^{2} = ____

Answer:

700

Explanation:

7 × 10^{2} =

10^{0} = 1;

10^{1} = 1 x 10 = 10;

10^{2} = 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: 10^{3}

Word form: the third power of ten

Explanation:

10 × 10 × 10

Base = 10;

Exponent = 3;

Exponent Form: 10^{3}

Word Form: the third power of ten

Question 7.

10 × 10 × 10 × 10 × 10

exponent form:

word form:

Type below:

__________

Answer:

Exponent form: 10^{5}

Word form: the fifth power of ten

Explanation:

10 × 10 × 10 × 10 × 10

Base = 10;

Exponent = 5;

Exponent Form: 10^{5}

Word Form: the fifth power of ten

**Find the value.**

Question 8.

10^{4} = ____

Answer:

10,000

Explanation:

10^{0} = 1;

10^{1} = 1 x 10 = 10;

10^{2} = 10 x 10 = 100;

10^{3} = 10 x 10 x 10 = 1,000;

10^{4} = 10 x 10 x 10 x 10 = 10,000;

Question 9.

2 × 10^{3} = ____

Answer:

2,000

Explanation:

2 × 10^{3} =

10^{0} = 1;

10^{1} = 1 x 10 = 10;

10^{2} = 10 x 10 = 100;

10^{3} = 10 x 10 x 10 = 1,000;

2 x 1,000 = 2,000

Question 10.

6 × 10^{4} = ____

Answer:

60,000

Explanation:

6 × 10^{4}

10^{0} = 1;

10^{1} = 1 x 10 = 10;

10^{2} = 10 x 10 = 100;

10^{3} = 10 x 10 x 10 = 1,000;

10^{4} = 10 x 10 x 10 x 10 = 10,000;

6 x 10,000 = 60,000

**Complete the pattern.**

Question 11.

7 × 10^{0} = 7 × 1 = _______

7 × 10^{1} = 7 × 10 = _______

7 × 10^{2} = 7 × 10 × 10 = _______

7 × 10^{3} = 7 × 10 × 10 × 10 = _______

7 × 10^{4} = 7 × 10 × 10 × 10 × 10 = _______

Answer:

7 × 10^{0} = 7 × 1 = 7

7 × 10^{1} = 7 × 10 = 70

7 × 10^{2} = 7 × 10 × 10 = 7 x 100 = 700

7 × 10^{3} = 7 × 10 × 10 × 10 = 7 x 1,000 = 7,000

7 × 10^{4} = 7 × 10 × 10 × 10 × 10 = 7 x 10,000 = 70,000

Explanation:

10^{0} = 1;

10^{1} = 1 x 10 = 10;

10^{2} = 10 x 10 = 100;

10^{3} = 10 x 10 x 10 = 1,000;

10^{4} = 10 x 10 x 10 x 10 = 10,000;

Question 12.

9 × 10^{0} = _______ = 9

9 × 10^{1} = _______ = 90

9 × 10^{2} = _______ = 900

9 × 10^{3} = _______ = 9,000

9 × 10^{4} = _______ = 90,000

Answer:

9 × 10^{0} = 9 x 1 = 9

9 × 10^{1} = 9 x 10 = 90

9 × 10^{2} = 9 x 10 x 10 = 900

9 × 10^{3} = 9 x 10 x 10 x 10= 9,000

9 × 10^{4} = 9 x 10 x 10 x 10 x 10 = 90,000

Explanation:

10^{0} = 1;

10^{1} = 1 x 10 = 10;

10^{2} = 10 x 10 = 100;

10^{3} = 10 x 10 x 10 = 1,000;

10^{4} = 10 x 10 x 10 x 10 = 10,000;

Question 13.

12 × 10^{0} = 12 × 1 = _______

12 × 10^{1} = 12 × 10 = _______

12 × 10^{2} = 12 × 10 × 10 = _______

12 × 10^{3} = 12 × 10 × 10 × 10 _______

12 × 10^{4} = 12 × 10 × 10 × 10 × 10 _______

Answer:

12 × 10^{0} = 12 × 1 = 12

12 × 10^{1} = 12 × 10 = 120

12 × 10^{2} = 12 × 10 × 10 = 1,200

12 × 10^{3} = 12 × 10 × 10 × 10 = 12,000

12 × 10^{4} = 12 × 10 × 10 × 10 × 10 = 120,000

10^{0} = 1;

10^{1} = 1 x 10 = 10;

10^{2} = 10 x 10 = 100;

10^{3} = 10 x 10 x 10 = 1,000;

10^{4} = 10 x 10 x 10 x 10 = 10,000;

Question 14.

10^{3} = 10 × 10^{n} What is the value of n?

Think: 10^{3} = 10 × () × (), or 10 × ()

The value of n is ……..

n = ______

Answer:

2

Explanation:

10^{3} = 10 × 10^{n}

10^{3} = 10 x 10 x 10 = 10 x 10^{2}

The value of n is 2

Question 15.

Explain how to write 50,000 using exponents.

Type below:

__________

Answer:

5 x 10^{4}

Explanation:

5 x 10,000

10^{0} = 1;

10^{1} = 1 x 10 = 10;

10^{2} = 10 x 10 = 100;

10^{3} = 10 x 10 x 10 = 1,000;

10^{4} = 10 x 10 x 10 x 10 = 10,000;

10,000 = 10 x 10 x 10 x 10 = 10^{4
}5 x 10^{4}

### 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 × 10^{2} sq mi

B. 3 × 10^{3} sq mi

C. 3 × 10^{4} sq mi

D. 3 × 10^{5} sq mi

Answer:

C. 3 × 10^{4} 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

10^{0} = 1;

10^{1} = 1 x 10 = 10;

10^{2} = 10 x 10 = 100;

10^{3} = 10 x 10 x 10 = 1,000;

10^{4} = 10 x 10 x 10 x 10 = 10,000;

10,000 = 10 x 10 x 10 x 10 = 10^{4
}3 x 10^{4}

Question 16.

b. How can you use a pattern to find the answer?

Type below:

__________

Answer:

3 x 10,000

10^{0} = 1;

10^{1} = 1 x 10 = 10;

10^{2} = 10 x 10 = 100;

10^{3} = 10 x 10 x 10 = 1,000;

10^{4} = 10 x 10 x 10 x 10 = 10,000;

10,000 = 10 x 10 x 10 x 10 = 10^{4
}3 x 10^{4}

Question 16.

c. Write a pattern using the whole number 3 and powers of ten.

3 × 10^{1} = 3 × 10 =

3 × 10^{2} = =

3 × 10^{3} = =

3 × 10^{4} = =

Type below:

__________

Answer:

3 × 10^{1} = 3 × 10 =

3 × 10^{2} = 3 x 10 x 10 = 300

3 × 10^{3} = 3 x 10 x 10 x 10 = 3,000

3 × 10^{4} = 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 × 10^{4} = 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 × 10^{1} miles

B. 8 × 10^{2} miles

C. 8 × 10^{3} miles

D. 8 × 10^{4} miles

Answer:

C. 8 × 10^{3} miles

Explanation:

The Earth’s diameter through the equator is about 8,000 miles.

8 x 1,000

10^{0} = 1;

10^{1} = 1 x 10 = 10;

10^{2} = 10 x 10 = 100;

10^{3} = 10 x 10 x 10 = 1,000;

1,000 = 10 x 10 x 10

8 x 1,000 = 8 x 10^{3}

Question 18.

The Earth’s circumference around the equator is about 25 × 10^{3} 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 × 10^{3} miles.

25 × 10^{3} miles;

10^{0} = 1;

10^{1} = 1 x 10 = 10;

10^{2} = 10 x 10 = 100;

10^{3} = 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 × 10^{1} = _______

1 × 10^{2} = _______

1 × 10^{3} = _______

Answer:

1 × 1 = 1

1 × 10^{1} = 10

1 × 10^{2} = 100

1 × 10^{3} = 1,000

Explanation:

1 × 1 = 1

1 × 10^{1} = 1 x 10 = 10

1 × 10^{2} = 1 x 10 x 10 = 100

1 × 10^{3} = 1 x 10 x 10 x 10 = 1,000

Question 3.

7 × 8 = 56

(7 × 8) × 10^{1} = _______

(7 × 8) × 10^{2} = _______

(7 × 8) × 10^{6} = _______

Answer:

7 × 8 = 56

(7 × 8) × 10^{1} = 560

(7 × 8) × 10^{2} = 5,600

(7 × 8) × 10^{6} = 56,000,000

Explanation:

7 × 8 = 56

(7 × 8) × 10^{1} = 56 x 10 = 560

(7 × 8) × 10^{2} = 56 x 10 x 10 = 5,600

(7 × 8) × 10^{6} = 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 × 10^{1} = 300

6 × 5 × 10^{3} = 3000

6 × 5 × 10^{4} = 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) × 10^{1} = _______

(9 × 5) × 10^{2} = _______

(9 × 5) × 10^{3} = _______

Answer:

9 × 5 = 45

(9 × 5) × 10^{1} = 450

(9 × 5) × 10^{2} = 4,500

(9 × 5) × 10^{3} = 45,000

Explanation:

9 × 5 = 45

(9 × 5) × 10^{1} = 45 x 10 = 450

(9 × 5) × 10^{2} = 45 x 10 x 10 = 4,500

(9 × 5) × 10^{3} = 45 x 10 x 10 x 10 = 45,000

Question 6.

3 × 7 = 21

(3 × 7) × 10^{1} = _______

(3 × 7) × 10^{2} = _______

(3 × 7) × 10^{3} = _______

Answer:

3 × 7 = 21

(3 × 7) × 10^{1} = 210

(3 × 7) × 10^{2} = 2,100

(3 × 7) × 10^{3} = 21,000

Explanation:

3 × 7 = 21

(3 × 7) × 10^{1} = 21 x 10 = 210

(3 × 7) × 10^{2} = 21 x 10 x 10 = 2,100

(3 × 7) × 10^{3} = 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) × 10^{1} = 200

(5 × 4) × 10^{2} = 2,000

(5 × 4) × 10^{3} = 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) × 10^{1} = 350

(5 × 7) × 10^{2} = 3,500

(5 × 7) × 10^{3} = 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) × 10^{1} = _______

(4 × 2) × 10^{2} = _______

(4 × 2) × 10^{3} = _______

Answer:

4 × 2 = 8

(4 × 2) × 10^{1} = 80

(4 × 2) × 10^{2} = 800

(4 × 2) × 10^{3} = 8,000

Explanation:

4 × 2 = 8

(4 × 2) × 10^{1} = 8 x 10 = 80

(4 × 2) × 10^{2} = 8 x 10 x 10 = 800

(4 × 2) × 10^{3} = 8 x 10 x 10 x 10 = 8,000

Question 10.

6 × 7 = 42

(6 × 7) × 10^{1} = _______

(6 × 7) × 10^{2} = _______

(6 × 7) × 10^{3} = _______

Answer:

6 × 7 = 42

(6 × 7) × 10^{1} = 420

(6 × 7) × 10^{2} = 4,200

(6 × 7) × 10^{3} = 42,000

Explanation:

6 × 7 = 42

(6 × 7) × 10^{1} = 42 x 10 = 420

(6 × 7) × 10^{2} = 42 x 10 x 10 = 4,200

(6 × 7) × 10^{3} = 42 x 10 x 10 x 10 = 42,000

**Use mental math and a pattern to find the product.**

Question 11.

(6 × 6) × 10^{1} = ____

Answer:

(6 × 6) × 10^{1} = 360

Explanation:

6 x 6 =36

(6 × 6) × 10^{1} = 36 x 10 = 360

Question 12.

(7 × 4) × 10^{3} = ____

Answer:

28,000

Explanation:

7 x 4 = 28

(7 × 4) × 10^{1} = 28 x 10 = 280

(7 × 4) × 10^{2} = 28 x 10 x 10 = 2,800

(7 × 4) × 10^{3} = 28 x 10 x 10 x 10 = 28,000

Question 13.

(9 × 8) × 10^{2} = ____

Answer:

7,200

Explanation:

(9 × 8) = 72

(9 × 8) × 10^{1} = 72 x 10 = 720

(9 × 8) × 10^{2} = 72 x 10 x 10 = 7,200

Question 14.

(4 × 3) × 10^{2} = ____

Answer:

1,200

Explanation:

(4 × 3) = 12

(4 × 3) × 10^{1} = 12 x 10 = 120

(4 × 3) × 10^{2} = 12 x 10 x 10 = 1,200

Question 15.

(2 × 5) × 10^{3} = ____

Answer:

10,000

Explanation:

(2 × 5) = 10

(2 × 5) × 10^{1} = 10 x 10 = 100

(2 × 5) × 10^{2} = 10 x 10 x 10 = 1,000

(2 × 5) × 10^{3} = 10 x 10 x 10 x 10 = 10,000

Question 16.

(2 × 8) × 10^{2} = ____

Answer:

1,600

Explanation:

(2 × 8) = 16

(2 × 8) × 10^{1 }= 16 x 10 = 160

(2 × 8) × 10^{2} = 16 x 10 x 10 = 1,600

Question 17.

(6 × 5) × 10^{3} = ____

Answer:

30,000

Explanation:

(6 × 5) = 30

(6 × 5) × 10^{1} = 30 x 10 = 300

(6 × 5) × 10^{2} = 30 x 10 x 10 = 3,000

(6 × 5) × 10^{3} = 30 x 10 x 10 x 10 = 30,000

Question 18.

(8 × 8) × 10^{4} = ____

Answer:

640,000

Explanation:

(8 × 8) = 64

(8 × 8) × 10^{1} = 64 x 10 = 640

(8 × 8) × 10^{2} = 64 x 10 x 10 = 6,400

(8 × 8) × 10^{3} = 64 x 10 x 10 x 10 = 64,000

(8 × 8) × 10^{4} = 64 x 10 x 10 x 10 x 10 = 640,000

Question 19.

(7 × 8) × 10^{4} = ____

Answer:

560,000

Explanation:

(7 × 8) = 56

(7 × 8) × 10^{1} = 56 x 10 = 560

(7 × 8) × 10^{2} = 56 x 10 x 10 = 5,600

(7 × 8) × 10^{3} = 56 x 10 x 10 x 10 = 56,000

(7 × 8) × 10^{4} = 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 10^{2}

50 dimes per roll × 30 rolls = (5 x 3) x (10 × 10) = 15 x 10^{2}

50 dimes per roll × 40 rolls = (5 x 4) x (20 × 10) = 20 x 10^{2}

50 dimes per roll × 50 rolls = (5 x 5) x (10 × 10) = 25 x 10^{2}

50 dimes per roll × 60 rolls = (5 x 6) x (10 × 10) = 30 x 10^{2}

50 dimes per roll × 70 rolls = (5 x 7) x (10 × 10) = 35 x 10^{2}

50 dimes per roll × 80 rolls = (5 x 8) x (10 × 10) = 40 x 10^{2}

50 dimes per roll × 90 rolls = (5 x 9) x (10 × 10) = 45 x 10^{2}

50 dimes per roll × 100 rolls = (5 x 10) x (10 × 10) = 50 x 10^{2}

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 10^{2}

40 quarters per roll × 30 rolls =(4 × 3) × (10 × 10) = 12 x 10^{2
}40 quarters per roll × 40 rolls =(4 × 4) × (10 × 10) = 16 x 10^{2
}40 quarters per roll × 50 rolls =(4 × 5) × (10 × 10) = 20 x 10^{2
}40 quarters per roll × 60 rolls =(4 × 6) × (10 × 10) = 24 x 10^{2
}40 quarters per roll × 70 rolls =(4 × 7) × (10 × 10) = 28 x 10^{2
}40 quarters per roll × 80 rolls =(4 × 8) × (10 × 10) = 32 x 10^{2
}40 quarters per roll × 90 rolls =(4 × 9) × (10 × 10) = 36 x 10^{2
}40 quarters per roll × 100 rolls =(4 × 10) × (10 × 10) = 40 x 10^{2}

Question 22.

Type below:

__________

Answer:

Explanation:

80 x 800 = 64 x 10^{3 }

80 x 6 = (8 x 6) x 10 = 48 x 10^{1}

80 x 70 = (8 x 7) x (10 x 10) = 56 x 10^{2}

80 x 9,000 = (8 x 9) x (10 x 10 x 10 x 10) = 64 x 10^{4}

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 10^{4}

90 x 6 = (9 x 6) x 10 = 54 x 10^{1}

90 x 70 = (9 x 7) x (10 x 10) = 63 x 10^{2}

90 x 800 = (9 x 8) x (10 x 10 x 10) = 72 x 10^{3}

**Problem Solving**

**Use the table for 24–26.**

Question 24.

What if you magnified the image of a cluster fly by 9 × 10^{3} ? What would the length appear to be?

____ mm

Answer:

9,000 mm

Explanation:

9 × 10^{3} = 9 x 10 x 10 x 10 = 9,000

Question 25.

If you magnified the image of a fire ant by 4 × 10^{3} and a tree hopper by 3 × 10^{3} , which insect would appear longer? How much longer?

____ mm

Answer:

10^{3} mm

Explanation:

fire ant: 4 × 10^{3} = 4 x 10 x 10 x 10 = 4,000 mm

tree hopper: 3 × 10^{3} = 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 = 10^{3}

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) × 10^{4}?

Options:

A. 3

B. 4

C. 5

D. 6

Answer:

C. 5

Explanation:

(5 × 4) × 10^{4} = 20 x 10^{4} = 2 x 10^{5}

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 8×10^{3} white blood cells. About how many platelets are in the sample?

______ platelets

Answer:

24 x 10^{4} platelets

Explanation:

Let the number of platelets = s.

s = 30 x 8×10^{3}

s = 30 x 8 x 10 x 10 x 10 = (3 x 8) x (10 x 10 x 10 x 10) = 24 x 10^{4}

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 10^{2} monocytes

Explanation:

Let the number of monocytes = S

S = 5 x 60 = 300 = 3 x 100

S = 3 x 10^{2}

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 × 10^{2} eosinophils in the sample, about how many lymphocytes are there?

______ lymphocytes

Answer:

2 × 10^{3} 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 × 10^{2} eosinophils in the sample

Then, Lymphocytes = 10 x 2 × 10^{2} eosinophils = 2 × 10^{3}

Question 32.

An average person has 6 × 10^{2} times as many red bloods cells as white blood cells. A small sample of blood has 7 × 10^{3} white blood cells. About how many red blood cells are in the sample?

______ red blood cells

Answer:

42 x 10^{5 } red blood cells

Explanation:

Let the red blood cells = S

S = 7 × 10^{3} x 6 × 10^{2 }

S = 42 x 10^{5 }

### 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.

10^{3} = ______

Answer:

1,000

Explanation:

10^{0} = 1;

10^{1} = 1 x 10 = 10;

10^{2} = 10 x 10 = 100;

10^{3} = 10 x 10 x 10 = 1,000;

Question 12.

6 × 10^{2} = ______

Answer:

600

Explanation:

6 × 10^{2}

10^{0} = 1;

10^{1} = 1 x 10 = 10;

10^{2} = 10 x 10 = 100;

6 x 100 = 600

Question 13.

4 × 10^{4} = ______

Answer:

40,000

Explanation:

4 × 10^{4}

10^{0} = 1;

10^{1} = 1 x 10 = 10;

10^{2} = 10 x 10 = 100;

10^{3} = 10 x 10 x 10 = 1,000;

10^{4} = 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) × 10^{3} = ______

Answer:

12,000

Explanation:

(3 × 4) × 10^{3}

10^{0} = 1;

10^{1} = 1 x 10 = 10;

10^{2} = 10 x 10 = 100;

10^{3} = 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)

Answer:

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)

Answer:

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 × 10^{4} sq m

B. 6 × 10^{3} sq m

C. 6 × 10^{2} sq m

D. 6 × 10^{1} sq m

Answer:

B. 6 × 103 sq m

Explanation:

6,000 square meters = 6 x 1,000 = 6 x 10 x 10 x 10 = 6 × 10^{3} 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

Answer:

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

Answer:

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 × ___ = ___

______

Answer:

4,776

Explanation:

**Estimate. Then find the product.**

Question 2.

Estimate: ___

6 0 8

× 8

———-

Estimate: ________

Product: 608 × 8 = ________

Answer:

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 = ________

Answer:

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 = ________

Answer:

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

**On Your Own**

**Estimate. Then find the product.**

Question 5.

Estimate:__

7 9 4

× 3

———-

Estimate: ________

Product:794 × 3 = ________

Answer:

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 = ________

Answer:

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 = ________

Answer:

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

Answer:

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:

__________

Answer:

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:

__________

Answer:

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: _______

Answer:

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: _______

Answer:

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: _______

Answer:

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: _______

Answer:

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: _______

Answer:

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: _______

Answer:

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: _______

Answer:

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: _______

Answer:

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 _

$ ______

Answer:

$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:

__________

Answer:

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:

__________

Answer:

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:

__________

Answer:

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:

__________

Answer:

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.

**On Your Own**

**Write an expression to match the words.**

Question 7.

José shared 12 party favors equally among 6 friends.

Type below:

__________

Answer:

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:

__________

Answer:

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:

__________

Answer:

Anna shared 36 apples to 9 friends.

Question 12.

35 – (16 + 11)

Type below:

__________

Answer:

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:

__________

Answer:

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

Answer:

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:

__________

Answer:

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:

__________

Answer:

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

Answer:

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

Answer:

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

_____

Answer:

14

Explanation:

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

Question 2.

10 + (25 – 10) ÷ 5

_____

Answer:

13

Explanation:

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

Question 3.

9 – (3 × 2) + 8

_____

Answer:

11

Explanation:

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

**On Your Own**

**Evaluate the numerical expression.**

Question 4.

(4 + 49) – 4 × 10

_____

Answer:

13

Explanation:

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

Question 5.

5 + 17 – 100 ÷ 5

_____

Answer:

Explanation:

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

Question 6.

36 – (8 + 5)

_____

Answer:

23

Explanation:

36 – (8 + 5) = 36 – 13 = 23

Question 7.

125 – (68 + 7)

_____

Answer:

50

Explanation:

125 – (68 + 7) = 125 – 75 = 50

Question 8.

(4 × 6) – 12

_____

Answer:

12

Explanation:

(4 × 6) – 12 = 24 – 12 = 12

Question 9.

3 × (22 – 2)

_____

Answer:

60

Explanation:

3 × (22 – 2) = 3 x 20 = 60

Question 10.

23 + (16 – 7)

_____

Answer:

32

Explanation:

23 + (16 – 7) = 23 + 9 = 32

Question 11.

(25 – 4) ÷ 3

_____

Answer:

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:

__________

Answer:

(100 – 30) ÷ 5 = 14

Explanation:

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

Question 13.

12 + 17 – 3 × 2

value: 23

Type below:

__________

Answer:

23

Explanation:

(12 + 17) – (3 × 2) = 29 – 6 = 23

Question 14.

9 + 5 ÷ 5 + 2

value: 12

Type below:

__________

Answer:

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:

__________

Answer:

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:

__________

Answer:

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:

__________

Answer:

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:

__________

Answer:

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:

__________

Answer:

(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

Answer:

(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

Answer:

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)

Answer:

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 +____

____

Answer:

12 + [(15 – 5) + (9 – 3)]

12 + [10 + 6]

12 + 16

28

Question 2.

5 × [(26 – 4) – (4 + 6)]

____

Answer:

5 × [(26 – 4) – (4 + 6)]

5 x [22 – 10]

5 x 12 = 60

Question 3.

36 ÷ [(18 – 10) – (8 – 6)]

____

Answer:

36 ÷ [(18 – 10) – (8 – 6)]

36 ÷ [8 – 2]

36 ÷ 6 = 6

**On Your Own**

**Evaluate the numerical expression.**

Question 4.

4 + [(16 – 4) + (12 – 9)]

____

Answer:

4 + [(16 – 4) + (12 – 9)]

4 + [12 + 3]

4 + 15 = 19

Question 5.

24 – [(10 – 7) + (16 – 9)]

____

Answer:

24 – [(10 – 7) + (16 – 9)]

24 – [3 + 7] = 24 – 10 = 14

Question 6.

16 ÷ [(13 + 7) – (12 + 4)]

____

Answer:

16 ÷ [(13 + 7) – (12 + 4)]

16 ÷ [20 – 16]

16 ÷ 4 = 4

Question 7.

5 × [(7 – 2) + (10 – 8)]

____

Answer:

5 × [(7 – 2) + (10 – 8)]

5 x [5 + 2]

5 x 7 = 35

Question 8.

[(17 + 8) + (29 – 12)] ÷ 6

____

Answer:

[(17 + 8) + (29 – 12)] ÷ 6

[25 + 17] ÷ 6

42 ÷ 6 = 7

Question 9.

[(6 × 7) + (3 × 4)] – 28

____

Answer:

[(6 × 7) + (3 × 4)] – 28

[42 + 12] – 28

54 – 28 = 26

Question 10.

3 × {[(12 – 8) × 2] + [(11 – 9) × 3]}

____

Answer:

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

____

Answer:

{[(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:

__________

Answer:

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:

__________

Answer:

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:

__________

Answer:

24 – 10 = 14 roses

Question 12.

d. What expression shows how many carnations Dan sells in one day?

Type below:

__________

Answer:

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:

__________

Answer:

(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:

__________

Answer:

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

Answer:

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

Answer:

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.

__________

Answer:

Distributive Property

**Concepts and Skills**

**Complete the sentence.**

Question 2.

7,000 is 10 times as much as _____

Answer:

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 _____

Answer:

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:

________

Answer:

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:

________

Answer:

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

Explanation:

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

**Find the value.**

Question 6.

10^{2} = _____

Answer:

100

Explanation:

10^{0} = 1;

10^{1} = 1 x 10 = 10;

10^{2} = 10 x 10 = 100;

Question 7.

3 × 10^{4} = _____

Answer:

30,000

Explanation:

3 × 10^{4}

10^{0} = 1;

10^{1} = 1 x 10 = 10;

10^{2} = 10 x 10 = 100;

10^{3} = 10 x 10 x 10 = 1,000;

10^{4} = 10 x 10 x 10 x 10 = 10,000;

3 x 10,000 = 30,000

Question 8.

8 × 10^{3} = _____

Answer:

8,000

Explanation:

8 × 10^{3}

10^{0} = 1;

10^{1} = 1 x 10 = 10;

10^{2} = 10 x 10 = 100;

10^{3} = 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: _____

Answer:

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: _____

Answer:

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: _____

Answer:

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 = _____

Answer:

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 = _____

Answer:

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 = _____

Answer:

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) = _____

Answer:

42 − (9 + 6)

42 – 15

27

Question 16.

15 + (22 − 4) ÷ 6 = _____

Answer:

15 + (22 − 4) ÷ 6

15 + (18 ÷ 6)

15 + 3

18

Question 17.

6 × [(5 × 7) − (7 + 8)] = _____

Answer:

6 × [(5 × 7) − (7 + 8)]

6 x [35 – 15]

6 x [20]

120

### Chapter Review/Test – Page No. 56

**Fill in the bubble completely to show your answer.**

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

Answer:

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.

8 x $35 = 8 x (30 + 5) = (8 x 30) + (8 x 5)

Question 20.

Mr. Rodriguez bought a supply of 20 reams of printer paper. Each ream contains 500 sheets of paper. How many sheets of printer paper are there?

Options:

A. 1,000

B. 5,000

C. 10,000

D. 100,000

Answer:

C. 10,000

Explanation:

Mr. Rodriguez bought a supply of 20 reams of printer paper. Each ream contains 500 sheets of paper.

500 x 20 = 10,000

Question 21.

Harvester ants are common in the southwestern United States. A single harvester ant colony may have as many as 90,000 members. What is that number written as a whole number multiplied by a power of ten?

Options:

A. 9 × 10^{4}

B. 9 × 10^{3}

C. 9 × 10^{2}

D. 9 × 10^{1}

Answer:

A. 9 × 10^{4}

Explanation:

Harvester ants are common in the southwestern United States. A single harvester ant colony may have as many as 90,000 members.

90,000

10^{0} = 1;

10^{1} = 1 x 10 = 10;

10^{2} = 10 x 10 = 100;

10^{3} = 10 x 10 x 10 = 1,000;

10^{4} = 10 x 10 x 10 x 10 = 10,000;

9 x 10,000 = 90,000 = 9 x 10^{4}

### Chapter Review/Test – Page No. 57

**Fill in the bubble completely to show your answer.**

Question 22.

Megan used the following expression to find the quotient of a division problem.

(4 × 12) + (4 × 6)

What was the division problem and the quotient?

Options:

A. 24 ÷ 4 = 6

B. 48 ÷ 4 = 12

C. 64 ÷ 4 = 16

D. 72 ÷ 4 = 18

Answer:

D. 72 ÷ 4 = 18

Explanation:

Megan used (4 × 12) + (4 × 6)

4 x (12 + 6)

4 x 18 = 72

72 ÷ 4 = 18

Question 23.

It is 1,325 feet from Kinsey’s house to her school. Kinsey walks to school each morning and gets a ride home each afternoon. How many feet does Kinsey walk to school in 5 days?

Options:

A. 6,725 feet

B. 6,625 feet

C. 6,525 feet

D. 5,625 feet

Answer:

B. 6,625 feet

Explanation:

It is 1,325 feet from Kinsey’s house to her school. Kinsey walks to school each morning and gets a ride home each afternoon.

1,325 feet x 5 = 6,625 feet

Question 24.

An adult elephant eats about 300 pounds of food each day. Which expression shows about how many pounds of food a herd of 12 elephants eats in 5 days?

Options:

A. 5 + (300 × 12)

B. 5 × (300 × 12)

C. (300 × 12) ÷ 5

D. (300 × 12) − 5

Answer:

B. 5 × (300 × 12)

Explanation:

An adult elephant eats about 300 pounds of food each day.

(300 x 12)

In 5 days, 5 × (300 × 12)

Question 25.

Carla can type 265 characters a minute on her computer keyboard. At that rate, how many characters can she type in 15 minutes?

Options:

A. 2,975

B. 3,875

C. 3,905

D. 3,975

Answer:

D. 3,975

Explanation:

Carla can type 265 characters a minute on her computer keyboard.

In 15 minutes, 265 x 15 = 3,975

### Chapter Review/Test – Page No. 58

**Constructed Response**

Question 26.

Donavan copied the problem below from the board. He missed one of the numbers needed to show his work. What number is missing in his work? Explain how you found the missing number

17 × 5 = ( ______ +7) × 5

= ( ______ × 5) + (7 × 5)

Answer:

Missing number is 10. Using the Distributive Property, the sum of the two number within the () has to be equal to the other factor 17.

10 + 7 = 17

17 × 5 = ( 10 +7) × 5

= ( 10 × 5) + (7 × 5)

**Performance Task**

Question 27.

Drew’s weekly allowance is $8.00. His friend Jan’s weekly allowance is $10. Drew spends $3 a week and Jan spends $4 a week.

A. Write two expressions to show how much money each person has at the end of the week. Use parentheses.

Drew has __ .

Jan has __ .

Type below:

__________

Answer:

Drew has ($8 – $3) .

Jan has ($10 – $4).

Question 27.

B. Drew and Jan decide that they want to put their money together to buy a video game. Write an expression that shows how much they can save each week. Explain.

Type below:

__________

Answer:

(8 – 3) + (10 – 4); Add the amount of money Drew and Jan have at the end of the week. This equals the amount they can save a week.

Question 27.

C. The video game Drew and Jan want to buy costs $55. Write an expression to show how many weeks it will take them to save enough to buy the video game. Use parentheses and brackets in your expression. Then evaluate the expression.

_____ weeks

Answer:

55 ÷ [(8 – 3) +(10 – 4)]

55 ÷ [5 + 6]

55 ÷ 11

5

It will take them 5 weeks to save the money from the game.

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