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**Lesson 1: Algebra • Multiplication Patterns with Decimals**

- Multiplication Patterns with Decimals – Page No. 165
- Multiplication Patterns with Decimals Lesson Check – Page No. 166

**Lesson 2: Investigate • Multiply Decimals and Whole Numbers**

- Multiply Decimals and Whole Numbers – Page No. 167
- Multiply Decimals and Whole Numbers Lesson Check – Page No. 168

**Lesson 3: Multiplication with Decimals and Whole Numbers**

- Multiplication with Decimals and Whole Numbers – Page No. 171
- Multiplication with Decimals and Whole Numbers Lesson Check – Page No. 172

**Lesson 4: Multiply Using Expanded Form**

- Multiply Using Expanded Form – Page No. 175
- Multiply Using Expanded Form Lesson Check – Page No. 176

**Lesson 5: Problem Solving • Multiply Money**

**Mid-Chapter Checkpoint**

**Lesson 6: Investigate • Decimal Multiplication**

**Lesson 7: Multiply Decimals**

- Multiply Decimals – Page No. 188
- Multiply Decimals Lesson Check – Page No. 189
- Multiply Decimals Lesson Check 1 – Page No. 190

**Lesson 8: Zeros in the Product**

**Review/Test**

- Review/Test – Page No. 195
- Review/Test – Page No. 196
- Review/Test – Page No. 197
- Review/Test – Page No. 198

**Complete the pattern.**

Question 1.

10^{0} × 17.04 = 17.04

10^{1} × 17.04 = 17.04

10^{2} × 17.04 = 17.04

10^{3} × 17.04 = 17.04

_____

Answer:

10^{0} × 17.04 = 17.04

10^{1} × 17.04 = 170.4

10^{2} × 17.04 = 1,704

10^{3} × 17.04 =17,040

Explanation:

As you multiply by increasing powers of 10, then the position of the decimal point moves towards the right side.

10^{0} × 17.04 = 1 x 17.04 = 17.04

10^{1} × 17.04 = 10 x 17.04 = 170.4

10^{2} × 17.04 = 100 x 17.04 = 1,704

10^{3} × 17.04 = 1000 x 17.04 = 17,040

**Complete the pattern.**

Question 2.

1 × 3.19 = _____

10 × 3.19 = _____

100 × 3.19 = _____

1,000 × 3.19 = _____

Answer:

1 × 3.19 = 3.19

10 × 3.19 = 31.9

100 × 3.19 = 319

1,000 × 3.19 = 3,190

As you multiply by increasing powers of 10, then the position of the decimal point moves towards the right side.

Question 3.

45.6 × 10^{0} = _____

45.6 × 10^{1} = _____

45.6 × 10^{2} = _____

45.6 × 10^{3} = _____

Answer:

45.6 × 10^{0} = 45.6

45.6 × 10^{1} = 456

45.6 × 10^{2} = 4,560

45.6 × 10^{3} = 45,600

Explanation:

As you multiply by increasing powers of 10, then the position of the decimal point moves towards the right side.

45.6 × 10^{0} = 45.6 x 1 = 45.6

45.6 × 10^{1} = 45.6 x 10 = 456

45.6 × 10^{2} = 45.6 x 100 = 4,560

45.6 × 10^{3} = 45.6 x 1000 = 45,600

Question 4.

1 × 6,391 = _____

0.1 × 6,391 = _____

0.01 × 6,391 = _____

Answer:

1 × 6,391 = 6,391

0.1 × 6,391 = 639.1

0.01 × 6,391 = 63.91

As you multiply by decreasing powers of 10, the position of the decimal point moves towards the left side

**On Your Own**

**Complete the pattern.**

Question 5.

1.06 × 1 = _____

1.06 × 10 = _____

1.06 × 100 = _____

1.06 × 1,000 = _____

Answer:

1.06 × 1 = 1.06

1.06 × 10 = 10.6

1.06 × 100 = 106

1.06 × 1,000 = 1,060

As you multiply by increasing powers of 10, then the position of the decimal point moves towards the right side.

Question 6.

1 × 90 = _____

0.1 × 90 = _____

0.01 × 90 = _____

Answer:

1 × 90 = 90

0.1 × 90 = 9.0 = 9

0.01 × 90 = 0.9

Explanation:

As you multiply by decreasing powers of 10, the position of the decimal point moves towards the left side

1 × 90 = 90

0.1 × 90 = 9.0

0.01 × 90 = 0.90

Question 7.

10^{0} × $0.19 = $ _____

10^{1} × $0.19 = $ _____

10^{2} × $0.19 = $ _____

10^{3} × $0.19 = $ _____

Answer:

10^{0} × $0.19 = $ 0.19

10^{1} × $0.19 = $ 1.9

10^{2} × $0.19 = $ 19

10^{3} × $0.19 = $ 190

Explanation:

As you multiply by increasing powers of 10, then the position of the decimal point moves towards the right side.

10^{0} × $0.19 = $ 0.19

10^{1} × $0.19 = $ 1.9

10^{2} × $0.19 = $ 19

10^{3} × $0.19 = $ 190

Question 8.

580 × 1 = _____

580 × 0.1 = _____

580 × 0.01 = _____

Answer:

580 × 1 = 580

580 × 0.1 = 58

580 × 0.01 = 5.8

Explanation:

As you multiply by increasing powers of 10, then the position of the decimal point moves towards the right side.

580 × 1 = 580

580 × 0.1 = 58.0 = 58

580 × 0.01 = 5.8

Question 9.

10^{0} × 80.72 = _____

10^{1} × 80.72 = _____

10^{2} × 80.72 = _____

10^{3} × 80.72 = _____

Answer:

10^{0} × 80.72 = 80.72

10^{1} × 80.72 = 807.2

10^{2} × 80.72 = 8,072

10^{3} × 80.72 = 80,720

Explanation:

As you multiply by decreasing powers of 10, the position of the decimal point moves towards the left side

10^{0} × 80.72 = 80.72

10^{1} × 80.72 = 807.2

10^{2} × 80.72 = 8,072

10^{3} × 80.72 = 80,720

Question 10.

1 × 7,230 = _____

0.1 × 7,230 = _____

0.01 × 7,230 = _____

Answer:

1 × 7,230 = 7,230

0.1 × 7,230 = 723

0.01 × 7,230 = 72.3

Explanation:

As you multiply by increasing powers of 10, then the position of the decimal point moves towards the right side.

1 × 7,230 = 7,230

0.1 × 7,230 = 723.0 = 723

0.01 × 7,230 = 72.3

**Algebra Find the value **

**of n.**

Question 11.

n × $3.25 = $325.00

n = _____

Answer:

n = 100

Explanation:

n × $3.25 = $325.00

n × $3.25 = $325.00

n x $325 x $0.01 = $325.00

n x $325 x $1/100 = $325.00

n = $325.00/$325 x 100

n = 1 x 100 = 100

Question 12.

0.1 × n = 89.5

n = _____

Answer:

n = 895

Explanation:

0.1 × n = 89.5

1/10 x n = 895 x 0.1

n = 895 x 0.1 x 10

n = 895

Question 13.

10^{3} × n = 630

n = _____

Answer:

n = 0.63

Explanation:

10^{3} × n = 630

1000 x n = 630

n = 630 x 1/1000

n = 630 x 0.001

n = 0.63

**What’s the Error?**

Question 14.

Kirsten is making lanyards for a convention. She needs to make 1,000 lanyards and knows that 1 lanyard uses 1.75 feet of cord. How much cord will Kirsten need?

Kirsten’s work is shown below.

1 × 1.75 = 1.75

10 × 1.75 = 10.75

100 × 1.75 = 100.75

1,000 × 1.75 = 1,000.75

Find and describe Kirsten’s error. | Solve the problem using the correct pattern. |

As you can see from the given pattern, by multiplying 1.75 by different multiplicands, she just replaced the whole number, the number before the decimal point (in our use number 1), with belonging. But this is not the way we multiply decimal numbers with different powers of number 10. |
1 x 1.75= 1.75 10 x 1.75= 17.5 100 x 1.75= 175 1,000 x 1.75= 1,750 |

So, Kirsten needs ______ feet of cord to make 1,000 lanyards.

Describe how Kirsten could have solved the problem without writing out the pattern needed.

Type below:

________

Answer:

Kirsten needs 1,750 feet of cord to make 1,000 lanyards.

that decimal point moves one Noce M the right for each increasing power of 10. So, the answer is 1,750 feet.

**Use the decimal model to find the product.**

Question 1.

5 × 0.06 =

_____

Answer:

5 × 0.06 = 0.3

Explanation:

The picture shows that 5 groups of 6 hundredths.

0.06 = 6 hundredths

Each square box shows 1/ 100.

So, shade 6 boxes 5 times to get the product.

Count the number of boxes shaded. There are 30 hundredths are shaded = 0.30 = 0.3

5 × 0.06 = 0.3

Question 2.

2 × 0.38 =

_____

Answer:

2 × 0.38 = 0.76

Explanation:

The picture shows that 2 groups of 38 hundredths.

0.38 = 38 hundredths

Each square box shows 1/ 100.

So, shade 38 boxes 2 times to get the product. 38 hundredths + 38 hundredths = 76 hundredths = 0.76.

Question 3.

4 × 0.24 =

_____

Answer:

4 × 0.24 = 0.96

Explanation:

4 groups of 24 hundredths

Each square box shows 1/ 100.

So, shade 24 boxes 4 times to get the product. 24 hundredths + 24 hundredths + 24 hundredths + 24 hundredths = 96 hundredths = 0.96.

**Find the product. Draw a quick picture.**

Question 4.

4 × 0.6 =

_____

Answer:

4 × 0.6 = 2.4

Explanation:

4 × 0.6

4 groups of 6 tenths

0.6 + 0.6 + 0.6 + 0.6 = 2.4

4 × 0.6 = 2.4

Question 5.

2 × 0.67 =

_____

Answer:

2 × 0.67 = 1.34

Explanation:

2 × 0.67

2 groups of 67 hundredths

0.67 + 0.67 = 1.34

2 × 0.67 = 1.34

Question 6.

3 × 0.62 =

_____

Answer:

3 × 0.62 = 1.86

Explanation:

3 × 0.62

3 groups of 62 hundredths

0.62 + 0.62 + 0.62 = 1.86

3 × 0.62 = 1.86

Question 7.

4 × 0.32 =

_____

Answer:

4 × 0.32 = 1.28

Explanation:

4 × 0.32

4 groups of 32 hundredths

0.32 + 0.32 + 0.32 + 0.32 = 1.28

4 × 0.32 = 1.28

Question 8.

Describe how you solved Exercise 7 using place value and renaming.

Type below:

________

Answer:

4 × 0.32

4 groups of 32 hundredths

There are 32 hundredths.

32 hundredths there are 30 tenths and 2 hundredths.

Combine the tenths and rename.

2 + 2 + 2 + 2 = 8

Combine the tenths and rename.

There are 3 tenths.

3 + 3 + 3 + 3 = 12; 2 tenths and 1 tens

Cross out the tenths you renamed.

Combine the ones and rename them.

0 + 0 + 0 + 0 + 1 = 1

1.28

4 × 0.32 = 1.28

**Use the table for 9–11.**

Question 9.

Each day a bobcat drinks about 3 times as much water as a Canada goose drinks. How much water can a bobcat drink in one day?

_____ liter

Answer:

0.72 liters

Explanation:

Each day a bobcat drinks about 3 times as much water as a Canada goose drinks.

Canada goose = 0.24 liters

bobcat drinks = 3 x 0.24

3 x 0.24 = 0.72 liters

Question 10.

River otters drink about 5 times as much water as a bald eagle drinks in a day. How much water can a river otter drink in one day?

_____ liter

Answer:

0.8 liter

Explanation:

River otters drink about 5 times as much water as a bald eagle drinks in a day.

bald eagle drinks 0.16 liters

5 times as 0.16 liters = 5 x 0.16 = 0.8 liter

Question 11.

Explain how you could use a quick picture to find the amount of water that a cat drinks in 5 days.

Type below:

________

Answer:

Explanation:

Cat drinks 0.15 liters of water in a day.

In 5 days, 5 x 0.15 = 0.75

Question 12.

Test Prep Jared has a parakeet that weighs 1.44 ounces. Susie has a Senegal parrot that weighs 3 times as much as Jared’s parakeet. How many ounces does Susie’s parrot weigh?

Options:

a. 0.32 ounce

b. 0.43 ounce

c. 4.32 ounces

d. 43.2 ounces

Answer:

c. 4.32 ounces

Explanation:

Jared has a parakeet that weighs 1.44 ounces. Susie has a Senegal parrot that weighs 3 times as much as Jared’s parakeet.

Susie’s parrot weigh 3 x 1.44 ounces = 4.32 ounces

**Place the decimal point in the product.**

Question 1.

6.81

× 7

———-

4767

Think: The place value of the decimal factor is hundredths.

Answer:

6.81 x 7 = 47.67

Explanation:

6.81 x 7 = 7 x 6.81

7 x (6 + 0.81) = (7 x 6) + (7 x 0.81) = 42 + 5.67 = 47.67

Question 2.

3.7

× 2

———-

74

_____

Answer:

7.4

Explanation:

3.7 x 2

3.7 x 10 = 37

37 x 2 = 74

37 x 0.1 = 3.7

74 x 0.1 = 7.4

Question 3.

19.34

× 5

———-

9670

_____

Answer:

96.7

Explanation:

19.34 x 100 = 1934

1934 x 5 = 9670

1934 x 0.01 = 19.34

9670 x 0.01 = 96.7

**Find the product.**

Question 4.

6.32

× 3

———-

_____

Answer:

18.96

Explanation:

6.32 x 100 = 632

632 x 3 = 1896

632 x 0.01 = 6.32

1896 x 0.01 = 18.96

Question 5.

4.5

× 8

———-

_____

Answer:

36

Explanation:

4.5 x 10 = 45

45 x 8 = 360

45 x 0.1 = 4.5

360 x 0.1 = 36.0

Question 6.

40.7

× 5

———-

_____

Answer:

203.5

Explanation:

40.7 x 10 = 407

407 x 5 = 2035

407 x 0.1 = 40.7

2035 x 0.1 = 203.5

**On Your Own**

**Find the product.**

Question 7.

4.93

× 7

———-

_____

Answer:

34.51

Explanation:

7 x 3 = 21 hundredths; 2 tenths and 1 hundredths

7 x 9 = 63 tenths; 63 + 2 tenths = 65 tenths; 6 ones and 5 tenths

4 x 7 = 28; 28 + 6 = 34 ones;

34.51

Question 8.

8.2

× 6

———-

_____

Answer:

49.2

Explanation:

6 x 2 = 12 tenths; 1 ones and 2 tenths

6 x 8 = 48; 48 + 1 = 49 ones

49.2

Question 9.

0.49

× 4

———-

_____

Answer:

1.96

Explanation:

9 x 4 = 36 hundredths; 3 tenths and 6 hundredths

4 x 4 = 16 tenths; 16 + 3 tenths = 19 tenths; 1 ones and 9 tenths

4 x 0 = 0; 0 + 1 = 1ones;

1.96

Question 10.

9.08

× 9

———-

_____

Answer:

81.72

Explanation:

9 x 8 = 72 hundredths; 7 tenths and 2 hundredths

9 x 0 = 0 tenths; 0 + 7 tenths = 7 tenths; 7 tenths

9 x 9 = 81; 81

81.72

Question 11.

7.55

× 8

———-

_____

Answer:

60.4

Explanation:

8 x 5 = 40 hundredths; 4 tenths and 0 hundredths

8 x 5 = 40 tenths; 40 + 4 tenths = 44 tenths; 4 ones and 4 tenths

8 x 7 = 56 ones; 56 + 4 = 60 ones

60.40 = 60.4

Question 12.

15.37

× 5

———-

_____

Answer:

76.85

Explanation:

5 x 7 = 35 hundredths; 3 tenths and 5 hundredths

5 x 3 = 15 tenths; 15 + 3 tenths = 18 tenths; 1 ones and 8 tenths

5 x 5 = 25 ones; 25 + 1 = 26 ones; 2 hundreds and 6 ones

5 x 1 = 5 hundreds; 5 + 2 = 7 hundreds

76.85

**Practice: Copy and Solve Find the product.**

Question 13.

8 × 7.2 = _____

Answer:

8 × 7.2 = 57.6

Explanation:

8 × 7.2 = 8 x (7 + 0.2) = (8 x 7) + (8 x 0.2) = 56 + 1.6 = 57.6

Question 14.

3 × 1.45 = _____

Answer:

3 × 1.45 = 4.35

Explanation:

3 x 1.45 = 3 x (1 + 0.45) = (3 x 1) + (3 x 0.45) = 3 + 1.35 = 4.35

Question 15.

9 × 8.6 = _____

Answer:

9 × 8.6 = 77.4

Explanation:

9 × 8.6 = 9 x (8 + 0.6) = (9 x 8) + (9 x 0.6) = 72 + 5.4 = 77.4

Question 16.

6 × 0.79 = _____

Answer:

6 × 0.79 = 4.74

Explanation:

6 x 0.79 = 4.74

Question 17.

4 × 9.3 = _____

Answer:

4 × 9.3 = 37.2

Explanation:

4 × 9.3 = 4 x (9 + 0.3) = (4 x 9) + (4 x 0.3) = 36 + 1.2 = 37.2

Question 18.

7 × 0.81 = _____

Answer:

7 × 0.81 = 5.67

Explanation:

7 × 0.81 = 5.67

Question 19.

6 × 2.08 = _____

Answer:

6 × 2.08 = 12.48

Explanation:

6 × 2.08 = 6 x (2 + 0.08) = (6 x 2) + (6 x 0.08) = 12 + 0.48 = 12.48

Question 20.

5 × 23.66 = _____

Answer:

5 × 23.66 = 118.3

Explanation:

5 × 23.66 = 5 x (23 + 0.66) = (5 x 23) + (5 x 0.66) = 115 + 3.3 = 118.3

**Use the table for 21–23.**

Question 21.

Sari has a bag containing 6 half dollars. What is the weight of the half dollars in Sari’s bag?

_____ grams

Answer:

68.04 grams

Explanation:

Sari has a bag containing 6 half dollars.

Half dollars = 11.34 grams

6 x 11.34 = 68.04 grams

The weight of the half dollars in Sari’s bag is 68.04 grams.

Question 22.

Felicia is running a game booth at a carnival. One of the games requires participants to guess the weight, in grams, of a bag of 9 dimes. What is the actual weight of the dimes in the bag?

_____ grams

Answer:

20.43 grams

Explanation:

Felicia is running a game booth at a carnival. One of the games requires participants to guess the weight, in grams, of a bag of 9 dimes.

9 x 2.27 grams = 20.43 grams

Question 23.

Chance has $2 in quarters. Blake has $5 in dollar coins. Whose coins have the greatest weight? Explain.

_________

Answer:

Dollar coins has the greatest weight than quarters.

Explanation:

$2 means 4 quarters = 4 x 5.67 = 22.68

$5 in dollar coins = 5 x 8.1 = 40.5

Dollar coins has the greatest weight than quarters.

Question 24.

Julie multiplies 6.27 by 7 and claims the product is 438.9. Explain without multiplying how you know Julie’s answer is not correct. Find the correct answer.

Type below:

_________

Answer:

6.27 has two decimal digits

438.9 has one decimal digit

Therefore, Julie’s answer is not correct.

6.27 x 7 = 43.89

Question 25.

Test Prep Every day on his way to and from school, Milo walks a total of 3.65 miles. If he walks to school 5 days, how many miles will Milo have walked?

_____ miles

Answer:

18.25 miles

Explanation:

Milo walks a total of 3.65 miles.

If he walks to school 5 days, 5 x 3.65 = 18.25 miles

**Draw a model to find the product.**

Question 1.

19 × 0.75 =

_____

Answer:

14.25

Explanation:

19 × 0.75

19 = 10 + 9

0.75 = 0.7 + 0.05

10 x 0.7 = 7

10 x 0.05 = 0.5

9 x 0.7 = 6.3

9 x 0.05 = 0.45

7 + 0.5 + 6.3 + 0.45 = 14.25

19 × 0.75 = 14.25

Question 2.

27 × 8.3 =

_____

Answer:

224.1

Explanation:

27 × 8.3 = 224.1

27 = 20 + 7

8.3 = 8 + 0.3

20 x 8 = 160

20 x 0.3 = 6

7 x 8 = 56

7 x 0.3 = 2.1

160 + 6 + 56 + 2.1 = 224.1

**Find the product.**

Question 3.

18 × 8.7 = _____

Answer:

18 × 8.7 = 156.6

Explanation:

8.7 x 10 = 87

18 x 87 = 1566

87 x 0.1 = 8.7

1566 x 0.1 = 156.6

Question 4.

23 × 56.1 = _____

Answer:

1290.3

Explanation:

56.1 x 10 = 561

561 x 23 = 12,903

561 x 0.1 = 56.1

12,903 x 0.1 = 1290.3

Question 5.

47 × 5.92 = _____

Answer:

278.24

Explanation:

5.92 x 100 = 592

592 x 47 = 27,824

592 x 0.01 = 5.92

27,824 x 0.01 = 278.24

**On Your Own**

**Draw a model to find the product.**

Question 6.

71 × 8.3 =

_____

Answer:

589.3

Explanation:

71 = 70 + 1

8.3 = 8 + 0.3

70 x 8 = 560

70 x 0.3 = 21

1 x 8 = 8

1 x 0.3 = 0.3

560 + 21 + 8 + 0.3 = 589.3

Question 7.

28 × 0.91 =

_____

Answer:

25.48

Explanation:

28 = 20 + 8

0.91 = 0.90 + 0.01

20 x 0.90 = 18

20 x 0.01 = 0.2

8 x 0.90 = 7.2

8 x 0.01 = 0.08

18 + 0.2 + 7.2 + 0.08 = 25.48

**Find the product.**

Question 8.

19 × 0.65 = _____

Answer:

19 × 0.65 = 12.35

Explanation:

0.65 x 100 = 65

65 x 19 = 1235

65 x 0.01 = 0.65

1235 x 0.01 = 12.35

Question 9.

34 × 98.3 = _____

Answer:

34 × 98.3 = 3342.2

Explanation:

98.3 x 10 = 983

983 x 34 = 33,422

983 x 0.1 = 98.3

33,422 x 0.1 = 3342.2

Question 10.

26 × 16.28 = _____

Answer:

26 × 16.28 = 423.28

Explanation:

16.28 x 100 = 1628

1628 x 26 = 42,328

1628 x 0.01 = 16.28

42,328 x 0.01 = 423.28

Question 11.

While researching facts on the planet Earth, Kate learned that a true Earth day is about 23.93 hours long. How many hours are in 2 weeks on Earth?

a. What are you being asked to find?

Type below:

_________

Answer:

We need to find How many hours are in 2 weeks on Earth? 2 weeks x 23.93 hours per day?

Question 11.

b. What information do you need to know to solve the problem?

Type below:

_________

Answer:

Number of days in a week

Hours per day

Question 11.

c. Write an expression to represent the problem to be solved.

Type below:

_________

Answer:

2 weeks = 14 days

14 x 23.93 hours

Question 11.

d. Show the steps you used to solve the problem.

Type below:

_________

Answer:

335.02 hours

Explanation:

23.93 = 23.93 x 100 = 2393

2393 x 14 = 33,502

2393 x 0.01 = 23.93

33502 x 0.01 = 335.02

Question 11.

e. Complete the sentences.

On Earth, there are about _____ hours in a day, _____ days in 1 week, and _____ days in two weeks.

Since _____ × _____ = _____ , there are about _____ hours in 2 weeks on Earth.

Type below:

_________

Answer:

On Earth, there are about 23.93 hours in a day, 7 days in 1 week, and 14 days in two weeks.

Since 23.93 × 14 = 335.02, there are about 335.02 hours in 2 weeks on Earth.

Question 12.

Michael’s favorite song is 3.19 minutes long. If he listens to the song 15 times on repeat, how long will he have listened to the same song?

_____ minutes

Answer:

47.85 minutes

Explanation:

Michael’s favorite song is 3.19 minutes long.

If he listens to the song 15 times, 15 x 3.19 = 47.85 minutes

Question 13.

Test Prep A car travels 56.7 miles in an hour. If it continues at the same speed, how far will the car travel in 12 hours?

Options:

a. 68.004 miles

b. 680.04 miles

c. 680.4 miles

d. 6,804 miles

Answer:

c. 680.4 miles

Explanation:

A car travels 56.7 miles in an hour.

In 12 hours, 12 x 56.7 = 680.4 hours

Question 1.

Manuel collects $45.18 for a fundraiser. Gerome collects $18.07 more than Manuel. Cindy collects 2 times as much as Gerome. How much money does Cindy collect for the fundraiser?

First, draw a diagram to show the amount Manuel collects.

Then, draw a diagram to show the amount Gerome collects.

Next, draw a diagram to show the amount Cindy collects.

Finally, find the amount each person collects.

Cindy collects ______ for the fundraiser.

Type below:

_________

Answer:

Manuel collects $45.18 for a fundraiser. Gerome collects $18.07 more than Manuel. Cindy collects 2 times as much as Gerome.

Manuel: $45.18

Gerome: $45.18 + $18.07 = $63.25

Cindy: 2 x $63.25 = $126.5

Question 2.

What if Gerome collects $9.23 more than Manuel? If Cindy still collects 2 times as much as Gerome, how much money would Cindy collect?

Type below:

_________

Answer:

Gerome collects $9.23 more than Manuel

Manuel: $45.18

Gerome: $45.18 + $9.23 = $54.41

Cindy: 2 x $54.41 = $108.82

Question 3.

It costs $5.15 to rent a kayak for 1 hour at a local state park. The price per hour stays the same for up to 5 hours of rental. After 5 hours, the cost is decreased to $3.75 per hour. How much would it cost to rent a kayak for 6 hours?

$ ______

Answer:

$29.5

Explanation:

It costs $5.15 to rent a kayak for 1 hour at a local state park. The price per hour stays the same for up to 5 hours of rental. After 5 hours, the cost is decreased to $3.75 per hour.

For first 5 hours, $5.15

Next hour after 5 hours, it decreased to $3.75

For 6 hours, 5 x $5.15 + 1 x $3.75

5 x $5.15 = $25.75

1 x $3.75 = $3.75

$25.75 + $3.75 = $29.5

Question 4.

Jenn buys a pair of jeans for $24.99. Her friend Karen spends $3.50 more for the same pair of jeans. Vicki paid the same price as Karen for the jeans but bought 2 pairs. How much did Vicki spend?

$ ______

Answer:

$56.98

Explanation:

Jenn buys a pair of jeans for $24.99.

Karen: $24.99 + $3.50 = $28.49

Vicky: 2 x $28.49 = $56.98

**Use the sign for 5–8.**

Question 5.

Austin shops at Surfer Joe’s Surf Shop before going to the beach. He buys 2 T-shirts, a pair of board shorts, and a towel. If he gives the cashier $60, how much change will Austin get back?

$ ______

Answer:

$2.86

Explanation:

T-Shirt = $12.75

Board Shorts = $25.99

Sandals = $8.95

Towel = $5.65

Sunglasses = $15.50

Austin shops at Surfer Joe’s Surf Shop before going to the beach. He buys 2 T-shirts, a pair of board shorts, and a towel.

(2 x $12.75) + ($25.99) + $5.65 = $25.5 + $31.64 = $57.14

$60 – $57.14 = $2.86

Question 6.

Maria buys 3 T-shirts and 2 pairs of sandals at Surfer Joe’s Surf Shop. How much does Maria spend?

$ ______

Answer:

$56.15

Explanation:

Maria buys 3 T-shirts and 2 pairs of sandals at Surfer Joe’s Surf Shop.

3 x $12.75 = $38.25

2 x $8.95 = $17.9

$38.25 + $17.9 = $56.15

Question 7.

Nathan receives a coupon in the mail for $10 off of a purchase of $100 or more. If he buys 3 pairs of board shorts, 2 towels, and a pair of sunglasses, will he spend enough to use the coupon? How much will his purchase cost?

Type below:

_________

Answer:

$94.77

Explanation:

3 pairs of board shorts, 2 towels, and a pair of sunglasses

3 x $25.99 = $77.97

2 x $5.65 = $11.3

Sunglasses = $15.50

$77.97 + $11.3 + $15.50 = $104.77

$10 off of a purchase of $100 or more

$104.77 – $10 = $94.77

Question 8.

Moya spends $33.90 on 3 different items. If she did not buy board shorts, which three items did Moya buy?

Type below:

_________

Answer:

T-Shirt, Towel, and Sunglasses

Explanation:

Moya spends $33.90 on 3 different items. If she did not buy board shorts,

T-Shirt = $12.75

Towel = $5.65

Sunglasses = $15.50

Question 9.

Test Prep At a donut shop in town, each donut costs $0.79. If Mr. Thomas buys a box of 8 donuts, how much will he pay for the donuts?

Options:

a. $6.32

b. $8.79

c. $63.20

d. $87.90

Answer:

a. $6.32

Explanation:

At a donut shop in town, each donut costs $0.79. If Mr. Thomas buys a box of 8 donuts, 8 x $0.79 = $6.32

**Concepts and Skills**

Question 1.

Explain how you can use a quick picture to find 3 × 2.7.

Type below:

________

Answer:

3 × 2.7 = 8.1;

As there are 8 ones and 1 tenths, we can draw eight square boxes and 1 line to represent 1 tenth.

**Complete the pattern.**

Question 2.

1 × 3.6 = _______

10 × 3.6 = _______

100 × 3.6 = _______

1000 × 3.6 = _______

Answer:

1 × 3.6 = 3.6

10 × 3.6 = 36

100 × 3.6 = 360

1000 × 3.6 = 3,600

Question 3.

10^{0} × 17.55 = _______

10^{1} × 17.55 = _______

10^{2} × 17.55 = _______

10^{3} × 17.55 = _______

Answer:

10^{0} × 17.55 = 17.55

10^{1} × 17.55 = 175.5

10^{2} × 17.55 = 1755

10^{3} × 17.55 = 17,550

Explanation:

10^{0} × 17.55 = 1 x 17.55 = 17.55

10^{1} × 17.55 = 10 x 17.55 = 175.5

10^{2} × 17.55 = 100 x 17.55 = 1755

10^{3} × 17.55 = 1000 x 17.55 = 17,550

Question 4.

1 × 29 = _______

0.1 × 29 = _______

0.01 × 29 = _______

Answer:

1 × 29 = 29

0.1 × 29 = 2.9

0.01 × 29 = 0.29

**Find the product.**

Question 5.

3.14

× 8

———–

_____

Answer:

25.12

Explanation:

8 x (3.14) = 8 x (3 + 0.14) = (8 x 3) + (8 x 0.14) = 24 + 1.12 = 25.12

Question 6.

17 × 0.67 = _____

Answer:

11.39

Explanation:

0.67 x 100 = 67

67 x 17 = 1139

67 x 0.01 = 0.67

1139 x 0.01 = 11.39

Question 7.

29 × 7.3 = _____

Answer:

211.7

Explanation:

29 × 7.3 = 29 x (7 + 0.3) = (29 x 7) + (29 x 0.3) = 203 + 8.7 = 211.7

**Draw a diagram to solve.**

Question 8.

Julie spends $5.62 at the store. Micah spends 5 times as much as Julie. Jeremy spends $6.72 more than Micah. How much money does each person spend?

Julie: $ _______

Micah: $ _______

Jeremy: $ _______

Answer:

Julie: $ 5.62

Micah spends 5 times as much as Julie = 5 x $5.62 = $28.1

Jeremy spends $6.72 more than Micah = $28.1 + $6.72 = $34.82

Question 9.

Sarah is cutting ribbons for a pep rally. The length of each ribbon needs to be 3.68 inches. If she needs 1,000 ribbons, what is the length of ribbon Sarah needs?

_____ inches

Answer:

3680 inches

Explanation:

Sarah is cutting ribbons for a pep rally. The length of each ribbon needs to be 3.68 inches.

If she needs 1,000 ribbons, 3.68 x 1,000 = 3680 inches

Question 10.

Adam is carrying books to the classroom for his teacher. Each books weighs 3.85 pounds. If he carries 4 books, how many pounds is Adam carrying?

_____ pounds

Answer:

15.4 pounds

Explanation:

Adam is carrying books to the classroom for his teacher. Each books weighs 3.85 pounds. If he carries 4 books, 4 x 3.85 = 15.4 pounds.

Question 11.

A car travels 54.9 miles in an hour. If the car continues at the same speed for 12 hours, how many miles will it travel?

_____ miles

Answer:

658.8 miles

Explanation:

A car travels 54.9 miles in an hour. If the car continues at the same speed for 12 hours, 12 x 54.9 = 658.8 miles

Question 12.

Charlie saves $21.45 each month for 6 months. In the seventh month, he only saves $10.60. How much money will Charlie have saved after 7 months?

$ __________

Answer:

$139.3

Explanation:

Charlie saves $21.45 each month for 6 months. In the seventh month, he only saves $10.60.

6 x $21.45 + $10.60 = $128.7 + $10.60 = $139.3

**Multiply. Use the decimal model.**

Question 1.

0.8 × 0.4 =

Answer:

0.8 × 0.4 = 0.32

Explanation:

The shaded and crossed parts represent the product.

32 hundredths = 0.32

Question 2.

0.1 × 0.7 =

_____

Answer:

0.1 × 0.7 = 0.7

Explanation:

Count the number of overlapped boxes to find the product. 7 tenths = 0.7

Question 3.

0.4 × 1.6 =

_____

Answer:

0.4 × 1.6 = 0.64

Explanation:

Count the red line crossed boxes to get the product.

4 x 16 = 64

0.1 x 0.1 = 0.01

64 x 0.01 = 0.64

Question 4.

0.3 × 0.4 =

_____

Answer:

0.3 × 0.4 = 0.12

Explanation:

3 x 4 = 12

0.1 x 0.1 = 0.01

12 x 0.01 = 0.12

Question 5.

0.9 × 0.6 =

_____

Answer:

0.9 x 0.6 = 0.54

Explanation:

9 x 6 = 54

0.1 x 0.1 = 0.01

54 x 0.01 = 0.54

Question 6.

0.5 × 1.2 =

_____

Answer:

0.5 × 1.2 = 0.60

Explanation:

Count the red line crossed boxes to get the product.

5 x 12 = 60

0.1 x 0.1 = 0.01

60 x 0.01 = 0.60

Question 7.

0.8 × 0.9 =

_____

Answer:

0.8 × 0.9 = 0.72

Explanation:

8 x 9 = 72

0.1 x 0.1 = 0.01

72 x 0.01 = 0.72

Question 8.

0.5 × 0.3 =

_____

Answer:

0.5 × 0.3 = 0.15

Explanation:

5 x 3 = 15

0.1 x 0.1 = 0.01

15 x 0.01 = 0.15

Question 9.

0.5 × 1.5 =

_____

Answer:

0.5 × 1.5 = 0.75

Explanation:

Count the red line crossed boxes to get the product.

5 x 15 = 75

0.1 x 0.1 = 0.01

75 x 0.01 = 0.75

Question 10.

Explain why when you multiply and find one tenth of one tenth, it is equal to one hundredth.

Type below:

_________

Answer:

When you do one-tenth of one-tenth, it is one-tenth over 10 —-> (1/10) /10

So, you can consider it as (1/10) / (10/1). This is only for simplicity.

Now, you have to multiply the denominator of the fraction in the numerator with the numerator of fraction in denominator i.e., 10 with 10 and this comes in denominator only.

and numerator of fraction in the numerator with the denominator of the fraction in denominator i.e., 1 with 1.

So, you get, (1*1) / (10*10) = 1/100

This is again the 10th part of one-tenth OR 100th part of 1 = one hundredth

**Sense or Nonsense?**

Question 11.

Randy and Stacy used models to find 0.3 of 0.5. Both Randy’s and Stacy’s models are shown below. Whose model makes sense? Whose model is nonsense? Explain your reasoning below each model. Then record the correct answer.

Randy’s Model

Stacy’s Model

0.3 × 0.5 =

• For the answer that is nonsense, describe the error the student made.

_________ model is correct

Answer:

Randy’s Model is correct. Stacy’s Model makes nonsense.

Because Stacy’s Model is showing 0.10 x 0.8 which is not equal to 0.3 x 0.5

Explanation:

Randy and Stacy used models to find 0.3 of 0.5

0.3 x 0.5 = 0.15

**Place the decimal point in the product.**

Question 1.

3.62

× 1.4

———-

5068

Think: A hundredth is being multiplied by a tenth. Use the pattern 0.01 × 0.1.

___

Answer:

5.068

Explanation:

3.62 x 100 = 362 = 362 x 0.01

1.4 x 10 = 14 = 14 x 0.1

362 x 14 = 5068

0.01 x 0.1 = 0.001

5068 x 0.001 = 5.068

Question 2.

6.8

×1.2

———-

816

_____

Answer:

8.16

Explanation:

6.8 x 10 = 68 = 68 x 0.1

1.2 x 10 = 12 = 12 x 0.1

68 x 12 = 816

0.1 x 0.1 = 0.01

816 x 0.01 = 8.16

Find the product.

Question 3.

0.9

× 0.8

———-

_____

Answer:

0.72

Explanation:

0.9 x 10 = 9 = 9 x 0.1

0.8 x 10 = 8 = 8 x 0.1

9 x 8 = 72

0.1 x 0.1 = 0.01

72 x 0.01 = 0.72

Question 4.

84.5

× 5.5

———-

_____

Answer:

464.75

Explanation:

84.5 x 10 = 845 = 845 x 0.1

5.5 x 10 = 55 = 55 x 0.1

845 x 55 = 46475

0.1 x 0.1 = 0.01

46475 x 0.01 = 464.75

Question 5.

2.39

×2.7

———-

_____

Answer:

6.453

Explanation:

2.39 x 100 = 239 = 239 x 0.01

2.7 x 10 = 27 = 27 x 0.1

239 x 27 = 6453

0.01 x 0.1 = 0.001

6453 x 0.001 = 6.453

**Find the product.**

Question 6.

7.9

× 3.4

———-

_____

Answer:

26.86

Explanation:

7.9 x 10 = 79 = 79 x 0.1

3.4 x 10 = 34 = 34 x 0.1

79 x 34 = 2686

0.1 x 0.1 = 0.01

2686 x 0.01 = 26.86

Question 7.

9.2

×5.6

———-

_____

Answer:

51.52

Explanation:

9.2 x 10 = 92 = 92 x 0.1

5.6 x 10 = 56 = 56 x 0.1

92 x 56 = 5152

0.1 x 0.1 = 0.01

5152 x 0.01 = 51.52

Question 8.

3.45

× 9.7

———-

_____

Answer:

33.465

Explanation:

3.45 x 100 = 345 = 345 x 0.01

9.7 x 10 = 97 = 97 x 0.1

345 x 97 = 33465

0.01 x 0.1 = 0.001

33465 x 0.001 = 33.465

Question 9.

45.3

× 0.8

———-

_____

Answer:

36.24

Explanation:

45.3 x 10 = 453 = 453 x 0.1

0.8 x 10 = 8 = 8 x 0.1

453 x 8 = 3624

0.1 x 0.1 = 0.01

3624 x 0.01 = 36.24

Question 10.

6.98

× 2.5

———-

_____

Answer:

17.450

Explanation:

6.98 x 100 = 698 = 698 x 0.01

2.5 x 10 = 25 = 25 x 0.1

698 x 25 = 17,450

0.01 x 0.1 = 0.001

17450 x 0.001 = 17.450

Question 11.

7.02

×3.4

———-

_____

Answer:

23.868

Explanation:

7.02 x 100 = 702 = 702 x 0.01

3.4 x 10 = 34 = 34 x 0.1

702 x 34 = 23868

0.01 x 0.1 = 0.001

23868 x 0.001 = 23.868

Question 12.

14.9

×0.35

———-

_____

Answer:

5.215

Explanation:

14.9 x 10 = 149 = 149 x 0.1

0.35 x 100 = 35 = 35 x 0.01

149 x 35 = 5215

0.1 x 0.01 = 0.001

5215 x 0.001 = 5.215

Question 13.

50.99

× 3.7

———-

_____

Answer:

188.663

Explanation:

50.99 x 100 = 5099 = 5099 x 0.01

3.7 x 10 = 37 = 37 x 0.1

5099 x 37 = 188663

0.01 x 0.1 = 0.001

188663 x 0.001 = 188.663

Question 14.

18.43

× 1.9

———-

_____

Answer:

35.017

Explanation:

18.43 x 100 = 1843 = 1843 x 0.01

1.9 x 10 = 19 = 19 x 0.1

1843 x 19 = 35017

0.01 x 0.1 = 0.001

35017 x 0.001 = 35.017

**Practice: Copy and Solve Find the product.**

Question 15.

3.4 × 5.2 = _____

Answer:

17.68

Explanation:

3.4 × 5.2

34 x 52 = 1768

0.1 x 0.1 = 0.01

1768 x 0.01 = 17.68

Question 16.

0.9 × 2.46 = _____

Answer:

2.214

Explanation:

9 x 246 = 2214

0.1 x 0.01 = 0.001

2214 x 0.001 = 2.214

Question 17.

9.1 × 5.7 = ____

Answer:

51.87

Explanation:

91 x 57 = 5187

0.1 x 0.1 = 0.01

5187 x 0.01 = 51.87

Question 18.

4.8 × 6.01 = _____

Answer:

28.848

Explanation:

48 x 601 = 28848

0.1 x 0.01 = 0.001

28848 x 0.001 = 28.848

Question 20.

7.6 × 18.7 = _____

Answer:

142.12

Explanation:

76 x 187 = 14212

0.1 x 0.1 = 0.01

14212 x 0.01 = 142.12

Question 21.

0.77 × 14.9 = _____

Answer:

114.73

Explanation:

77 x 149 = 11473

0.01 x 0.1 = 0.01

11473 x 0.01 = 114.73

Question 22.

3.3 × 58.14 = _____

Answer:

191.862

Explanation:

33 x 5814 = 191862

0.1 x 0.01 = 0.001

191862 x 0.001 = 191.862

Question 23.

Charlie has an adult Netherlands dwarf rabbit that weighs 1.2 kilograms. Cliff’s adult Angora rabbit weighs 2.9 times as much as Charlie’s rabbit. How much does Cliff’s rabbit weigh?

_____ kilograms

Answer:

3.48 kilograms

Explanation:

Charlie has an adult Netherlands dwarf rabbit that weighs 1.2 kilograms. Cliff’s adult Angora rabbit weighs 2.9 times as much as Charlie’s rabbit.

1.2 x 2.9 = 3.48 kilograms

Question 24.

John has pet rabbits in an enclosure that has an area of 30.72 square feet. The enclosure Taylor is planning to build for his rabbits will be 2.2 times as large as John’s. What will be the area of the enclosure Taylor is planning to build?

_____ square feet

Answer:

67.584 square feet

Explanation:

John has pet rabbits in an enclosure that has an area of 30.72 square feet. The enclosure Taylor is planning to build for his rabbits will be 2.2 times as large as John’s.

30.72 x 2.2 = 67.584 square feet

Question 25.

A zoo is planning a new building for the penguin exhibit. First, they made a model that was 1.3 meters tall. Then, they made a more detailed model that was 1.5 times as tall as the first model. The building will be 2.5 times as tall as the height of the detailed model. What will be the height of the building?

_____ meters

Answer:

4.875 meters

Explanation:

A zoo is planning a new building for the penguin exhibit. First, they made a model that was 1.3 meters tall. Then, they made a more detailed model that was 1.5 times as tall as the first model.

1.3 x 1.5 = 1.95

The building will be 2.5 times as tall as the height of the detailed model.

2.5 x 1.95 = 4.875 meters

Question 26.

Leslie and Paul both solve the multiplication problem 5.5 x 4.6. Leslie says the answer is 25.30. Paul says the answer is 25.3. Whose answer is correct? Explain your reasoning.

Type below:

_________

Answer:

Both answers are correct. Because 25.30 = 25.3. The zeros have no value after the decimal point of a number.

Explanation:

5.5 x 4.6

55 x 46 = 2530

0.1 x 0.1 = 0.01

2530 x 0.01 = 25.30 = 25.3

Question 27.

Test Prep A vine in Mr. Jackson’s garden is 3.6 feet long. When it is measured again, it is 2.1 times as long. How long is the vine?

Options:

a. 5.7 feet

b. 6.6 feet

c. 7.5 feet

d. 7.56 feet

Answer:

a. 5.7 feet

Explanation:

A vine in Mr. Jackson’s garden is 3.6 feet long. When it is measured again, it is 2.1 times as long.

3.6 + 2.1 = 5.7 feet

**Write zeros in the product.**

Question 1.

0.05

× 0.7

———-

Answer:

Explanation:

□35

Think: Hundredths are multiplied by tenths. What should be the place value of the product?

_____

Answer:

0.035

Explanation:

5 x 7 = 35

0.01 x 0.1 = 0.001

35 x 0.001 = 0.035

Question 2.

0.2

× 0.3

———-

_____

Answer:

0.06

Explanation:

2 x 3 = 6

0.1 x 0.1 = 0.01

6 x 0.01 = 0.06

Question 3.

0.02

× 0.2

———-

_____

Answer:

0.004

Explanation:

2 x 2 = 4

0.01 x 0.1 = 0.001

4 x 0.001 = 0.004

**Find the product.**

Question 4.

$0.05

× 0.8

———-

$ _____

Answer:

$0.04

Explanation:

5 x 8 = 40

0.01 x 0.1 = 0.001

40 x 0.001 = 0.040 = 0.04

Question 5.

0.09

× 0.7

———-

_____

Answer:

0.063

Explanation:

9 x 7 = 63

0.01 x 0.1 = 0.001

63 x 0.001 = 0.063

Question 6.

0.2

× 0.1

———-

_____

Answer:

0.02

Explanation:

2 x 1 = 2

0.1 x 0.1 = 0.01

2 x 0.01 = 0.02

**On Your Own**

**Find the product.**

Question 7.

0.3

× 0.3

———-

_____

Answer:

0.09

Explanation:

3 x 3 = 9

0.1 x 0.1 = 0.01

9 x 0.01 = 0.09

Question 8.

0.05

× 0.3

———-

_____

Answer:

0.015

Explanation:

5 x 3 = 15

0.01 x 0.1 = 0.001

15 x 0.001 = 0.015

Question 9.

0.02

× 0.4

———-

_____

Answer:

0.008

Explanation:

2 x 4 = 8

0.01 x 0.1 = 0.001

8 x 0.001 = 0.008

Question 10.

$0.40

× 0.1

———-

$ _____

Answer:

$0.04

Explanation:

40 x 1 = 40

0.10 x 0.1 = 0.010

40 x 0.010 = 0.04

Question 11.

0.09

× 0.2

———-

_____

Answer:

0.018

Explanation:

9 x 2 = 18

0.01 x 0.1 = 0.001

18 x 0.001 = 0.018

Question 12.

$ 0.05

× 0.6

———-

_____

Answer:

$0.3

Explanation:

5 x 6 = 30

0.01 x 0.1 = 0.001

30 x 0.001 = 0.30 = 0.3

Question 13.

0.04

× 0.5

———-

_____

Answer:

0.020

Explanation:

4 x 5 = 20

0.01 x 0.1 = 0.001

20 x 0.001 = 0.020

Question 14.

0.06

× 0.8

———-

_____

Answer:

0.048

Explanation:

6 x 8 = 48

0.01 x 0.1 = 0.001

48 x 0.001 = 0.048

**Algebra Find the value of n.**

Question 15.

0.03 × 0.6 = n

n = _____

Answer:

n = 0.018

Explanation:

0.03 × 0.6 = n

0.018 = n

n = 0.018

Question 16.

n × 0.2 = 0.08

n = _____

Answer:

n = 0.4

Explanation:

n × 0.2 = 0.08

n = 0.08/0.2

n = 0.4

Question 17.

0.09 × n = 0.063

n = _____

Answer:

n = 0.7

Explanation:

0.09 × n = 0.063

n = 0.063/0.09

n = 0.7

Question 18.

On an average day, a garden snail can travel about 0.05 mile. If a snail travels 0.2 times as far as the average distance in a day, how far can it travel?

a. What are you being asked to find?

Type below:

_________

Answer:

We need to find how far snail travels on 0.2 times as far as the average distance in a day?

Question 18.

b. What information will you use to solve the problem?

Type below:

_________

Answer:

On an average day, a garden snail can travel about 0.05 miles.

0.2 times as far as the average distance in a day

Question 18.

c. How will you use multiplication and place value to solve the problem?

Type below:

_________

Answer:

0.2 x 0.05

Question 18.

d. Show how you will solve the problem.

Type below:

_________

Answer:

2 x 5 = 10

0.1 x 0.01 = 0.001

10 x 0.001 = 0.010 = 0.01

Question 18.

e. Fill in the bubble for the correct answer choice above.

Options:

a. 0.7 mile

b. 0.25 mile

c. 0.1 mile

d. 0.01 mile

Answer:

d. 0.01 mile

Question 19.

In a science experiment, Tania uses 0.8 ounce of water to create a reaction. She wants the next reaction to be 0.1 times the size of the previous reaction. How much water should she use?

Options:

a. 0.08 ounce

b. 0.09 ounce

c. 0.8 ounce

d. 0.9 ounce

Answer:

a. 0.08 ounce

Explanation:

In a science experiment, Tania uses 0.8 ounce of water to create a reaction. She wants the next reaction to be 0.1 times the size of the previous reaction.

0.8 x 0.1 = 0.08 ounce

Question 20.

Michael multiplies 0.2 by a number. He records the product as 0.008. What number did Michael use?

Options:

a. 0.016

b. 0.04

c. 0.28

d. 0.4

Answer:

b. 0.04

Explanation:

Michael multiplies 0.2 by a number. He records the product as 0.008.

0.2 x n = 0.008

n = 0.008/0.2

n = 0.04

Michael use 0.04

**Check Concepts**

Question 1.

Explain how estimation helps you to place the decimal point when multiplying 3.9 × 5.3.

Type below:

_________

Answer:

3.9 × 5.3

39 x 53 = 2067

0.1 x 0.1 = 0.01

2067 x 0.01 = 20.67

**Complete the pattern.**

Question 2.

1 × 7.45 = _______

10 × 7.45 = _______

100 × 7.45 = _______

1,000 × 7.45 = _______

Answer:

1 × 7.45 = 7.45

10 × 7.45 = 74.5

100 × 7.45 = 745

1,000 × 7.45 = 7,450

Question 3.

10^{0} × 376.2 = _______

10^{1} × 376.2 = _______

10^{2} × 376.2 = _______

10^{3} × 376.2 = _______

Answer:

10^{0} × 376.2 = 376.2

10^{1} × 376.2 = 3,762

10^{2} × 376.2 = 37,620

10^{3} × 376.2 = 376,200

Explanation:

10^{0} × 376.2 = 1 x 376.2 = 376.2

10^{1} × 376.2 = 10 x 376.2 = 3,762

10^{2} × 376.2 = 100 x 376.2 = 37,620

10^{3} × 376.2 = 1000 x 376.2 = 376,200

Question 4.

1 × 191 = _______

0.1 × 191 = _______

0.01 × 191 = _______

Answer:

1 × 191 = 191

0.1 × 191 = 19.1

0.01 × 191 = 1.91_

**Find the product.**

Question 5.

5 × 0.89 = _____

Answer:

4.45

Explanation:

5 × 0.89

5 x 9 = 45 hundredths; 4 tenths and 5 hundredths

5 x 8 = 40 tenths; 40 + 4 tenths = 44 tenths; 4 ones and 4 tenths

5 x 0 = 0; 0 + 4 = 4 ones

4.45

Question 6.

9 × 2.35 = _____

Answer:

21.15

Explanation:

9 × 2.35

9 x 5 = 45 hundredths; 4 tenths and 5 hundredths

9 x 3 = 27 tenths; 27 + 4 tenths = 31 tenths; 3 ones and 1 tenth

9 x 2 = 18; 18 + 3 = 21 ones

21.15

Question 7.

23 × 8.6 = _____

Answer:

197.8

Explanation:

23 x 8.6

23 x 6 = 138 tenths; 13 ones and 8 tenths

23 x 8 = 184 ones; 184 + 13 = 197 ones

197.8

Question 8.

7.3 × 0.6 = _____

Answer:

4.38

Explanation:

73 x 6 = 438

0.1 x 0.1 = 0.01

438 x 0.01 = 4.38

Question 9.

0.09 × 0.7 = _____

Answer:

0.063

Explanation:

9 x 7 = 63

0.01 x 0.1 = 0.001

63 x 0.001 = 0.063

Question 10.

0.8 × $0.40 = $ _____

Answer:

$0.32

Explanation:

8 x 4 = 32

0.1 x 0.1 = 0.01

32 x 0.01 = 0.32

**Draw a diagram to solve.**

Question 11.

In January, Dawn earns $9.25 allowance. She earns 3 times as much in February. If during March, she earns $5.75 more than she did in February, how much allowance does Dawn earn in March?

$ _________

Answer:

$33.5

Explanation:

In January, Dawn earns $9.25 allowance.

February: 3 x $9.25 = $27.75

March: $27.75 + $5.75 = $33.5

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

Question 12.

Janet hikes a trail at a local forest each day. The trail is 3.6 miles long, and she has hiked 5 days in the past week. How many miles has Janet hiked in the past week?

Options:

A. 18 miles

B. 15.3 miles

C. 11 miles

D. 8.6 miles

Answer:

A. 18 miles

Explanation:

Janet hikes a trail at a local forest each day. The trail is 3.6 miles long, and she has hiked 5 days in the past week.

3.6 x 5 = 18 miles

Question 13.

To earn money for his vacation, Grayson works at a local shop on weekends. His job is to cut bricks of fudge into 0.25 pound squares. If he cuts 36 equal-sized squares on Saturday, how many pounds of fudge has Grayson cut?

Options:

A. 7.25 pounds

B. 9 pounds

C. 90 pounds

D. 72.5 pounds

Answer:

B. 9 pounds

Explanation:

To earn money for his vacation, Grayson works at a local shop on weekends. His job is to cut bricks of fudge into 0.25 pound squares. If he cuts 36 equal-sized squares on Saturday,

0.25 x 36 = 9 pounds

Question 14.

James is making a scale model of his bedroom. The model is 0.6 feet wide. If the actual room is 17.5 times as wide as the model, what is the width of James’s room?

Options:

A. 18.1 feet

B. 17.11 feet

C. 16.9 feet

D. 10.5 feet

Answer:

D. 10.5 feet

Explanation:

James is making a scale model of his bedroom. The model is 0.6 feet wide. If the actual room is 17.5 times as wide as the model,

0.6 x 17.5 = 10.5 feet

Question 15.

The cost of admission to the matinee showing at a movie theater is $6.75. If 7 friends want to see the matinee showing of their favorite movie, how much will it cost?

Options:

A. $11.25

B. $14.75

C. $42.75

D. $47.25

Answer:

D. $47.25

Explanation:

The cost of admission to the matinee showing at a movie theater is $6.75. If 7 friends want to see the matinee showing of their favorite movie,

7 x $6.75 = $47.25

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

Question 16.

On Friday, Gail talks for 38.4 minutes on her cell phone. On Saturday, she uses 5.5 times as many minutes as she did on Friday. How long does Gail talk on her cell phone on Saturday?

Options:

A. 2.112 minutes

B. 21.12 minutes

C. 211.2 minutes

D. 2,112 minutes

Answer:

C. 211.2 minutes

Explanation:

On Friday, Gail talks for 38.4 minutes on her cell phone. On Saturday, she uses 5.5 times as many minutes as she did on Friday.

38.4 x 5.5 = 211.2 minutes

Question 17.

Harry walks to a produce market to buy bananas. If a pound of bananas costs $0.49, how much will Harry pay for 3 pounds of bananas?

Options:

A. $1.47

B. $3.49

C. $5.49

D. $10.47

Answer:

A. $1.47

Explanation:

Harry walks to a produce market to buy bananas. If a pound of bananas costs $0.49,

For 3 pound, 3 x $0.49 = $1.47

Question 18.

At Anne’s Fabric Emporium, a yard of chiffon fabric costs $7.85. Lee plans to purchase 0.8 yard for a craft project. How much money will Lee spend on chiffon fabric?

Options:

A. $0.63

B. $6.28

C. $7.05

D. $8.65

Answer:

B. $6.28

Explanation:

At Anne’s Fabric Emporium, a yard of chiffon fabric costs $7.85. Lee plans to purchase 0.8 yard for a craft project.

0.8 x $7.85 = $6.28

Question 19.

Mitchell has $18.79 in his savings account. Jeremy has 3 times as much as Mitchell. Maritza has $4.57 more than Jeremy. How much money does Maritza have in her savings account?

Options:

A. $13.71

B. $32.50

C. $56.37

D. $60.94

Answer:

D. $60.94

Explanation:

Mitchell: $18.79

Jeremy: 3 x $18.79 = $56.37

Maritza: $56.37 + $4.57 = $60.94

**Constructed Response**

Question 20.

A river otter eats about 0.15 times its weight in food each day. At the Baytown Zoo, the male river otter weighs 5 pounds. About how much food will the otter at the zoo consume each day? Explain how you found your answer.

_____ pounds

Answer:

0.75 pounds

Explanation:

A river otter eats about 0.15 times its weight in food each day. At the Baytown Zoo, the male river otter weighs 5 pounds.

0.15 x 5 = 0.75 pounds

**Performance Task**

Question 21.

The cost of admission to the Baytown Zoo is shown below. Use the table to answer the questions.

A. A family of 2 adults and 1 child plans to spend the day at the Baytown Zoo. How much does admission for the family cost? Explain how you found your answer.

$ _____

Answer:

$39.75

Explanation:

Senior Citizen = $10.50

Adult = $15.75

Child = $8.25

A family of 2 adults and 1 child plans to spend the day at the Baytown Zoo.

(2 x $15.75) + $8.25

$31.5 + $8.25 = $39.75

Question 21.

B. Describe another way you could solve the problem.

Type below:

________

Answer:

(2 x $15.75) + $8.25

$15.75 + $15.75 + $8.25 = $39.75

Question 21.

C. What if 2 more tickets for admission are purchased? If the two additional tickets cost $16.50, determine what type of tickets the family purchases.

Explain how you can determine the answer without calculating.

Options:

a. Senior tickets

b. Adult tickets

c. Child tickets

Answer:

c. Child tickets

Explanation:

if 2 more tickets for admission are purchased? If the two additional tickets cost $16.50,

$39.75 + $16.50 = $56.25

Two additional children’s tickets are purchased. Since senior citizen tickets cost about $10 each, then 2 tickets would cost about $20, which is too much. Adult tickets cost about $16 each, so 2 adult tickets would cost about $32, which is too much. Children’s tickets cost about $8, and 2 tickets would be about $16 which is correct.