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

- Division Patterns with Decimals – Page No. 203
- Division Patterns with Decimals Lesson Check – Page No. 204

**Lesson 2: Investigate • Divide Decimals by Whole Numbers**

- Divide Decimals by Whole Numbers – Page No. 207
- Divide Decimals by Whole Numbers Lesson Check – Page No. 208

**Lesson 3: Estimate Quotients**

**Lesson 4: Division of Decimals by Whole Numbers**

- Division of Decimals by Whole Numbers – Page No. 215
- Division of Decimals by Whole Numbers Lesson Check – Page No. 216

**Mid-Chapter Checkpoint**

**Lesson 5: Investigate • Decimal Divisions**

**Lesson 6: Divide Decimals**

**Lesson 7: Write Zeros in the Dividend**

**Lesson 8: Problem Solving • Decimal Operations**

**Chapter 5 Review/Test**

- Review/Test – Page No. 235
- Review/Test – Page No. 236
- Review/Test – Page No. 237
- Review/Test – Page No. 238

**Complete the pattern.**

Question 1.

456 ÷ 10^{0} = 456

456 ÷ 10^{1} = 45.6

456 ÷ 10^{2} = 4.56

Think: The dividend is being divided by an increasing power of 10, so the decimal point will move to the left one place for each increasing power of 10.

456 ÷ 10^{3} = _____

Answer:

456 ÷ 10^{3} = 0.456

Explanation:

The dividend is being divided by an increasing power of 10, so the decimal point will move to the left one place for each increasing power of 10.

456 ÷ 10^{0} = 456

456 ÷ 10^{1} = 45.6

456 ÷ 10^{2} = 4.56

456 ÷ 10^{3} = 0.456

**Complete the pattern.**

Question 2.

225 ÷ 10^{0} = _____

225 ÷ 10^{1} = _____

225 ÷ 10^{2} = _____

225 ÷ 10^{3} = _____

Answer:

225 ÷ 10^{0} = 225

225 ÷ 10^{1} = 22.5

225 ÷ 10^{2} = 2.25

225 ÷ 10^{3} = 0.25

Explanation:

The dividend is being divided by an increasing power of 10, so the decimal point will move to the left one place for each increasing power of 10.

225 ÷ 10^{0} = 225/1 = 225

225 ÷ 10^{1} = 225/10 = 22.5

225 ÷ 10^{2} = 225/100 = 2.25

225 ÷ 10^{3} = 225/1,000 = 0.25

Question 3.

605 ÷ 10^{0} = _____

605 ÷ 10^{1} = _____

605 ÷ 10^{2} = _____

605 ÷ 10^{3} = _____

Answer:

605 ÷ 10^{0} = 605

605 ÷ 10^{1} = 60.5

605 ÷ 10^{2} = 6.05

605 ÷ 10^{3} = 0.605

Explanation:

The dividend is being divided by an increasing power of 10, so the decimal point will move to the left one place for each increasing power of 10.

605 ÷ 10^{0} = 605/1 = 605

605 ÷ 10^{1} = 605/10 = 60.5

605 ÷ 10^{2} = 605/100 = 6.05

605 ÷ 10^{3} = 605/1,000 = 0.605

Question 4.

74.3 ÷ 1 = _____

74.3 ÷ 10 = _____

74.3 ÷ 100 = _____

Answer:

74.3 ÷ 1 = 74.3

74.3 ÷ 10 = 7.43

74.3 ÷ 100 = 0.743

Explanation:

The dividend is being divided by an increasing power of 10, so the decimal point will move to the left one place for each increasing power of 10.

74.3 ÷ 10^{0} = 74.3 ÷ 1 = 74.3

74.3 ÷ 10^{1} = 74.3 ÷ 10 = 7.43

74.3 ÷ 10^{2} = 74.3 ÷ 100 = 0.743

**On Your Own**

**Complete the pattern.**

Question 5.

156 ÷ 1 = _____

156 ÷ 10 = _____

156 ÷ 100 = _____

156 ÷ 1,000 = _____

Answer:

156 ÷ 1 = 156

156 ÷ 10 = 15.6

156 ÷ 100 = 1.56

156 ÷ 1,000 = 0.156

Explanation:

The dividend is being divided by an increasing power of 10, so the decimal point will move to the left one place for each increasing power of 10.

156 ÷ 1 = 156

156 ÷ 10 = 15.6

156 ÷ 100 = 1.56

156 ÷ 1,000 = 0.156

Question 6.

32 ÷ 1 = _____

32 ÷ 10 = _____

32 ÷ 100 = _____

32 ÷ 1,000 = _____

Answer:

32 ÷ 1 = 32

32 ÷ 10 = 3.2

32 ÷ 100 = 0.32

32 ÷ 1,000 = 0.032

Explanation:

The dividend is being divided by an increasing power of 10, so the decimal point will move to the left one place for each increasing power of 10.

32 ÷ 1 = 32

32 ÷ 10 = 3.2

32 ÷ 100 = 0.32

32 ÷ 1,000 = 0.032

Question 7.

16 ÷ 10^{0} = _____

16 ÷ 10^{1} = _____

16 ÷ 10^{2} = _____

16 ÷ 10^{3} = _____

Answer:

16 ÷ 10^{0} = 16

16 ÷ 10^{1} = 1.6

16 ÷ 10^{2} = 0.16

16 ÷ 10^{3} = 0.016

Explanation:

The dividend is being divided by an increasing power of 10, so the decimal point will move to the left one place for each increasing power of 10.

16 ÷ 10^{0} = 16

16 ÷ 10^{1} = 1.6

16 ÷ 10^{2} = 0.16

16 ÷ 10^{3} = 0.016

Question 8.

12.7 ÷ 1 = _____

12.7 ÷ 10 = _____

12.7 ÷ 100 = _____

12.7 ÷ 1,000 = _____

Answer:

12.7 ÷ 1 = 12.7

12.7 ÷ 10 = 1.27

12.7 ÷ 100 = 0.127

12.7 ÷ 1,000 = 0.0127

Explanation:

The dividend is being divided by an increasing power of 10, so the decimal point will move to the left one place for each increasing power of 10.

12.7 ÷ 1 = 12.7

12.7 ÷ 10 = 1.27

12.7 ÷ 100 = 0.127

12.7 ÷ 1,000 = 0.0127

Question 9.

92.5 ÷ 10^{0} = _____

92.5 ÷ 10^{1} = _____

92.5 ÷ 10^{2} = _____

92.5 ÷ 10^{3} = _____

Answer:

92.5 ÷ 10^{0} = 92.5

92.5 ÷ 10^{1} = 9.25

92.5 ÷ 10^{2} = 0.925

92.5 ÷ 10^{3} = 0.0925

Explanation:

The dividend is being divided by an increasing power of 10, so the decimal point will move to the left one place for each increasing power of 10.

92.5 ÷ 10^{0} = 92.5

92.5 ÷ 10^{1} = 9.25

92.5 ÷ 10^{2} = 0.925

92.5 ÷ 10^{3} = 0.0925

Question 10.

86.3 ÷ 10^{0} = _____

86.3 ÷ 10^{1} = _____

86.3 ÷ 10^{2} = _____

86.3 ÷ 10^{3} = _____

Answer:

86.3 ÷ 10^{0} = 86.3

86.3 ÷ 10^{1} = 8.63

86.3 ÷ 10^{2} = 0.863

86.3 ÷ 10^{3} = 0.0863

Explanation:

The dividend is being divided by an increasing power of 10, so the decimal point will move to the left one place for each increasing power of 10.

86.3 ÷ 10^{0} = 86.3

86.3 ÷ 10^{1} = 8.63

86.3 ÷ 10^{2} = 0.863

86.3 ÷ 10^{3} = 0.0863

**Algebra Find the value of n.**

Question 11.

268 ÷ n = 0.268

n = _____

Answer:

n = 1000

Explanation:

268 ÷ n = 0.268

268 = n x 0.268

n = 268 ÷ 0.268

n = 1000

Question 12.

n ÷ 10^{2} = 0.123

n = _____

Answer:

n = 12.3

Explanation:

n ÷ 10^{2} = 0.123

n = 0.123 x 10^{2}

n = 0.123 x 100

n = 12.3

Question 13.

n ÷ 10^{1} = 4.6

n = _____

Answer:

n = 46

Explanation:

n ÷ 10^{1} = 4.6

n = 4.6 x 10^{1}

n = 4.6 x 10

n = 46

**Use the table to solve 14–16.**

Question 14.

If each muffin contains the same amount of cornmeal, how many kilograms of cornmeal are in each corn muffin?

_____ kilograms

Answer:

0.15 kilograms

Explanation:

There are 1,000 muffins. Cornmeal = 150 Kg

If each muffin contains the same amount of cornmeal, 150 ÷ 1000 = 0.15

0.15 kilograms of cornmeal is in each corn muffin

Question 15.

If each muffin contains the same amount of sugar, how many kilograms of sugar, to the nearest thousandth, are in each corn muffin?

_____ kilograms

Answer:

0.07 kilograms

Explanation:

There are 1,000 muffins. Sugar = 66.7 kilograms

If each muffin contains the same amount of sugar, 66.7 ÷ 1000 = 0.0667.

0.0667 kilograms of sugar is in each corn muffin.

The thousandth digit is 6. 6 > 5

So, 0.07

Question 16.

The bakery decides to make only 100 corn muffins on Tuesday. How many kilograms of sugar will be needed?

_____ kilograms

Answer:

0.007 kilograms

Explanation:

The bakery decides to make only 100 corn muffins on Tuesday.

As 0.07 kilograms required for 1,000 muffins,

for 100 muffins, (100 x 0.07) ÷ 1000 = 0.007

Question 17.

Explain how you know that the quotient 47.3 ÷ 10^{1} is equal to the product 47.3 × 0.1.

Type below:

_________

Answer:

Quotient 47.3 ÷ 10^{1} = 47.3 ÷ 10 = 4.73. The power of 10^{1} = 10.

47.3 × 0.1 = 4.73.

By dividing 10 to a number is equal to the multiplying 0.1 to that number.

Question 18.

Test Prep Ella used 37.2 pounds of apples to make applesauce. She used one-tenth as many pounds of sugar as pounds of apples. How many pounds of sugar did Ella use?

Options:

a. 372 pounds

b. 3.72 pounds

c. 0.372 pound

d. 0.0372 pound

Answer:

b. 3.72 pounds

Explanation:

Ella used 37.2 pounds of apples to make applesauce. She used one-tenth as many pounds of sugar as pounds of apples.

37.2 ÷ 10 = 3.72 pounds

**Use the model to complete the number sentence.**

Question 1.

1.6 ÷ 4 =

_____

Answer:

1.6 ÷ 4 = 0.4

Explanation:

1.6 ÷ 4

Share your model among 4 equal groups.

Since 1 whole cannot be shared among 4 groups without regrouping, cut your model apart to show the tenths.

1 ones = 10 tenths

10 + 6 = 16 tenths

There are 16 tenths in 1.6.

Share the tenths equally among the 4 groups.

There are 0 ones and 16 tenths in each group.

Decimal for the amount in each group = 0.4

1.6 ÷ 4 = 0.4

Question 2.

3.42 ÷ 3 =

_____

Answer:

3.42 ÷ 3 = 1.14

Explanation:

3.42 ÷ 3

Share your model among 3 equal groups.

1 whole in each group. So, 3 wholes shared equally in 3 groups. 1 ones

**3 ÷ 3 = 1 ones**

3 tenths shared equally in 3 groups. 1 tenth has remained. 1 tenth

**3 ÷ 3 = 1 tenths**

1 tenth = 10 hundredths.

10 + 2 = 12 hundredths.

Share 12 hundredths equally among the 3 groups.

**12 hundredths ÷ 3 = 4 hundredths.**

Decimal for the amount in each group = 1.14

3.42 ÷ 3 = 1.14

**Divide. Use base-ten blocks.**

Question 3.

1.8 ÷ 3 = _____

Answer:

1.8 ÷ 3 = 0.6

Explanation:

1.8 ÷ 3

Share your model among 3 equal groups.

Since 1 whole cannot be shared among 3 groups without regrouping, cut your model apart to show the tenths. **0 ones**

1 ones = 10 tenths

10 + 8 = 18 tenths

There are 18 tenths in 1.8.

Share the 18 tenths equally among the 3 groups.

**18 ÷ 3 = 6**

There are 0 ones and 18 tenths in each group.

Decimal for the amount in each group = 0.6

1.8 ÷ 3 = 0.6

Question 4.

3.6 ÷ 4 = _____

Answer:

3.6 ÷ 4 = 0.9

Explanation:

3.6 ÷ 4

Share your model among 4 equal groups.

Since 3 whole cannot be shared among 4 groups without regrouping, cut your model apart to show the tenths. **0 ones**

1 ones = 10 tenths

30 + 6 = 36 tenths

There are 36 tenths in 3.6.

Share the 36 tenths equally among the 4 groups.

There are 0 ones and 36 tenths in each group.

**36 ÷ 4 = 9**

Decimal for the amount in each group = 0.9

3.6 ÷ 4 = 0.9

Question 5.

2.5 ÷ 5 = _____

Answer:

2.5 ÷ 5 = 0.5

Explanation:

2.5 ÷ 5

Share your model among 5 equal groups.

Since 2 whole cannot be shared among 5 groups without regrouping, cut your model apart to show the tenths. **0 ones**

1 ones = 10 tenths

20 + 5 = 25 tenths

There are 25 tenths in 2.5.

Share the 25 tenths equally among the 5 groups.

There are 0 ones and 25 tenths in each group.

**25 ÷ 5 = 5**

Decimal for the amount in each group = 0.5

2.5 ÷ 5 = 0.5

Question 6.

2.4 ÷ 8 = _____

Answer:

2.4 ÷ 8 = 0.3

Explanation:

2.4 ÷ 8

Share your model among 8 equal groups.

Since 2 whole cannot be shared among 8 groups without regrouping, cut your model apart to show the tenths. **0 ones**

1 ones = 10 tenths

20 + 4 = 24 tenths

There are 24 tenths in 2.4.

Share the 24 tenths equally among the 8 groups.

There are 0 ones and 24 tenths in each group.

**24 ÷ 8 = 3**

Decimal for the amount in each group = 0.3

2.4 ÷ 8 = 0.3

Question 7.

3.78 ÷ 3 = _____

Answer:

3.78 ÷ 3 = 1.26

Explanation:

3.78 ÷ 3

Share your model among 3 equal groups.

1 whole in each group. So, 3 wholes shared equally in 3 groups.

**3 ÷ 3 = 1 ones**

6 tenths shared equally in 3 groups. 1 tenth has remained.

**6 ÷ 3 = 2 tenths**

1 tenth = 10 hundredths.

10 + 8 = 18 hundredths.

Share 18 hundredths equally among the 3 groups.

**18 hundredths ÷ 3 = 6 hundredths.**

Decimal for the amount in each group = 1.26

3.78 ÷ 3 = 1.26

Question 8.

1.33 ÷ 7 = _____

Answer:

1.33 ÷ 7 = 0.19

Explanation:

1.33 ÷ 7

Share your model among 7 equal groups.

Since 1 whole cannot be shared among 7 groups without regrouping, cut your model apart to show the tenths. **0 ones**

1 ones = 10 tenths

10 + 3 = 13 tenths

There are 13 tenths in 1.3.

Share the 13 tenths equally among the 7 groups.

Share 7 tenths equally among the 3 groups. 6 tenths remained.

**7 ÷ 7 = 1 tenths**

Since 6 tenths cannot be shared among 7 groups without regrouping, cut your model apart to show the tenths.

1 tenths = 10 hundredths

60 + 3 = 63 hundredths

Share 63 hundredths equally among the 7 groups.

**63 ÷ 7 = 9 hundredths**

Decimal for the amount in each group = 0.19

1.33 ÷ 7 = 0.19

Question 9.

4.72 ÷ 4 = _____

Answer:

4.72 ÷ 4 = 1.18

Explanation:

4.72 ÷ 4

Share your model among 4 equal groups.

1 whole in each group. So, 4 wholes shared equally in 4 groups. 1 ones

**4 ÷ 4 = 1 ones**

4 tenths shared equally in 4 groups. 3 tenths have remained.

**4 ÷ 4 = 1 tenths**

1 tenth = 10 hundredths.

30 + 2 = 32 hundredths.

Share 32 hundredths equally among the 4 groups.

**32 hundredths ÷ 4 = 8 hundredths.**

Decimal for the amount in each group = 1.18

4.72 ÷ 4 = 1.18

Question 10.

2.52 ÷ 9 = _____

Answer:

2.52 ÷ 9 = 0.28

Explanation:

2.52 ÷ 9

Share your model among 9 equal groups.

Since 2 whole cannot be shared among 9 groups without regrouping, cut your model apart to show the tenths.

**9 ÷ 9 = 1 ones**

1 ones = 10 tenths

20 + 5 = 25 tenths

There are 25 tenths in 2.5.

Share the 18 tenths equally among the 9 groups. 7 tenths remained.

**18 ÷ 9 = 2 tenths**

1 tenth = 10 hundredths.

70 + 2 hundredths = 72 hundredths

Share the 72 hundredths equally among the 9 groups.

**72 ÷ 9 = 8**

Decimal for the amount in each group = 0.28

2.52 ÷ 9 = 0.28

Question 11.

6.25 ÷ 5 = _____

Answer:

6.25 ÷ 5 = 1.25

Explanation:

6.25 ÷ 5

Share your model among 5 equal groups.

1 whole in each group. So, 5 wholes shared equally in 5 groups. 1 whole remained.

**5 ÷ 5 = 1 ones **

1 ones = 10 tenths

10 + 2 = 12 tenths

10 tenths shared equally in 5 groups. 2 tenths have remained.

**10 ÷ 5 = 2 tenths**

1 tenth = 10 hundredths.

20 + 5 = 25 hundredths.

Share 25 hundredths equally among the 5 groups.

**25 hundredths ÷ 5 = 5 hundredths.**

Decimal for the amount in each group = 1.25

6.25 ÷ 5 = 1.25

**What’s the Error?**

Question 12.

Aida is making banners from a roll of paper that is 4.05 meters long. She will cut the paper into 3 equal lengths. How long will each banner be?

Look how Aida solved the problem. Solve the problem and correct

Find the error. the error.

So, Aida said that each banner would be _________ meters long, but each banner should be _________ meters long.

Type below:

_________

Answer:

So, Aida said that each banner would be 4.05 meters long, but each banner should be 1.35 meters long.

So, 1 ones, 3 tenths, and 5 hundredths are shared among 3 groups.

But Aida draws only one whole and 5 hundredths among 3 groups.

Explanation:

Aida is making banners from a roll of paper that is 4.05 meters long. She will cut the paper into 3 equal lengths.

4.05 ÷ 3

Share your model among 3 equal groups.

1 whole in each group. So, 3 wholes shared equally in 5 groups. 1 whole remained.

**3 ÷ 3 = 1 ones **

1 ones = 10 tenths

10 + 0 = 10 tenths

9 tenths shared equally in 3 groups. 1 tenth remained.

**9 ÷ 3 = 3 tenths**

1 tenth = 10 hundredths.

10 + 5 = 15 hundredths.

Share 6 hundredths equally among the 3 groups.

**15 hundredths ÷ 3 = 5 hundredths.**

Decimal for the amount in each group = 1.35

4.05 ÷ 3 = 1.35

Question 12.

• Describe Aida’s error.

Type below:

_________

Answer:

So, Aida said that each banner would be 4.05 meters long, but each banner should be 1.35 meters long.

So, 1 ones, 3 tenths, and 5 hundredths are shared among 3 groups.

But Aida draws only one whole and 5 hundredths among 3 groups.

Question 12.

• What if the roll of paper were 4.35 meters long? How long would each banner be?

Type below:

_________

Answer:

1.45 meters long

Explanation:

If the roll paper were 4.35 meters long,

4.35 ÷ 3

Share your model among 3 equal groups.

1 whole in each group. So, 3 wholes shared equally in 5 groups. 1 whole remained.

**3 ÷ 3 = 1 ones **

1 ones = 10 tenths

10 + 3 = 13 tenths

12 tenths shared equally in 3 groups. 1 tenth remained.

**12 ÷ 3 = 4 tenths**

1 tenth = 10 hundredths.

10 + 5 = 15 hundredths.

Share 6 hundredths equally among the 3 groups.

**15 hundredths ÷ 3 = 5 hundredths.**

Decimal for the amount in each group = 1.45

4.35 ÷ 3 = 1.45

**Use compatible numbers to estimate the quotient.**

Question 1.

28.8 ÷ 9

Type below:

_________

Answer:

About to 3

Explanation:

28.8 is closer to 30

9 is closer to 10

30 ÷ 10 = 3

Question 2.

393.5 ÷ 41

_____ ÷ _____ = _____

Answer:

400 ÷ 40 = 10

Explanation:

Use a whole number greater than the dividend.

393.5 is closer to 400

41 is closer to 40

400 ÷ 40 = 10

Use a whole number less than the dividend.

393.5 is closer to 360

41 is closer to 40

360 ÷ 40 = 9

The quotient should be between 9 and 10.

393.5 is closer to 400.

So, the answer is about 10

**Estimate the quotient.**

Question 3.

161.7 ÷ 7

_____

Answer:

About 23

Explanation:

161.7 is closer to 161

161 ÷ 7 = 23

Question 4.

17.9 ÷ 9

_____

Answer:

About 2

Explanation:

17.9 is closer to 18

18 ÷ 9 = 2

Question 5.

145.4 ÷ 21

_____

Answer:

about 7

Explanation:

Use a whole number greater than the dividend.

145.4 is closer to 160

21 is closer to 20

160 ÷ 20 = 8

Use a whole number less than the dividend.

145.4 is closer to 140

21 is closer to 20

140 ÷ 20 = 7

The quotient should be between 7 and 8.

145.4 is closer to 140.

So, the answer is about 7

**On Your Own**

**Estimate the quotient.**

Question 6.

15.5 ÷ 4

_____

Answer:

About 4

Explanation:

15.5 is closer to 16

16 ÷ 4 = 4

Question 7.

394.8 ÷ 7

_____

Answer:

About 60

Explanation:

394.8 is closer to 420

420 ÷ 7 = 60

About 60

Question 8.

410.5 ÷ 18

_____

Answer:

About 22

Explanation:

410.5 is closer to 396

396 ÷ 18 = 22

Question 9.

72.1 ÷ 7

_____

Answer:

About 10

Explanation:

72.1 is closer to 70

70 ÷ 7 = 10

Question 10.

32.4 ÷ 52

_____

Answer:

About 1

Explanation:

32.4 is closer to 52

52 ÷ 52 = 1

Question 11.

$134.42 ÷ 28

$ _____

Answer:

about 4

Explanation:

Use a whole number greater than the dividend.

$134.42 is closer to 150

28 is closer to 30

150 ÷ 30 = 5

Use a whole number less than the dividend.

$134.42 is closer to 120

28 is closer to 30

120 ÷ 30 = 4

The quotient should be between 4 and 5.

$134.42 is closer to $120.

So, the answer is about 4

Question 12.

21.8 ÷ 4

_____

Answer:

About 5

Explanation:

21.8 is closer to 20

20 ÷ 4 = 5

Question 13.

3.4 ÷ 5

_____

Answer:

About 1

Explanation:

3.4 is closer to 5

5 ÷ 5 = 1

About 1

Question 14.

$759.92 ÷ 42

$ _____

Answer:

About $18

Explanation:

$759.92 is closer to $756

$756 ÷ 42 = 18

About 18

Question 15.

157.5 ÷ 38

_____

Answer:

About 4

Explanation:

157.5 is closer to 152

152 ÷ 38 = 4

Question 16.

379.2 ÷ 6

_____

Answer:

About 63

Explanation:

379.2 is closer to 378

378 ÷ 6 = 63

Question 17.

108.4 ÷ 21

_____

Answer:

About 5

Explanation:

108.4 is closer to 100

21 is closer to 20

100 ÷ 20 = 5

**Use the table to solve 18–20.**

Question 18.

Estimate the average daily snowfall for Alaska’s greatest 7-day snowfall.

_____ inches

Answer:

26 inches

Explanation:

Alaska = 186.9 inches snowfall for 7 days.

For 1 day, 186.9 ÷ 7

186.9 is closer to 182

1825 ÷ 7 = 26 inches

Question 19.

How does the estimate of the average daily snowfall for Wyoming’s greatest 7-day snowfall compare to the estimate of the average daily snowfall for South Dakota’s greatest 7-day snowfall?

Type below:

_________

Answer:

South Dakota’s snowfall is greater than Wyoming’s snowfall.

Explanation:

Wyoming’s = 84.5 inches snowfall for 7 days.

For 1 day, 84.5 ÷ 7

84.5 is closer to 84

84 ÷ 7 = 12 inches

South Dakota’s = 112.7 inches snowfall for 7 days.

For 1 day, 112.7 ÷ 7

112.7 is closer to 112

112 ÷ 7 = 16 inches

Question 20.

The greatest monthly snowfall total in Alaska is 297.9 inches. This happened in February, 1953. Compare the daily average snowfall for February, 1953, with the average daily snowfall for Alaska’s greatest 7-day snowfall. Use estimation.

Type below:

_________

Answer:

The average snowfall of Alaska in February, 1953 is greater than snowfall for Alaska’s greatest 7-day snowfall.

Explanation:

Alaska = 186.9 inches snowfall for 7 days.

For 1 day, 186.9 ÷ 7

186.9 is closer to 182

1825 ÷ 7 = 26 inches

Alaska = 297.9 inches snowfall for 7 days.

For 1 day, 297.9 ÷ 7

297.9 is closer to 294

294 ÷ 7 = 42 inches

Question 21.

What’s the Error? During a 3-hour storm, it snowed 2.5 inches. Jacob said that it snowed an average of about 8 inches per hour.

Type below:

_________

Answer:

During a 3-hour storm, it snowed 2.5 inches.

For 1 hour, 2.5 ÷ 3 = 0.833

Jacob said that it snowed an average of about 8 inches per hour. He missed the remained inches.

Question 22.

Test Prep A plant grew 23.8 inches over 8 weeks. Which is the best estimate of the average number of inches the plant grew each week?

Options:

a. 0.2 inch

b. 0.3 inch

c. 2 inch

d. 3 inch

Answer:

d. 3 inch

Explanation:

A plant grew 23.8 inches over 8 weeks.

23.8 is closer to 24

24 ÷ 8 = 3 inch

**Write the quotient with the decimal point placed correctly.**

Question 1.

4.92 ÷ 2 = 246

_____

Answer:

2.46

Explanation:

Divide. 4 ones ÷ 2

Multiply. 2 × 2 ones = 4 ones. Subtract. 4 ones − 4 ones = 0

Check. 4 ones shared among 2 groups as 2 wholes.

Divide. 9 tenths ÷ 2

Multiply. 2 × 4 tenths = 8 tenths. Subtract. 9 tenths − 8 tenths = 1 tenths

Check. 8 tenths shared among 2 groups as 4 tenths. 1 tenth remained.

1 tenth = 10 hundredths.

10 + 2 = 12 hundredths

Divide. 12 hundredths ÷ 2

Multiply. 2 × 6 hundredths = 12 hundredths. Subtract. 12 hundredths − 12 hundredths = 0 hundredths

Check. 12 hundredths shared among 2 groups as 6 hundredths.

So, 2.46

Question 2.

50.16 ÷ 38 = 132

_____

Answer:

1.32

Explanation:

Divide. 50 ones ÷ 38

Multiply. 38 × 1 ones = 38 ones. Subtract. 50 ones − 38 ones = 12 ones

Check. 38 ones shared among 38 groups as 1 whole.

12 one(s) cannot be shared among 38 groups without regrouping.

120 + 1 = 121 tenths

Divide. 121 tenths ÷ 38

Multiply. 38 x 3 tenths = 114 tenths. Subtract. 121 tenths − 114 tenths = 7 tenths

Check. 114 tenths shared among 38 groups as 3 tenths. 7 tenths remained.

1 tenth = 10 hundredths.

70 + 6 = 76 hundredths

Divide. 76 hundredths ÷ 38

Multiply. 38 x 2 hundredths = 76 hundredths. Subtract. 76 hundredths − 76 hundredths = 0 hundredths

Check. 76 hundredths shared among 38 groups as 2 hundredths.

So, 1.32

**Divide.**

Question 3.

5)\(\overline { 8.65 }\)

_____

Answer:

1.73

Explanation:

8.65 ÷ 5

Divide. 8 ones ÷ 5

Multiply. 5 × 1 ones = 5ones. Subtract. 8 ones − 5 ones = 3 ones

Check. 5 ones shared among 5 groups as 1 whole.

3 one(s) cannot be shared among 5 groups without regrouping.

30 + 6 = 36 tenths

Divide. 36 tenths ÷ 5

Multiply. 5 x 7 tenths = 35 tenths. Subtract. 36 tenths − 35 tenths = 7 tenths

Check. 35 tenths shared among 5 groups as 7 tenths.

1 tenths(s) cannot be shared among 5 groups without regrouping.

1 tenth = 10 hundredths.

10 + 5 = 15 hundredths

Divide. 15 hundredths ÷ 5

Multiply. 5 x 3 hundredths = 15 hundredths. Subtract. 15 hundredths − 15 hundredths = 0 hundredths

Check. 15 hundredths shared among 5 groups as 3 hundredths.

So, 1.73

Question 4.

3)\(\overline { 2.52 }\)

_____

Answer:

0.84

Explanation:

2.52 ÷ 3

2 one(s) cannot be shared among 3 groups without regrouping.

20 + 5 = 25 tenths

Divide. 25 tenths ÷ 3

Multiply. 3 x 8 tenths = 24 tenths. Subtract. 25 tenths − 24 tenths = 1 tenths

Check. 24 tenths shared among 3 groups as 8 tenths.

1 tenths(s) cannot be shared among 3 groups without regrouping.

1 tenth = 10 hundredths.

10 + 2 = 12 hundredths

Divide. 12 hundredths ÷ 3

Multiply. 3 x 4 hundredths = 12 hundredths. Subtract. 12 hundredths − 12 hundredths = 0 hundredths

Check. 12 hundredths shared among 3 groups as 4 hundredths.

So, 0.84

Question 5.

27)\(\overline { 97.2 }\)

_____

Answer:

3.6

Explanation:

97.2 ÷ 27

Divide. 97 ones ÷ 27

Multiply. 27 x 3 ones = 81 ones. Subtract. 97 ones − 81 ones = 16 ones

Check. 81 ones shared among 27 groups as 3 whole.

16 one(s) cannot be shared among 27 groups without regrouping.

160 + 2 = 162 tenths

Divide. 162 tenths ÷ 27

Multiply. 27 x 6 tenths = 162 tenths. Subtract. 162 tenths − 162 tenths = 0 tenths

Check. 162 tenths shared among 27 groups as 6 tenths.

So, 3.6

**On Your Own**

**Divide.**

Question 6.

6)\(\overline { 8.94 }\)

_____

Answer:

1.49

Explanation:

8.94 ÷ 6

Divide. 8 ones ÷ 6

Multiply. 6 × 1 ones = 6 ones. Subtract. 8 ones − 6 ones = 2 ones

Check. 6 ones shared among 6 groups as 1 whole.

2 one(s) cannot be shared among 6 groups without regrouping.

20 + 9 = 29 tenths

Divide. 29 tenths ÷ 6

Multiply. 6 x 4 tenths = 24 tenths. Subtract. 29 tenths − 24 tenths = 5 tenths

Check. 24 tenths shared among 6 groups as 4 tenths.

5 tenths(s) cannot be shared among 6 groups without regrouping.

1 tenth = 10 hundredths.

50 + 4 = 54 hundredths

Divide. 54 hundredths ÷ 6

Multiply. 6 x 9 hundredths = 54 hundredths. Subtract. 54 hundredths − 54 hundredths = 0 hundredths

Check. 54 hundredths shared among 6 groups as 54 hundredths.

So, 1.49

Question 7.

5)\(\overline { 3.75 }\)

_____

Answer:

0.75

Explanation:

3.75 ÷ 5

3 one(s) cannot be shared among 5 groups without regrouping.

30 + 7 = 37 tenths

Divide. 37 tenths ÷ 5

Multiply. 5 x 7 tenths = 35 tenths. Subtract. 37 tenths − 35 tenths = 2 tenths

Check. 35 tenths shared among 5 groups as 7 tenths.

2 tenths(s) cannot be shared among 5 groups without regrouping.

1 tenth = 10 hundredths.

20 + 5 = 25 hundredths

Divide. 25 hundredths ÷ 5

Multiply. 5 x 5 hundredths = 25 hundredths. Subtract. 25 hundredths − 25 hundredths = 0 hundredths

Check. 25 hundredths shared among 5 groups as 25 hundredths.

So, 0.75

Question 8.

19)\(\overline { 55.1 }\)

_____

Answer:

2.9

Explanation:

55.1 ÷ 19

Divide. 55 ones ÷ 19

Multiply. 19 × 2 ones = 38 ones. Subtract. 55 ones − 38 ones = 17 ones

Check. 38 ones shared among 19 groups as 2 whole.

17 one(s) cannot be shared among 19 groups without regrouping.

170 + 1 = 171 tenths

Divide. 171 tenths ÷ 19

Multiply. 19 x 9 tenths = 171 tenths. Subtract. 171 tenths − 171 tenths = 0 tenths

Check. 171 tenths shared among 19 groups as 9 tenths.

So, 2.9

Question 9.

23)\(\overline { 52.9 }\)

_____

Answer:

2.3

Explanation:

52.9 ÷ 23

Divide. 52 ones ÷ 23

Multiply. 23 × 2 ones = 46 ones. Subtract. 52 ones − 46 ones = 6 ones

Check. 46 ones shared among 23 groups as 2 whole.

6 one(s) cannot be shared among 23 groups without regrouping.

60 + 9 = 69 tenths

Divide. 69 tenths ÷ 23

Multiply. 23 x 3 tenths = 69 tenths. Subtract. 69 tenths − 69 tenths = 0 tenths

Check. 69 tenths shared among 23 groups as 3 tenths.

So, 2.3

Question 10.

8)\(\overline { $8.24 }\)

$ _____

Answer:

Explanation:

8.24 ÷ 8

Divide. 8 ones ÷ 8

Multiply. 8 × 1 ones = 8 ones. Subtract. 8 ones − 8 ones = 0 ones

Check. 8 ones shared among 8 groups as 1 whole.

2 tenths(s) cannot be shared among 8 groups without regrouping.

1 tenth = 10 hundredths.

20 + 4 = 24 hundredths

Divide. 24 hundredths ÷ 8

Multiply. 8 x 3 hundredths = 24 hundredths. Subtract. 24 hundredths − 24 hundredths = 0 hundredths

Check. 24 hundredths shared among 8 groups as 3 hundredths.

So, 1.03

Question 11.

5)\(\overline { 44.5 }\)

_____

Answer:

Explanation:

44.5 ÷ 5

Divide. 44 ones ÷ 5

Multiply. 5 x 8 ones = 40 ones. Subtract. 44 ones − 40 ones = 4 ones

Check. 40 ones shared among 5 groups as 8 wholes.

4 one(s) cannot be shared among 5 groups without regrouping.

40 + 5 = 45 tenths

Divide. 45 tenths ÷ 5

Multiply. 5 x 9 tenths = 45 tenths. Subtract. 45 tenths − 45 tenths = 0 tenths

Check. 45 tenths shared among 5 groups as 9 tenths.

So, 8.9

**Practice: Copy and Solve Divide.**

Question 12.

3)\(\overline { $7.71 }\)

$_____

Answer:

2.57

Explanation:

7.71 ÷ 3

Divide. 7 ones ÷ 3

Multiply. 3 x 2 ones = 6 ones. Subtract. 7 ones − 6 ones = 1 ones

Check. 6 ones shared among 3 groups as 2 wholes.

1 one(s) cannot be shared among 3 groups without regrouping.

10 + 7 = 17 tenths

Divide. 17 tenths ÷ 3

Multiply. 3 x 5 tenths = 15 tenths. Subtract. 17 tenths − 15 tenths = 2 tenths

Check. 15 tenths shared among 3 groups as 5 tenths.

2 tenths(s) cannot be shared among 3 groups without regrouping.

1 tenth = 10 hundredths.

20 + 1 = 21 hundredths

Divide. 21 hundredths ÷ 3

Multiply. 3 x 7 hundredths = 21 hundredths. Subtract. 21 hundredths − 21 hundredths = 0 hundredths

Check. 21 hundredths shared among 3 groups as 7 hundredths.

So, 2.57

Question 13.

14)\(\overline { 79.8 }\)

_____

Answer:

5.7

Explanation:

79.8 ÷ 14

Divide. 79 ones ÷ 14

Multiply. 14 x 5 ones = 70 ones. Subtract. 79 ones − 70 ones = 9 ones

Check. 70 ones shared among 14 groups as 5 wholes.

9 one(s) cannot be shared among 14 groups without regrouping.

90 + 8 = 98 tenths

Divide. 98 tenths ÷ 14

Multiply. 14 x 7 tenths = 98 tenths. Subtract. 98 tenths − 98 tenths = 0 tenths

Check. 98 tenths shared among 14 groups as 7 tenths.

So, 5.7

Question 14.

33)\(\overline { 25.41 }\)

_____

Answer:

0.77

Explanation:

25.41 ÷ 33

Divide. 25 ones ÷ 33

25 one(s) cannot be shared among 33 groups without regrouping.

250 + 4 = 254 tenths

Divide. 254 tenths ÷ 33

Multiply. 33 x 7 tenths = 231 tenths. Subtract. 254 tenths − 231 tenths = 23 tenths

Check. 231 tenths shared among 33 groups as 7 tenths.

23 tenths(s) cannot be shared among 33 groups without regrouping.

1 tenth = 10 hundredths.

230 + 1 = 231 hundredths

Divide. 231 hundredths ÷ 33

Multiply. 33 x 7 hundredths= 231 hundredths. Subtract. 231 hundredths− 231 hundredths = 0 hundredths

Check. 231 tenths shared among 33 groups as 7 tenths.

So, 0.77

Question 15.

7)\(\overline { 15.61 }\)

_____

Answer:

2.23

Explanation:

15.61 ÷ 7

Divide. 15 ones ÷ 7

Multiply. 7 x 2 ones = 14 ones. Subtract. 15 ones − 14 ones = 1 ones

Check. 14 ones shared among 7 groups as 2 wholes.

1 one(s) cannot be shared among 7 groups without regrouping.

10 + 6 = 16 tenths

Divide. 16 tenths ÷ 7

Multiply. 7 x 2 tenths = 14 tenths. Subtract. 16 tenths − 14 tenths = 2 tenths

Check. 14 tenths shared among 7 groups as 2 tenths.

2 tenths(s) cannot be shared among 7 groups without regrouping.

1 tenth = 10 hundredths.

20 + 1 = 21 hundredths

Divide. 21 hundredths ÷ 7

Multiply. 7 x 3 hundredths = 21 hundredths. Subtract. 21 hundredths − 21 hundredths = 0 hundredths

Check. 21 hundredths shared among 7 groups as 3 hundredths.

So, 2.23

Question 16.

14)\(\overline { 137.2 }\)

_____

Answer:

9.8

Explanation:

137.2 ÷ 14

Divide. 137 ones ÷ 14

Multiply. 14 x 9 ones = 126 ones. Subtract. 137 ones − 126 ones = 11 ones

Check. 126 ones shared among 14 groups as 9 wholes.

11 one(s) cannot be shared among 14 groups without regrouping.

110 + 2 = 112 tenths

Divide. 112 tenths ÷ 14

Multiply. 14 x 8 tenths = 112 tenths. Subtract. 112 tenths − 112 tenths = 0 tenths

Check. 112 tenths shared among 14 groups as 8 tenths.

So, 9.8

Question 17.

34)\(\overline { 523.6 }\)

_____

Answer:

15.4

Explanation:

523.6 ÷ 34

Divide. 523 ones ÷ 34

Multiply. 34 x 15 ones = 510 ones. Subtract. 523 ones − 510 ones = 13 ones

Check. 510 ones shared among 34 groups as 15 wholes.

13 one(s) cannot be shared among 34 groups without regrouping.

130 + 6 = 136 tenths

Divide. 136 tenths ÷ 34

Multiply. 34 x 4 tenths = 136 tenths. Subtract. 136 tenths − 136 tenths = 0 tenths

Check. 136 tenths shared among 34 groups as 4 tenths.

So, 15.4

**Algebra Write the unknown number for each ■.**

Question 18.

■ ÷ 5 = 1.21

■ = _____

Answer:

6.05

Explanation:

■ ÷ 5 = 1.21

■ = 1.21 x 5

■ = 6.05

Question 19.

46.8 ÷ 1.2 = ■

■ = _____

Answer:

39

Explanation:

46.8 ÷ 1.2 = ■

39 = ■

Question 20.

34.1 ÷ ■ = 22

■ = _____

Answer:

1.55

Explanation:

34.1 ÷ ■ = 22

■ = 34.1 ÷ 22

■ = 1.55

Question 21.

The standard width of 8 lanes in swimming pools used for competitions is 21.92 meters. The standard width of 9 lanes is 21.96 meters. How much wider is each lane when there are 8 lanes than when there are 9 lanes?

a. What are you asked to find?

Type below:

_________

Answer:

We have to find how much wider is each line When there are 8 lanes than when there are 9 lanes.

Question 21.

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

Type below:

_________

Answer:

Division

Subtraction

Question 21.

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

Type below:

_________

Answer:

21.92 ÷ 8 = 2.74 meters

21.96 ÷ 9 = 2.44 meters

2.74 – 2.44 = 0.30 meters

Question 21.

d. Complete the sentences.

Each lane is ______ meters wide when there are 8 lanes.

Each lane is ______ meters wide when there are 9 lanes.

Since ______ – ______ = ______ , the lanes are ______ meter(s) wider when there are 8 lanes than when there are 9 lanes.

Type below:

_________

Answer:

Each lane is 2.74 meters wide when there are 8 lanes.

Each lane is 2.44 meters wide when there are 9 lanes.

Since 2.74 – 2.44 = 0.30, the lanes are 0.30 meter(s) wider when there are 8 lanes than when there are 9 lanes.

Question 21.

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

Options:

a. 0.30 meter

b. 2.44 meters

c. 2.74 meters

d. 22.28 meters

Answer:

a. 0.30 meter

Question 22.

Robert pays $32.04 for 6 student tickets to the basketball game. What is the cost of each student ticket?

Options:

a. $192.24

b. $53.40

c. $26.04

d. $5.34

Answer:

d. $5.34

Explanation:

Robert pays $32.04 for 6 student tickets to the basketball game.

$32.04 ÷ 6 = $5.34

Question 23.

Jasmine uses 14.24 pounds of fruit for 16 servings of fruit salad. If each serving contains the same amount of fruit, how much fruit is in each serving?

Options:

a. 0.089 pound

b. 0.89 pound

c. 1.76 pounds

d. 17.6 pounds

Answer:

b. 0.89 pound

Explanation:

Jasmine uses 14.24 pounds of fruit for 16 servings of fruit salad. If each serving contains the same amount of fruit, 14.24 ÷ 16 = 0.89 pounds

**Concepts and Skills**

Question 1.

Explain how the position of the decimal point changes in a quotient as you divide by increasing powers of 10.

Type below:

_________

Answer:

Dividing a number by ten shifts the decimal point of the dividend one place to the left, making that into a smaller number, the desired quotient, which is one-tenth of the dividend.

Question 2.

Explain how you can use base-ten blocks to find 2.16 ÷ 3.

Type below:

_________

Answer:

0.72

Explanation:

2.16 ÷ 3

There are 2 ones, 1 tenths, and 6 hundredths.

2.16 ÷ 3 =

2 ones cannont be shared for 3 groups.

So, write 2 ones as 20 tenths.

20 + 1 = 21 tenths.

21 tenths ÷ 3 = 7 tenths.

7 tenths shared amount 3 groups = 21 tenths

6 hundredths ÷ 3 = 2 hundredths.

2 hundredths shared amount 3 groups = 6 hundredths.

0.72

**Complete the pattern.**

Question 3.

223 ÷ 1 = _______

223 ÷ 10 = _______

223 ÷ 100 = _______

223 ÷ 1000 = _______

Answer:

223 ÷ 1 = 223

223 ÷ 10 = 22.3

223 ÷ 100 = 2.23

223 ÷ 1000 = 0.223

Explanation:

223 ÷ 1 = 223

223 ÷ 10 = 22.3

223 ÷ 100 = 2.23

223 ÷ 1000 = 0.223

Question 4.

61 ÷ 1 = 61

61 ÷ 10 = 6.1

61 ÷ 100 = 0.61

61 ÷ 1,000 = 0.061

Answer:

61 ÷ 1 = 61

61 ÷ 10 = 6.1

61 ÷ 100 = 0.61

61 ÷ 1,000 = 0.061

Explanation:

Question 5.

57.4 ÷ 10^{0} = _______

57.4 ÷ 10^{1} = _______

57.4 ÷ 10^{2} = _______

Answer:

57.4 ÷ 10^{0} = 57.4

57.4 ÷ 10^{1} = 5.74

57.4 ÷ 10^{2} = 0.574

Explanation:

57.4 ÷ 10^{0} = 57.4 ÷ 1 = 57.4

57.4 ÷ 10^{1} = 57.4 ÷ 10 = 5.74

57.4 ÷ 10^{2} = 57.4 ÷ 100 = 0.574

**Estimate the quotient.**

Question 6.

31.9 ÷ 4 = ______

Answer:

About 8

Explanation:

31.9 is closer to 32

32 ÷ 4 = 8

Question 7.

6.1 ÷ 8 = ______

Answer:

About 8

Explanation:

6.1 is closer to 64

64 ÷ 8 = 8

Question 8.

492.6 ÷ 48 = ______

Answer:

About 10

Explanation:

492.6 is closer to 480

480 ÷ 48 = 10

**Divide.**

Question 9.

5)\(\overline { 4.35 }\)

_____

Answer:

0.87

Explanation:

4.35 ÷ 5

Divide. 8 ones ÷ 5

4 one(s) cannot be shared among 5 groups without regrouping.

40 + 3 = 43 tenths

Divide. 43 tenths ÷ 5

Multiply. 5 x 8 tenths = 40 tenths. Subtract. 43 tenths − 40 tenths = 3 tenths

Check. 40 tenths shared among 5 groups as 8 tenths.

3 tenths(s) cannot be shared among 5 groups without regrouping.

1 tenth = 10 hundredths.

30 + 5 = 35 hundredths

Divide. 35 hundredths ÷ 5

Multiply. 5 x 7 hundredths = 35 hundredths. Subtract. 35 hundredths − 35 hundredths = 0 hundredths

Check. 35 hundredths shared among 5 groups as 7 hundredths.

So, 0.87

Question 10.

8)\(\overline { 9.92 }\)

_____

Answer:

1.24

Explanation:

9.92 ÷ 8

Divide. 9 ones ÷ 8

Multiply. 8 × 1 ones = 8 ones. Subtract. 9 ones − 8 ones = 1 ones

Check. 8 ones shared among 8 groups as 1 whole.

1 one(s) cannot be shared among 8 groups without regrouping.

10 + 9 = 19 tenths

Divide. 19 tenths ÷ 8

Multiply. 8 x 2 tenths = 16 tenths. Subtract. 19 tenths − 16 tenths = 3 tenths

Check. 16 tenths shared among 8 groups as 2 tenths.

3 tenths(s) cannot be shared among 8 groups without regrouping.

1 tenth = 10 hundredths.

30 + 2 = 32 hundredths

Divide. 32 hundredths ÷ 8

Multiply. 8 x 4 hundredths = 32 hundredths. Subtract. 32 hundredths − 32 hundredths = 0 hundredths

Check. 32 hundredths shared among 8 groups as 4 hundredths.

So, 1.24

Question 11.

61)\(\overline { 207.4 }\)

_____

Answer:

3.4

Explanation:

207.4 ÷ 61

Divide. 207 ones ÷ 61

Multiply. 61 x 3 ones = 183 ones. Subtract. 207 ones − 183 ones = 24 ones

Check. 183 ones shared among 61 groups as 3 wholes.

24 one(s) cannot be shared among 61 groups without regrouping.

240 + 4 = 244 tenths

Divide. 244 tenths ÷ 61

Multiply. 61 x 4 tenths = 244 tenths. Subtract. 244 tenths − 244 tenths = 0 tenths

Check. 244 tenths shared among 61 groups as 4 tenths.

So, 3.4

Question 12.

The Westside Bakery uses 440 pounds of flour to make 1,000 loaves of bread. Each loaf contains the same amount of flour. How many pounds of flour are used in each loaf of bread?

_____ pounds

Answer:

0.440 pounds

Explanation:

The Westside Bakery uses 440 pounds of flour to make 1,000 loaves of bread. Each loaf contains the same amount of flour.

440/1000 = 0.440 pounds

Question 13.

Elise pays $21.75 for 5 student tickets to the fair. What is the cost of each student ticket?

$ _____

Answer:

$4.35

Explanation:

Elise pays $21.75 for 5 student tickets to the fair.

$21.75/5 = $4.35

Question 14.

Jason has a piece of wire that is 62.4 inches long. He cuts the wire into 3 equal pieces. Estimate the length of 1 piece of wire.

_____ in

Answer:

20.8 inches

Explanation:

Jason has a piece of wire that is 62.4 inches long. He cuts the wire into 3 equal pieces.

62.4/3 = 20.8 inches

Question 15.

Elizabeth uses 23.25 ounces of granola and 10.5 ounces of raisins for 15 servings of trail mix. If each serving contains the same amount of trail mix, how much trail mix is in each serving?

_____ ounces

Answer:

2.25 ounces

Explanation:

Elizabeth uses 23.25 ounces of granola and 10.5 ounces of raisins for 15 servings of trail mix.

23.25 + 10.5 = 33.75

33.75/15 = 2.25 ounces

**Use the model to complete the number sentence.**

Question 1.

1.2 ÷ 0.3 =

_____

Answer:

1.2 ÷ 0.3 = 4

Explanation:

There are 4 groups of 3 tenths.

So, 1.2 ÷ 0.3 = 4

Question 2.

0.45 ÷ 0.09 =

_____

Answer:

0.45 ÷ 0.09 = 5

Explanation:

There are 5 groups. Each group has 9 hundredths.

0.09 x 5 = 0.45

So, 0.45 ÷ 0.09 = 5

Question 3.

0.96 ÷ 0.24 =

_____

Answer:

0.96 ÷ 0.24 = 4

Explanation:

There are 4 groups. Each group has 2 tenths and 4 hundredths. 24 hundredths

0.24 x 4 = 0.96

0.96 ÷ 0.24 = 4

Question 4.

1 ÷ 0.5 =

_____

Answer:

2

Explanation:

There are 2 groups. Each group has 5 tenths.

0.5 x 2 = 1.0 = 1

1 ÷ 0.5 = 2

**Divide. Use decimal models.**

Question 5.

1.8 ÷ 0.6 =

_____

Answer:

3

Explanation:

1.8

There are 1 one(s) and 8 tenth(s).

Cut 1.8 to show groups of 0.6.

There are 3 groups of 1.8 tenths.

1.8 ÷ 0.6 = 3

Question 6.

1.2 ÷ 0.3 =

_____

Answer:

4

Explanation:

1.2

There are 1 one(s) and 2 tenth(s).

Cut 1.2 to show groups of 0.3.

There are 4 groups of 1.2 tenths.

1.2 ÷ 0.3 = 4

Question 7.

0.24 ÷ 0.04 =

_____

Answer:

6

Explanation:

0.24

There are 0 one(s) and 2 tenth(s) and 4 hundredth(s).

Cut 0.24 to show groups of 0.04.

There are 6 groups of 0.04 hundredths.

0.24 ÷ 0.04 = 6

Question 8.

1.75 ÷ 0.35 =

_____

Answer:

5

Explanation:

1.75

There are 1 one(s) and 7 tenth(s) and 5 hundredth(s).

Cut 1.75 to show groups of 0.35.

There are 5 groups of 1.75 hundredths.

1.75 ÷ 0.35 = 5

Question 9.

2 ÷ 0.4 =

_____

Answer:

5

Explanation:

2

There are 2 one(s).

Cut 2 to show groups of 0.4.

There are 5 groups of 2 ones.

2 ÷ 0.4 = 5

Question 10.

2.7 ÷ 0.9 =

_____

Answer:

3

Explanation:

2.7

There are 2 one(s) and 7 tenth(s).

Cut 2.7 to show groups of 0.9.

There are 3 groups of 2.7 tenths.

2.7 ÷ 0.9 = 3

Question 11.

1.24 ÷ 0.62 =

_____

Answer:

2

Explanation:

1.24

There are 1 one(s), 2 tenth(s) and 4 hundredth(s).

Cut 1.24 to show groups of 0.62.

There are 2 groups of 1.24 hundredths.

1.24 ÷ 0.62 = 2

Question 12.

0.84 ÷ 0.14 =

_____

Answer:

6

Explanation:

0.84

There are 0 one(s), 8 tenth(s) and 4 hundredth(s).

Cut 0.84 to show groups of 0.14.

There are 6 groups of 0.84 hundredths.

0.84 ÷ 0.14 = 6

Question 13.

1.6 ÷ 0.4 =

_____

Answer:

4

Explanation:

1.6

There are 1 one(s) and 6 tenth(s).

Cut 1.6 to show groups of 0.4.

There are 4 groups of 1.6 tenths.

1.6 ÷ 0.4 = 4

**Use the model to find the unknown value.**

Question 14.

2.4 ÷ □ = 3

_____

Answer:

0.8

Explanation:

2.4 ÷ □ = 3

There are 3 groups with 8 tenths in each group.

So, 2.4 ÷ 0.8 = 3

The unknown number is 0.8

Question 15.

□ ÷ 0.32 = 4

_____

Answer:

1.28

Explanation:

□ ÷ 0.32 = 4

There are 4 groups with 32 hundredths in each group.

So, 0.32 x 4 = 1.28

The unknown number is 1.28

Question 16.

Make a model to find 0.6 ÷ 0.15. Describe your model.

_____

Answer:

0.6 ÷ 0.15

Divide 6 tenths into 15 hundredths each group.

15 hundredths + 15 hundredths + 15 hundredths + 15 hundredths

4 groups.

0.6 ÷ 0.15 = 4

Question 17.

Explain, using the model, what the equation represents in Exercise 15.

Type below:

_________

Answer:

Using the decimal model, we have to find the value of 0.6 ÷ 0.15

0.6 ÷ 0.15 = 4

**Pose a Problem**

Question 18.

Emilio buys 1.2 kilograms of grapes. He separates the grapes into packages that contain 0.3 kilogram of grapes each. How many packages of grapes does Emilio make?

1.2 ÷ 0.3 = 4

Emilio made 4 packages of grapes.

Write a new problem using a different amount for the weight in each package. The amount should be a decimal with tenths. Use a total amount of 1.5 kilograms of grapes. Then use decimal models to solve your problem.

Pose a problem. Solve your problem. Draw a picture of the

model you used to solve your problem.

• Explain why you chose the amount you did for your problem.

Type below:

_________

Answer:

Emilio buys 1.5 kilograms of grapes. He separates the grapes into packages that contain 0.5 kilogram of grapes each.

1.5/0.5 = 3

3 groups

**Copy and complete the pattern.**

Question 1.

45 ÷ 9 = _____

4.5 ÷ _____ = 5

_____ ÷ 0.09 = 5

Answer:

45 ÷ 9 = 5

4.5 ÷ 0.9 = 5

0.45 ÷ 0.09 = 5

Explanation:

45 ÷ 9 = 5

4.5 ÷ _____ = 5

45 ÷ 10 = 4.5. So, 9 ÷ 10 = 0.9

4.5 ÷ 0.9 = 5

_____ ÷ 0.09 = 5

0.9 ÷ 10 = 0.09

4.5 ÷ 10 = 0.45

0.45 ÷ 0.09 = 5

Question 2.

175 ÷ 25 = _____

17.5 ÷ _____ = 7

_____ ÷ 0.25 = 7

Answer:

175 ÷ 25 = 7

17.5 ÷ 2.5 = 7

1.75 ÷ 0.25 = 7

Explanation:

175 ÷ 25 = 7

17.5 ÷ _____ = 7

175 ÷ 10 = 17.5. So, 25 ÷ 10 = 2.5

17.5 ÷ 2.5 = 7

_____ ÷ 0.25 = 7

2.5 ÷ 10 = 0.25

17.5 ÷ 10 = 1.75

1.75 ÷ 0.25 = 7

Question 3.

164 ÷ 2 = _____

16.4 ÷ _____ = 82

_____ ÷ 0.02 = 82

Answer:

164 ÷ 2 = 82

16.4 ÷ 0.2 = 82

1.64 ÷ 0.02 = 82

Explanation:

164 ÷ 2 = 82

16.4 ÷ _____ = 82

164 ÷ 10 = 16.4

2 ÷ 10 = 0.2

16.4 ÷ 0.2 = 82

_____ ÷ 0.02 = 82

0.2 ÷ 10 = 0.02

16.4 ÷ 10 = 1.64

1.64 ÷ 0.02 = 82

**Divide.**

Question 4.

1.6)\(\overline { 9.6 }\) = _____

Answer:

6

Explanation:

9.6 ÷ 1.6

9.6 x 10 = 96

1.6 x 10 = 16

96 ÷ 16 = 6

So, 9.6 ÷ 1.6 = 6

Question 5.

0.3)\(\overline { 0.24 }\) = _____

Answer:

0.8

Explanation:

0.24 ÷ 0.3

0.24 x 10 = 2.4

0.3 x 10 = 3

2.4 ÷ 3 = 0.8

0.24 ÷ 0.3 = 0.8

Question 6.

3.45 ÷ 1.5 = _____

Answer:

2.3

Explanation:

3.45 ÷ 1.5

3.45 x 10 = 34.5

1.5 x 10 = 15

34.5 ÷ 15 = 2.3

3.45 ÷ 1.5 = 2.3

**On Your Own**

**Divide.**

Question 7.

0.6)\(\overline { 13.2 }\) = _____

Answer:

22

Explanation:

13.2 ÷ 0.6

13.2 x 10 = 132

0.6 x 10 = 6

132 ÷ 6 = 22

13.2 ÷ 0.6 = 22

Question 8.

0.3)\(\overline { 0.9 }\) = _____

Answer:

3

Explanation:

0.9 ÷ 0.3

0.9 x 10 = 9

0.3 x 10 = 3

9 ÷ 3 = 3

0.9 ÷ 0.3 = 3

Question 9.

0.26)\(\overline { 1.56 }\) = _____

Answer:

6

Explanation:

1.56 ÷ 0.26

1.56 x 100 = 156

0.26 x 100 = 26

156 ÷ 26 = 6

1.56 ÷ 0.26 = 6

Question 10.

0.45)\(\overline { 5.85 }\) = _____

Answer:

13

Explanation:

5.85 ÷ 0.45

5.85 x 100 = 585

0.45 x 100 = 45

585 ÷ 45 = 13

Question 11.

0.3)\(\overline { 0.69 }\) = _____

Answer:

2.3

Explanation:

0.69 ÷ 0.3

0.69 x 10 = 6.9

0.3 x 10 = 3

6.9 ÷ 3 = 2.3

Question 12.

3.6 ÷ 0.4 = _____

Answer:

9

Explanation:

3.6 ÷ 0.4

3.6 x 10 = 36

0.4 x 10 = 4

36 ÷ 4 = 9

3.6 ÷ 0.4 = 9

Question 13.

1.26 ÷ 2.1 = _____

Answer:

0.6

Explanation:

1.26 ÷ 2.1

1.26 x 10 = 12.6

2.1 x 10 = 21

12.6 ÷ 21 = 0.6

Question 14.

7.84 ÷ 0.28 = _____

Answer:

28

Explanation:

7.84 ÷ 0.28

7.84 x 100 = 784

0.28 x 100 = 28

784 ÷ 28 = 28

7.84 ÷ 0.28 = 28

Question 15.

9.28 ÷ 2.9 = _____

Answer:

3.2

Explanation:

9.28 ÷ 2.9

9.28 x 10 = 92.8

2.9 x 10 = 29

92.8 ÷ 29 = 3.2

9.28 ÷ 2.9 = 3.2

**Use the table to solve 16—19.**

Question 16.

Connie paid $1.08 for pencils. How many pencils did she buy?

_____ pencils

Answer:

9 pencils

Explanation:

1 pencil = $0.12

Connie paid $1.08 for pencils.

$1.08 ÷ $0.12 = 9

she buys 9 pencils

Question 17.

Albert has $2.16. How many more pencils can he buy than markers?

_____

Answer:

Albert can buy 12 more pencils than markers

Explanation:

Albert has $2.16.

1 pencil = $0.12

$2.16/$0.12 = 18 pencils

1 marker = $0.36

$2.16/$0.36 = 6 markers

18 – 6 = 12 more pencils

Question 18.

How many erasers can Ayita buy for the same amount that she would pay for one notepad?

_____ erasers

Answer:

Ayita can buy 13 erasers with one notepad money.

Explanation:

1 notepad = $0.65

$0.65/$0.05 = 13

Ayita can buy 13 erasers with one notepad money.

Question 19.

Ramon paid $3.25 for notepads and $1.44 for markers. What is the total number of items he bought?

_____ items

Answer:

9 items

Explanation:

Ramon paid $3.25 for notepads.

$3.25/$0.65 = 5

He paid $1.44 for markers

$1.44/$0.36 = 4

5 + 4 = 9

He bought 9 items

Question 20.

What’s the Error? Katie divided 4.25 by 0.25 and got a quotient of 0.17.

_____

Answer:

Katie divided 4.25 by 0.25

4.25 ÷ 0.25

4.25 x 100 = 425

0.25 x 100 = 25

425 ÷ 25 = 17

4.25 ÷ 0.25 = 17

But he said 0.17

Question 21.

Test Prep Marcus bought apples that cost $0.45 per pound. He paid $1.35 for the apples. How many pounds of apples did he buy?

Options:

a. 0.3 pound

b. 2.8 pounds

c. 3 pounds

d. 30 pounds

Answer:

c. 3 pounds

Explanation:

Marcus bought apples that cost $0.45 per pound.

He paid $1.35 for the apples.

$1.35 ÷ $0.45 = 3 pounds

**Write the quotient with the decimal point placed correctly.**

Question 1.

5 ÷ 0.8 = 625

_____

Answer:

5 ÷ 0.8 = 6.25

Explanation:

5 ÷ 0.8 = 5 ÷ 0.800

50 ÷ 8 = 6.25

Divide 5 ÷ 0.8 until you get remainder 0

Divide: 50 ÷ 8 = 6

8 x 6 = 48; Subtract: 50 – 48 = 2

Divide: 20 ÷ 8 = 2;

Subtract: 20 – 16 = 4

Divide: 40 ÷ 8 = 5

8 x 5 = 40; Subtract: 40 – 40 = 0

So, 6.25

Question 2.

26.1 ÷ 6 = 435

_____

Answer:

Explanation:

26.1 ÷ 6 = 26.1 ÷ 6.0

261 ÷ 60.0

Divide 26.1 ÷ 6 until you get remainder 0

Divide: 261 ÷ 60 = 4;

60 x 4 = 240 Subtract: 261 – 240 = 21

Divide: 210 ÷ 60 = 3

60 x 3 = 180; Subtract: 210 – 180 = 30

Divide: 300 ÷ 60 = 5;

60 x 5 = 300; Subtract: 300 – 300 = 0

261 ÷ 60 = 4.35

Question 3.

0.42 ÷ 0.35 = 12

_____

Answer:

1.2

Explanation:

0.42 ÷ 0.35 = 42 ÷ 35

Divide 0.42 ÷ 0.35 until you get remainder 0

Divide: 42 ÷ 35 = 1;

35 x 1 = 35 Subtract: 42 – 35 = 7

Divide: 70 ÷ 35 = 2

35 x 2 = 70; Subtract: 70 – 70 = 0

0.42 ÷ 0.35 = 1.2

Question 4.

80 ÷ 50 = 16

_____

Answer:

1.6

Explanation:

80 ÷ 50

8 ÷ 5

Divide 8 ÷ 5

5 x 1 = 5 : Subtract: 8 – 5 = 3

Divide 30 ÷ 5 = 6

80 ÷ 50 = 1.6

**Divide.**

Question 5.

4)\(\overline { 32.6 }\) = _____

Answer:

8.15

Explanation:

32.6 ÷ 4

Divide: 32/4 = 8

8 x 4 = 32; Subtract: 32 – 32 = 0

Divide: 6/4 = 1

4 x 1 = 4; Subtract: 6 – 4 = 2

Add zero

20 ÷ 4 = 5

So, 8.15

Question 6.

1.2)\(\overline { 9 }\) = _____

Answer:

0.1333

Explanation:

1.2/9 = 12/90; 12 < 90

12 cannot be divided by 90. So add zero to 12.

120/90 = 1; 120 – 90 = 30; 30 < 90

300/90 = 3; 300 – 270 = 30

So, 0.13333

Question 7.

15)\(\overline { 42 }\) = _____

Answer:

2.8

Explanation:

42/15 = 2

15 x 2 = 30; 42 – 30 = 12

120/15 = 8;

So, 2.8

Question 8.

0.14)\(\overline { 0.91 }\) = _____

Answer:

6.5

Explanation:

0.91/0.14 = 91/14

91/14 = 6

14 x 6 = 84; 91 – 84 = 7; 7 < 14

70/14 = 5

So, 6.5

**On Your Own**

**Divide.**

Question 9.

8)\(\overline { 84 }\) = _____

Answer:

10.5

Explanation:

84/8 = 10

8 x 10 = 80; 84 – 80 = 4;4 < 8

40/8 = 5

So, 10.5

Question 10.

2.5)\(\overline { 4 }\) = _____

Answer:

Explanation:

4/2.5 = 40/25

40/25 = 1;

40 – 25 = 15; 15 < 25

150/25 = 6

So, 1.6

Question 11.

5)\(\overline { 16.2 }\) = _____

Answer:

3.24

Explanation:

16.2/5 = 162/50

162/50 = 3

50 x 3 = 150; 162 – 150 = 12; 12 < 50

120/50 = 2

50 x 2 = 100; 120 – 100 = 20; 20 < 50

200/50 = 4

So, 3.24

Question 12.

0.6)\(\overline { 2.7 }\) = _____

Answer:

4.5

Explanation:

2.7/0.6 = 27/6

27/6 = 4

4 x 6 = 24; 27 – 24 = 3; 3 < 6

30/6 = 5

So, 4.5

Question 13.

18 ÷ 7.5 = _____

Answer:

2.4

Explanation:

18/7.5 = 180/75

180/75 = 2

75 x 2 = 150; 180 – 150 = 30; 30 < 75

300/75 = 4

So, 2.4

Question 14.

34.8 ÷ 24 = _____

Answer:

1.45

Explanation:

34.8/24 = 348/240

348/240 = 1;

240 x 1 = 240; 348 – 240 = 108 < 240

1080/240 = 4

240 x 4 = 960; 1080 – 960 = 120; 120 < 240

1200/240 = 5

So, 1.45

Question 15.

5.16 ÷ 0.24 = _____

Answer:

21.5

Explanation:

5.16/0.24 = 516/24

516/24 = 21

24 x 21 = 504: 516 – 504 = 12; 12 < 24

120/24 = 5;

So, 21.5

Question 16.

81 ÷ 18 = _____

Answer:

4.5

Explanation:

81/18 = 4

18 x 4 = 72; 81 – 72 = 9; 9 < 18

90/18 = 5

4.5

**Practice: Copy and Solve Divide.**

Question 17.

1.6)\(\overline { 20 }\) = _____

Answer:

12.5

Explanation:

20/1.6 = 200/16

200/16 = 12

16 x 12 = 192; 200 – 192 = 8; 8 < 16

80/16 = 5;

12.5

Question 18.

15)\(\overline { 4.8 }\) = _____

Answer:

0.32

Explanation:

4.8/15 = 48/150; 48 < 150

480/150 = 3

150 x 3 = 450; 480 – 450 = 30 < 150

300/150 = 2

0.32

Question 19.

0.54)\(\overline { 2.43 }\) = _____

Answer:

4.5

Explanation:

2.43/0.54 = 243/54

243/54 = 4

54 x 4 = 216; 243 – 216 = 27 < 54

270/54 = 5

4.5

Question 20.

28)\(\overline { 98 }\) = _____

Answer:

3.5

Explanation:

98/28 = 3

28 x 3 = 84; 98 – 84 = 14 < 28

140/28 = 5

3.5

Question 21.

1.8 ÷ 12 = _____

Answer:

0.15

Explanation:

1.8/12 = 18/120; 18 < 120

180/120 = 1;

120 x 1 = 120; 180 – 120 = 60; 60 < 120

600/120 = 5

0.15

Question 22.

3.5 ÷ 2.5 = _____

Answer:

1.4

Explanation:

3.5/2.5 = 35/25

35/25 = 1;

25 x 1 = 25; 35 – 25 = 10; 10 < 25

100/25 = 4

1.4

Question 23.

40 ÷ 16 = _____

Answer:

2.5

Explanation:

40/16 = 2

16 x 2 = 32; 40 – 32 = 8 < 16

80/16 = 5

2.5

Question 24.

2.24 ÷ 0.35 = _____

Answer:

6.4

Explanation:

2.24/0.35 = 224/35

224/35 = 6

35 x 6 = 210; 224 – 210 = 14 < 35

140/35 = 4

6.4

**Solve.**

Question 25.

Jerry takes trail mix on hikes. A package of dried apricots weighs 25.5 ounces. Jerry divides the apricots equally among 6 bags of trail mix. How many ounces of apricots are in each bag?

_____ ounces

Answer:

4.25 ounces

Explanation:

Jerry takes trail mix on hikes. A package of dried apricots weighs 25.5 ounces. Jerry divides the apricots equally among 6 bags of trail mix.

25.5/6 = 4.25 ounces

Question 26.

Amy has 3 pounds of raisins. She divides the raisins equally into 12 bags. How many pounds of raisins are in each bag? Tell how many zeros you had to write at the end of the dividend.

_____ pound

Answer:

4 pound

Explanation:

Amy has 3 pounds of raisins. She divides the raisins equally into 12 bags.

12/3 = 4 pound. There are no zeros required at the end of the dividend.

Question 27.

Find 65 ÷ 4. Write your answer using a remainder, a fraction, and a decimal. Then tell which form of the answer you prefer. Explain your choice.

Type below:

_________

Answer:

65 ÷ 4 = 16 and 1 remainder.

Fraction = 65/4

65/4 = 16.25

The decimal answer is best to choose as there are no mathematical operations required.

Question 28.

Test Prep Todd has a piece of rope that is 1.6 meters long. He cuts the rope into 5 equal pieces. What is the length of each piece?

Options:

a. 0.8 meter

b. 0.32 meter

c. 3.2 meters

d. 8 meters

Answer:

b. 0.32 meter

Explanation:

Todd has a piece of rope that is 1.6 meters long. He cuts the rope into 5 equal pieces.

1.6/5 = 0.32 meter

**Connect to Science**

**Rate of Speed Formula**

The formula for velocity, or rate of speed, is r = d ÷ t, where r represents rate of speed, d represents distance, and t represents time. For example, if an object travels 12 feet in 10 seconds, you can find its rate of speed by using the formula.

r = d ÷ t

r = 12 ÷ 10

r = 1.2 feet per second

Use division and the formula for rate of speed to solve.

Question 29.

A car travels 168 miles in 3.2 hours. Find the car’s rate of speed in miles per hour.

_____ miles per hour

Answer:

52.5 miles per hour

Explanation:

168/3.2 = 52.5 miles per hour

Question 30.

A submarine travels 90 kilometers in 4 hours. Find the submarine’s rate of speed in kilometers per hour.

_____ kilometers per hour

Answer:

22.5 kilometers per hour

Explanation:

A submarine travels 90 kilometers in 4 hours.

For an hour, 90/4 = 22.5 kilometers per hour

Question 1.

Hector spent $36.75 for 2 DVDs with the same cost. The sales tax was $2.15. Hector also used a coupon for $1.00 off his purchase. How much did each DVD cost?

First, make a flowchart to show the information and show how you would work backward.

Type below:

_________

Answer:

Question 1.

Then, work backward to find the cost of 2 DVDs.

Type below:

_________

Answer:

Price of the DVD is s

2s + $2.15 – $1.00 = $36.75

2s = $35.60

Question 1.

Finally, find the cost of one DVD.

So, each DVD costs ________ .

$ _____

Answer:

2s = $35.60

s = $35.60/2

s = $17.8

Question 2.

What if Hector spent $40.15 for the DVDs, the sales tax was $2.55, and he didn’t have a coupon? How much would each DVD cost?

$ _____

Answer:

Explanation:

If Hector spent $40.15 for the DVDs. The sales tax was $2.55, and he didn’t have a coupon

Price of the DVD is s

2s + $2.55 = $40.15

2s = $37.60

s = $18.8

Each DVD price =$18.8

Question 3.

Sophia spent $7.30 for school supplies. She spent $3.00 for a notebook and $1.75 for a pen. She also bought 3 large erasers. If each eraser had the same cost, how much did she spend for each eraser?

$ _____

Answer:

$0.85

Explanation:

Sophia spent $7.30 for school supplies. She spent $3.00 for a notebook and $1.75 for a pen.

$3.00 + $1.75 = $4.75

$7.30 – $4.75 = $2.55

If she bought 3 erasers, $2.55/3 = $0.85

Each eraser cost = $0.85

Question 4.

The change from a gift purchase was $3.90. Each of 6 students donated an equal amount for the gift. How much change should each student receive?

$ _____

Answer:

$0.65

Explanation:

The change from a gift purchase was $3.90. Each of 6 students donated an equal amount for the gift.

$3.90/6 = $0.65

Question 5.

If you divide this mystery number by 4, add 8, and multiply by 3, you get 42. What is the mystery number?

_____

Answer:

24

Explanation:

Let the unknown number = s.

(s/4 + 8) x 3 = 42

s/4 + 8 = 42/3

s/4 + 8 = 14

s/4 = 6

s = 6 x 4 = 24

s = 24

Question 6.

A mail truck picks up two boxes of mail from the post office. The total weight of the boxes is 32 pounds. One box is 8 pounds heavier than the other box. How much does each box weigh?

Type below:

_________

Answer:

20 pounds.

other box = 12 pounds

Explanation:

If one box weight is s, the other box weight is 8 pounds heavier than the other box. s – 8.

Total weight of two boxes =32

s + s – 8 = 32

2s = 40

s = 20

Question 7.

Stacy buys 3 CDs in a set for $29.98. She saved $6.44 by buying the set instead of buying the individual CDs. If each CD costs the same amount, how much does each of the 3 CDs cost when purchased individually?

$ _____

Answer:

$12.14

Explanation:

Stacy buys 3 CDs in a set for $29.98. She saved $6.44 by buying the set instead of buying the individual CDs.

Cost to buy 3 CDs = $29.98 + $6.44 = $36.42

$36.42/3 = $12.14

Question 8.

A school cafeteria sold 1,280 slices of pizza the first week, 640 the second week, and 320 the third week. If this pattern continues, in what week will the cafeteria sell 40 slices? Explain how you got your answer.

_____ th week

Answer:

sixth week

Explanation:

A school cafeteria sold 1,280 slices of pizza the first week, 640 the second week, and 320 the third week.

1280, 640, 320

1280/2 = 640

640/2 = 320

320/2 = 160

160/2 = 80

80/2 = 40

6th term shows 40. So, the answer is the sixth week.

Question 9.

Test Prep While working at the school store, John sold a jacket for $40.00 and notebooks for $1.50 each. If he collected $92.50, how many notebooks did he sell?

Options:

a. 3.5

b. 6.1

c. 35

d. 61

Answer:

c. 35

Explanation:

John sold a jacket for $40.00 and notebooks for $1.50 each.

$40 + $1.50S = $92.50

$1.50S = $52.5

S = $52.5/$1.50 = 35

**Concepts and Skills**

**Complete the pattern.**

Question 1.

341 ÷ 1 = ________

341 ÷ 10 = ________

341 ÷ 100 = ________

341 ÷ 1,000 = ________

Answer:

341 ÷ 1 = 341

341 ÷ 10 = 34.1

341 ÷ 100 = 3.41

341 ÷ 1,000 = 0.341

Explanation:

341 ÷ 1 = 341

341 ÷ 10 = 34.1

341 ÷ 100 = 3.41

341 ÷ 1,000 = 0.341

Question 2.

15 ÷ 1 = ________

15 ÷ 10 = ________

15 ÷ 100 = ________

15 ÷ 1,000 = ________

Answer:

15 ÷ 1 = 15

15 ÷ 10 = 1.5

15 ÷ 100 = 0.15

15 ÷ 1,000 = 0.015

Explanation:

15 ÷ 1 = 15

15 ÷ 10 = 1.5

15 ÷ 100 = 0.15

15 ÷ 1,000 = 0.015

Question 3.

68.2 ÷ 10^{0} = ________

68.2 ÷ 10^{1} = ________

68.2 ÷ 10^{2} = ________

Answer:

68.2 ÷ 10^{0} = 68.2

68.2 ÷ 10^{1} = 6.82

68.2 ÷ 10^{2} = 0.682

Explanation:

68.2 ÷ 10^{0} = 68.2 ÷ 1 = 68.2

68.2 ÷ 10^{1} = 68.2 ÷ 10 = 6.82

68.2 ÷ 10^{2} = 68.2 ÷ 100 = 0.682

**Estimate the quotient.**

Question 4.

49.3 ÷ 6 = _____

Answer:

About 8

Explanation:

49.3 is closer to 48

48 ÷ 6 = 8

Question 5.

3.5 ÷ 4 = _____

Answer:

about 1

Explanation:

3.5 is closer to 4

4 ÷ 4 = 1

Question 6.

396.5 ÷ 18 = _____

Answer:

About 22

Explanation:

396.5 is closer to 396

396 ÷ 18 = 22

**Divide.**

Question 7.

6)\(\overline { 3.24 }\) = _____

Answer:

0.54

Explanation:

3.24 ÷ 6

Divide. 3 ones ÷ 6

3 one(s) cannot be shared among 6 groups without regrouping.

30 + 2 = 32 tenths

Divide. 32 tenths ÷ 6

Multiply. 6 x 5 tenths = 30 tenths. Subtract. 32 tenths − 30 tenths = 2 tenths

Check. 30 tenths shared among 6 groups as 5 tenths.

2 tenths(s) cannot be shared among 6 groups without regrouping.

1 tenth = 10 hundredths.

20 + 4 = 24 hundredths

Divide. 24 hundredths ÷ 6

Multiply. 6 x 4 hundredths = 24 hundredths. Subtract. 24 hundredths − 24 hundredths = 0 hundredths

Check. 24 hundredths shared among 6 groups as 4 hundredths.

So, 0.54

Question 8.

5)\(\overline { 6.55 }\) = _____

Answer:

1.51

Explanation:

6.55 ÷ 5

Divide. 6 ones ÷ 5

Multiply. 5 × 1 ones = 5 ones. Subtract. 6 ones − 5 ones = 1 ones

Check. 5 ones shared among 5 groups as 1 whole.

1 one(s) cannot be shared among 5 groups without regrouping.

10 + 5 = 15 tenths

Divide. 15 tenths ÷ 5

Multiply. 5 x 3 tenths = 15 tenths. Subtract. 15 tenths − 15 tenths = 0 tenths

Check. 35 tenths shared among 5 groups as 3 tenths.

Divide. 5 hundredths ÷ 5

Multiply. 5 x 1 hundredths = 5 hundredths. Subtract. 5 hundredths − 5 hundredths = 0 hundredths

Check. 5 hundredths shared among 5 groups as 1 hundredth.

So, 1.51

Question 9.

26)\(\overline { 96.2 }\) = _____

Answer:

3.7

Explanation:

96.2 ÷ 26

Divide. 96 ones ÷ 26

Multiply. 26 × 3 ones = 78 ones. Subtract. 96 ones − 78 ones = 18 ones

Check. 78 ones shared among 26 groups as 3 wholes.

18 one(s) cannot be shared among 26 groups without regrouping.

180 + 2 = 182 tenths

Divide. 182 tenths ÷ 26

Multiply. 26 x 7 tenths = 182 tenths. Subtract. 182 tenths − 182 tenths = 0 tenths

So, 3.7

Question 10.

1.08 ÷ 0.4 = _____

Answer:

2.7

Explanation:

1.08 ÷ 0.4

1.08 x 10 = 10.8

0.4 x 10 = 4

10.8 ÷ 4 = 2.7

Question 11.

8.84 ÷ 0.68 = _____

Answer:

13

Explanation:

8.84 ÷ 0.68

8.84 x 100 = 884

0.68 x 100 = 68

884 ÷ 68 = 13

Question 12.

7.31 ÷ 1.7 = _____

Answer:

4.3

Explanation:

7.31 ÷ 1.7

7.31 x 10 = 73.1

1.7 x 10 = 17

73.1 ÷ 17 = 4.3

Question 13.

9.18 ÷ 0.9 = _____

Answer:

10.2

Explanation:

9.18 ÷ 0.9

9.18 x 10 = 91.8

0.9 x 10 = 9

91.8 ÷ 9 = 10.2

Question 14.

12.7 ÷ 5 = _____

Answer:

2.54

Explanation:

12.7 ÷ 5

12.7 x 10 = 127

5 x 10 = 50

127 ÷ 50 = 2.54

Question 15.

8.33 ÷ 0.34 = _____

Answer:

24.5

Explanation:

8.33 ÷ 0.34

8.33 x 100 = 833

0.34 x 100 = 34

833 ÷ 34 = 24.5

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

Question 16.

The Orchard Pie Company uses 95 pounds of apples to make 100 pies. Each pie contains the same amount of apples. How many pounds of apples are used in each pie?

Options:

A. 0.095 pound

B. 0.95 pound

C. 9.5 pounds

D. 95 pounds

Answer:

B. 0.95 pound

Explanation:

The Orchard Pie Company uses 95 pounds of apples to make 100 pies. Each pie contains the same amount of apples.

95/100 = 0.95 pounds

Question 17.

During a special sale, all CDs have the same price. Mr. Ortiz pays $228.85 for 23 CDs. Which is the best estimate of the price of each CD?

Options:

A. $9

B. $10

C. $12

D. $13

Answer:

B. $10

Explanation:

During a special sale, all CDs have the same price. Mr. Ortiz pays $228.85 for 23 CDs.

$228.85/23 = $9.95

Question 18.

Ryan earns $20.16 working for 3 hours. How much does he earn per hour?

Options:

A. $60.48

B. $6.82

C. $6.72

D. $6.71

Answer:

C. $6.72

Explanation:

Ryan earns $20.16 working for 3 hours.

$20.16/3 = $6.72

Question 19.

Anna hikes 6.4 miles during a 4-day vacation. If she hikes the same distance each day, how many miles does she hike each day?

Options:

A. 1.06 miles

B. 1.1 miles

C. 1.4 miles

D. 1.6 miles

Answer:

D. 1.6 miles

Explanation:

Anna hikes 6.4 miles during a 4-day vacation. If she hikes the same distance each day, 6.4/4 = 1.6 miles

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

Question 20.

Karina pays $1.92 for pencil erasers. The erasers cost $0.08 each. How many erasers does she buy?

Options:

A. 2.4

B. 2.5

C. 24

D. 25

Answer:

C. 24

Explanation:

Karina pays $1.92 for pencil erasers. The erasers cost $0.08 each.

$1.92/$0.08 = 24

Question 21.

Wyatt has 25.4 ounces of fruit juice. He divides the juice equally into 4 glasses. How much juice is in each glass?

Options:

A. 6 ounces

B. 6.35 ounces

C. 6.4 ounces

D. 6.45 ounces

Answer:

B. 6.35 ounces

Explanation:

Wyatt has 25.4 ounces of fruit juice. He divides the juice equally into 4 glasses.

25.4/4 = 6.35 ounces

Question 22.

Jacob walks 70.4 feet in 0.2 hour. If he walks at the same rate the whole time, what is his speed in feet per hour?

Options:

A. 352 feet per hour

B. 140.8 feet per hour

C. 35.2 feet per hour

D. 14.08 feet per hour

Answer:

A. 352 feet per hour

Explanation:

Jacob walks 70.4 feet in 0.2 hour. If he walks at the same rate the whole time,

7.4/0.2 = 352 feet per hour

Question 23.

Meghan earns $20.00 by walking dogs. She uses all of her earnings to buy a shirt for $12.85 and some stickers for $0.65 each. How many stickers does she buy?

Options:

A. 4.65

B. 11

C. 46

D. 110

Answer:

B. 11

Explanation:

Meghan earns $20.00 by walking dogs. She uses all of her earnings to buy a shirt for $12.85 and some stickers for $0.65 each.

$20 – $12.85 = $7.15

$7.15/$0.65 = 11

**Constructed Response**

Question 24.

Percy buys tomatoes that cost $0.58 per pound. He pays $2.03 for the tomatoes. How many pounds of tomatoes does he buy? Show your work using words, pictures, or numbers. Explain how you know your answer is reasonable.

_____ pounds

Answer:

3.5 pounds

Explanation:

Percy buys tomatoes that cost $0.58 per pound. He pays $2.03 for the tomatoes.

$2.03/$0.58

200/50 = 4; Using Compitable numbers

Multiply the divisor by a power of 10 to make it a whole number. Then, multiply the dividend by the same power of 10.

0.58 x 100 = 58

2.03 x 100 = 203

203/58

Divide until you have an amour less than the divisor left over.

Insert a decimal point and a zero at the end of the dividend.

Place a decimal point in the quotient above the decimal point in the dividend.

203/58 = 3.5 pounds

**Performance Task**

Question 25.

Isabella is buying art supplies. The table at the right shows the prices of the items she wants to buy.

A Isabella spends $2.25 on poster boards. How many poster boards does she buy?

_____ posters

Answer:

3 posters

Explanation:

1 Poster Board = $0.75.

Isabella spends $2.25 on poster boards.

$2.25/$0.75 = 3

Question 25.

B Isabella spends $4.87 on paintbrushes and paint. How many of each item does she buy? Explain how you found your answer.

_______ paint brushes

_______ jars of paint

Answer:

2 paint brushes

3 jars of paint

Explanation:

paintbrushes = $0.95

Paint = $0.99

If she buys 2 paint brushes and 2 paints, she spent $1.9 for paintbrushes and $1.98 for 2 paints. The remaining amount is $0.99. So, she can buy one more paint with them. So, she can buy 2 paint brushes and 3 jars of paint.

Question 25.

C. Isabella spends less than $14.00 for glass beads, paintbrushes, poster board, and paint. She spends $1.68 on beads and $3.96 on paint. She buys more than 3 poster boards and more than 3 paintbrushes. Find how many ounces of glass beads and how many jars of paint she buys. Then, suggest the number of poster boards and paintbrushes she might buy for the total spent.

Type below:

_________

Answer:

Isabella spends less than $14.00 for glass beads, paintbrushes, poster board, and paint.

She spends $1.68 on beads and $3.96 on paint.

Each beads = $0.28

$1.68/$0.28 = 6 beads

Each paint = $0.99

$3.96/$0.99 = 4 paints

$14 – ($1.68 + $3.96) = $8.36.

So, $8.36 needs to spend on more than 3 poster boards and more than 3 paintbrushes.

So, Each poster board = $0.75

paintbrushes = $0.95

If she buys more than 3, 3 x $0.75 = $2.25

$0.95 x 3 = $2.85

$2.25 + $2.85 = $5.1

So, $8.36 – $5.1 = $3.26

If $0.75 x 3 = $2.25

$0.95 x 1 = $0.95

$2.25 + $0.95 = 3.2

So, she can buy 3 + 3 = 6 poster boards

and 3 + 1 = 4 paintbrushes.