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Lesson 1: Algebra • Division Patterns with Decimals

Lesson 2: Investigate • Divide Decimals by Whole Numbers

Lesson 3: Estimate Quotients

Lesson 4: Division of Decimals by Whole Numbers

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

### Share and Show – Page No. 203

Complete the pattern.

Question 1.
456 ÷ 100 = 456
456 ÷ 101 = 45.6
456 ÷ 102 = 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 ÷ 103 = _____

456 ÷ 103 = 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 ÷ 100 = 456
456 ÷ 101 = 45.6
456 ÷ 102 = 4.56
456 ÷ 103 = 0.456

Complete the pattern.

Question 2.
225 ÷ 100 = _____
225 ÷ 101 = _____
225 ÷ 102 = _____
225 ÷ 103 = _____

225 ÷ 100 = 225
225 ÷ 101 = 22.5
225 ÷ 102 = 2.25
225 ÷ 103 = 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 ÷ 100 = 225/1 = 225
225 ÷ 101 = 225/10 = 22.5
225 ÷ 102 = 225/100 = 2.25
225 ÷ 103 = 225/1,000 = 0.25

Question 3.
605 ÷ 100 = _____
605 ÷ 101 = _____
605 ÷ 102 = _____
605 ÷ 103 = _____

605 ÷ 100 = 605
605 ÷ 101 = 60.5
605 ÷ 102 = 6.05
605 ÷ 103 = 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 ÷ 100 = 605/1 = 605
605 ÷ 101 = 605/10 = 60.5
605 ÷ 102 = 605/100 = 6.05
605 ÷ 103 = 605/1,000 = 0.605

Question 4.
74.3 ÷ 1 = _____
74.3 ÷ 10 = _____
74.3 ÷ 100 = _____

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 ÷ 100 = 74.3 ÷ 1 = 74.3
74.3 ÷ 101 = 74.3 ÷ 10 = 7.43
74.3 ÷ 102 = 74.3 ÷ 100 = 0.743

Complete the pattern.

Question 5.
156 ÷ 1 = _____
156 ÷ 10 = _____
156 ÷ 100 = _____
156 ÷ 1,000 = _____

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 = _____

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 ÷ 100 = _____
16 ÷ 101 = _____
16 ÷ 102 = _____
16 ÷ 103 = _____

16 ÷ 100 = 16
16 ÷ 101 = 1.6
16 ÷ 102 = 0.16
16 ÷ 103 = 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 ÷ 100 = 16
16 ÷ 101 = 1.6
16 ÷ 102 = 0.16
16 ÷ 103 = 0.016

Question 8.
12.7 ÷ 1 = _____
12.7 ÷ 10 = _____
12.7 ÷ 100 = _____
12.7 ÷ 1,000 = _____

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 ÷ 100 = _____
92.5 ÷ 101 = _____
92.5 ÷ 102 = _____
92.5 ÷ 103 = _____

92.5 ÷ 100 = 92.5
92.5 ÷ 101 = 9.25
92.5 ÷ 102 = 0.925
92.5 ÷ 103 = 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 ÷ 100 = 92.5
92.5 ÷ 101 = 9.25
92.5 ÷ 102 = 0.925
92.5 ÷ 103 = 0.0925

Question 10.
86.3 ÷ 100 = _____
86.3 ÷ 101 = _____
86.3 ÷ 102 = _____
86.3 ÷ 103 = _____

86.3 ÷ 100 = 86.3
86.3 ÷ 101 = 8.63
86.3 ÷ 102 = 0.863
86.3 ÷ 103 = 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 ÷ 100 = 86.3
86.3 ÷ 101 = 8.63
86.3 ÷ 102 = 0.863
86.3 ÷ 103 = 0.0863

Algebra Find the value of n.

Question 11.
268 ÷ n = 0.268
n = _____

n = 1000

Explanation:
268 ÷ n = 0.268
268 = n x 0.268
n = 268 ÷ 0.268
n = 1000

Question 12.
n ÷ 102 = 0.123
n = _____

n = 12.3

Explanation:
n ÷ 102 = 0.123
n = 0.123 x 102
n = 0.123 x 100
n = 12.3

Question 13.
n ÷ 101 = 4.6
n = _____

n = 46

Explanation:
n ÷ 101 = 4.6
n = 4.6 x 101
n = 4.6 x 10
n = 46

### Problem Solving – Page No. 204

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

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

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

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 ÷ 101 is equal to the product 47.3 × 0.1.
Type below:
_________

Quotient 47.3 ÷ 101 = 47.3 ÷ 10 = 4.73. The power of 101 = 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

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

### Share and Show – Page No. 207

Use the model to complete the number sentence.

Question 1.
1.6 ÷ 4 =

_____

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 =

_____

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 = _____

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 = _____

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 = _____

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 = _____

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 = _____

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 = _____

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 = _____

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 = _____

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 = _____

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

### Problem Solving – Page No. 208

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:
_________

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:
_________

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:
_________

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

### Share and Show – Page No. 211

Use compatible numbers to estimate the quotient.

Question 1.
28.8 ÷ 9
Type below:
_________

Explanation:
28.8 is closer to 30
9 is closer to 10
30 ÷ 10 = 3

Question 2.
393.5 ÷ 41
_____ ÷ _____ = _____

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.

Estimate the quotient.

Question 3.
161.7 ÷ 7
_____

Explanation:
161.7 is closer to 161
161 ÷ 7 = 23

Question 4.
17.9 ÷ 9
_____

Explanation:
17.9 is closer to 18
18 ÷ 9 = 2

Question 5.
145.4 ÷ 21
_____

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.

Estimate the quotient.

Question 6.
15.5 ÷ 4
_____

Explanation:
15.5 is closer to 16
16 ÷ 4 = 4

Question 7.
394.8 ÷ 7
_____

Explanation:
394.8 is closer to 420
420 ÷ 7 = 60

Question 8.
410.5 ÷ 18
_____

Explanation:
410.5 is closer to 396
396 ÷ 18 = 22

Question 9.
72.1 ÷ 7
_____

Explanation:
72.1 is closer to 70
70 ÷ 7 = 10

Question 10.
32.4 ÷ 52
_____

Explanation:
32.4 is closer to 52
52 ÷ 52 = 1

Question 11.
$134.42 ÷ 28$ _____

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.

Question 12.
21.8 ÷ 4
_____

Explanation:
21.8 is closer to 20
20 ÷ 4 = 5

Question 13.
3.4 ÷ 5
_____

Explanation:
3.4 is closer to 5
5 ÷ 5 = 1

Question 14.
$759.92 ÷ 42$ _____

About $18 Explanation:$759.92 is closer to $756$756 ÷ 42 = 18

Question 15.
157.5 ÷ 38
_____

Explanation:
157.5 is closer to 152
152 ÷ 38 = 4

Question 16.
379.2 ÷ 6
_____

Explanation:
379.2 is closer to 378
378 ÷ 6 = 63

Question 17.
108.4 ÷ 21
_____

Explanation:
108.4 is closer to 100
21 is closer to 20
100 ÷ 20 = 5

### Problem Solving – Page No. 212

Use the table to solve 18–20.

Question 18.
Estimate the average daily snowfall for Alaska’s greatest 7-day snowfall.
_____ inches

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:
_________

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:
_________

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:
_________

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

d. 3 inch

Explanation:
A plant grew 23.8 inches over 8 weeks.
23.8 is closer to 24
24 ÷ 8 = 3 inch

### Share and Show – Page No. 215

Write the quotient with the decimal point placed correctly.

Question 1.
4.92 ÷ 2 = 246
_____

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
_____

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)$$\overline { 8.65 }$$
_____

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)$$\overline { 2.52 }$$
_____

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)$$\overline { 97.2 }$$
_____

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

Divide.

Question 6.
6)$$\overline { 8.94 }$$
_____

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)$$\overline { 3.75 }$$
_____

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)$$\overline { 55.1 }$$
_____

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)$$\overline { 52.9 }$$
_____

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)$$\overline { 7.71 }$$$_____

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)$$\overline { 79.8 }$$
_____

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)$$\overline { 25.41 }$$
_____

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)$$\overline { 15.61 }$$
_____

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)$$\overline { 137.2 }$$
_____

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)$$\overline { 523.6 }$$
_____

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
■ = _____

6.05

Explanation:
■ ÷ 5 = 1.21
■ = 1.21 x 5
■ = 6.05

Question 19.
46.8 ÷ 1.2 = ■
■ = _____

39

Explanation:
46.8 ÷ 1.2 = ■
39 = ■

Question 20.
34.1 ÷ ■ = 22
■ = _____

1.55

Explanation:
34.1 ÷ ■ = 22
■ = 34.1 ÷ 22
■ = 1.55

### UNLOCK the Problem – Page No. 216

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:
_________

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:
_________

Division
Subtraction

Question 21.
c. Show the steps you used to solve the problem.
Type below:
_________

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:
_________

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

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 ### Mid-Chapter Checkpoint – Page No. 217 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 ÷ 100 = _______ 57.4 ÷ 101 = _______ 57.4 ÷ 102 = _______ Answer: 57.4 ÷ 100 = 57.4 57.4 ÷ 101 = 5.74 57.4 ÷ 102 = 0.574 Explanation: 57.4 ÷ 100 = 57.4 ÷ 1 = 57.4 57.4 ÷ 101 = 57.4 ÷ 10 = 5.74 57.4 ÷ 102 = 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 ### Mid-Chapter Checkpoint – Page No. 218 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 ### Share and Show – Page No. 221 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 ### Problem Solving – Page No. 222 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 ### Share and Show – Page No. 225 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 ### Problem Solving – Page No. 226 Use the table to solve 16—19. Question 16. Connie paid$1.08 for pencils. How many pencils did she buy?
_____ pencils

9 pencils

Explanation:
1 pencil = $0.12 Connie paid$1.08 for pencils.
$1.08 ÷$0.12 = 9

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

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 ### Share and Show – Page No. 229 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 ### Problem Solving – Page No. 230 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 ### Share and Show – Page No. 233 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:
_________

Question 1.
Then, work backward to find the cost of 2 DVDs.
Type below:
_________

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 $1.75 for a pen. She also bought 3 large erasers. If each eraser had the same cost, how much did she spend for each eraser?$ _____

$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 ### On Your Own – Page No. 234 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 $6.44 by buying the set instead of buying the individual CDs. If each CD costs the same amount, how much does each of the 3 CDs cost when purchased individually?$ _____

$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

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

### Chapter Review/Test – Page No. 235

Concepts and Skills

Complete the pattern.

Question 1.
341 ÷ 1 = ________
341 ÷ 10 = ________
341 ÷ 100 = ________
341 ÷ 1,000 = ________

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 = ________

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 ÷ 100 = ________
68.2 ÷ 101 = ________
68.2 ÷ 102 = ________

68.2 ÷ 100 = 68.2
68.2 ÷ 101 = 6.82
68.2 ÷ 102 = 0.682

Explanation:
68.2 ÷ 100 = 68.2 ÷ 1 = 68.2
68.2 ÷ 101 = 68.2 ÷ 10 = 6.82
68.2 ÷ 102 = 68.2 ÷ 100 = 0.682

Estimate the quotient.

Question 4.
49.3 ÷ 6 = _____

Explanation:
49.3 is closer to 48
48 ÷ 6 = 8

Question 5.
3.5 ÷ 4 = _____

Explanation:
3.5 is closer to 4
4 ÷ 4 = 1

Question 6.
396.5 ÷ 18 = _____

Explanation:
396.5 is closer to 396
396 ÷ 18 = 22

Divide.

Question 7.
6)$$\overline { 3.24 }$$ = _____

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)$$\overline { 6.55 }$$ = _____

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)$$\overline { 96.2 }$$ = _____

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 = _____

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 = _____

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 = _____

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 = _____

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 = _____

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 = _____

24.5

Explanation:
8.33 ÷ 0.34
8.33 x 100 = 833
0.34 x 100 = 34
833 ÷ 34 = 24.5

### Chapter Review/Test – Page No. 236

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

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

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

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

### Chapter Review/Test – Page No. 237

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

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

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

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 ### Chapter Review/Test – Page No. 238 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

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.

### Conclusion

We have given Go Math Grade 5 Answer Key Chapter 5 Divide Decimals here for free of cost. Learn the Simple Tricks and Tips to Solve Various Models on Divide Decimals. Step by Step Solutions is provided for all the Questions to make it easy for you to understand.

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