Name

Practice

6-1

Fractions and Division Write a division expression for each fraction.

4. _38 7. _79

2.

1 _

5.

5 __

8.

18 __

6

12 25

1ⴜ6 5 ⴜ 12 18 ⴜ 25

Write each division expression as a fraction. 10. 7 ⫼ 12 13. 1 ⫼ 8 16. 5 ⫼ 9

__ 7 12 _ 1 8 _ 5 9

11.

2⫼ 5

14.

7 ⫼ 10

17.

11 ⫼ 21

_ 2

5 __ 7 10 __ 11 21

3. _27 3 6. __ 17 99 9. ___ 100

2ⴜ7 3 ⴜ 17 99 ⴜ 100

12. 8 ⫼ 11 15. 6 ⫼ 13 18. 13 ⫼ 100

Practice 6-1

4 ⴜ 10 3ⴜ8 7ⴜ9

4 1. __ 10

__ 8

11 __ 6 13 ___ 13 100

19. Zane was telling his mother that he learned about rational numbers in school. Which is the definition of a rational number? A Any number that can be shown as the quotient of two integers B Any number that can be shown as the product of two integers C Any number that can be written as an integer D Any integer that can be written as a decimal 20. Tanisha used the division expression 2 ⫼ 5 to equally divide two same-size pizzas among five people. Which fraction represents each person’s share of the pizza? A _52 B _25 C _27 D _57 21. Writing to Explain Can the division expression ⫺4 ⫼ 15 be shown as a fraction? If yes, write the fraction. Explain why or why not.

© Pearson Education, Inc. 6

Yes, both numbers are integers, so they can be ⴚ4 . written as the fraction ___ 15

Topic 6

23

Name

Reteaching

6-1

Fractions and Division

Write _58 as a division expression.

Write 3 ⴜ 8 as a fraction.

Think: _18 of 5 wholes.

Think: 3 wholes divided into 8 equal parts. Each part is equal to _38 .

0

5 8

1

2

3

4

5

0

3 8

1

2

3

Shortcut: The numerator is 5, so the dividend is 5. The denominator is 8, so the divisor is 8.

Shortcut: The dividend is 3, so the numerator is 3. The divisor is 8, so the denominator is 8.

So _58 ⫽ 5 ⫼ 8.

So 3 ⫼ 8 ⫽ _38.

Write a division expression for each fraction.

1ⴜ4

1. _14

2ⴜ5 5ⴜ7

2. _25 5. _57

1 4

0

3. _78 4 6. __ 15

7ⴜ8 4 ⴜ 15

1 3 4. __ 10 10 7. __ 13

Write each division expression as a fraction. 8. 4 ⫼ 5 11. 1 ⫼ 6

_ 4 5

9. 2 ⫼ 3

6

12. 9 ⫼ 10

_ 1

_ 2 3

10. 2 ⫼ 9

10

13. 11 ⫼ 12

__ 9

3 ⴜ 10 10 ⴜ 13 _ 2 9

__ 11 12

14. Writing to Explain Explain how to write seventeen divided by twenty as a division expression and as a fraction.

Sample answer: Write symbols for the words: 17 ⴜ 20. Use the dividend as the numerator and the divisor as the denominator to write a 17 . fraction: __ 20

22

Topic 6

© Pearson Education, Inc. 6

Reteaching 6-1

You can think of fractions as division: The numerator is the same as the dividend and the denominator is the same as the divisor.

Name

Practice

6-2

Fractions and Decimals Write a decimal and a fraction in simplest form for each shaded portion. 1.

2.

21 0.21, ___ 100

1 0.1, __ 10

Write each decimal as a fraction in simplest form.

6. 0.27

20

___ 27 30422_T08_8-2PR-1 100

4. 0.31 7. 0.375

___ 31

_ 3

100

5. 0.82 30422_T08_8-2PR-2

8

8. 0.920

__ 41 __ 23

Practice 6-2

3. 0.15

__ 3

50

25

Convert each fraction to a decimal. 56 9. ___ 100 8 12. __ 50

0.56 0.16

90 10. ___ 200 57 13. __ 60

0.45 0.95

9 11. __ 25

14. _78

0.36 0.875

46 on the hundredths 15. Draw a Picture Show ___ 200 grid. Then write the fraction as a decimal.

0.23

16. About _25 of the students in the after school program have a cell phone. Which decimal is equivalent to _25 ? A 0.2 B 0.25 C 0.4 D 0.5

30422_T08_8-2PR-3

© Pearson Education, Inc. 6

17. Writing to Explain Solve the problem. Then explain how you 12 of the students are found the answer. In Tori’s favorite class, __ 25 girls. Write a decimal that represents the number of boys in the class.

12 as a decimal, 0.52; Sample answer: I wrote __ 25 0.48, and then I subtracted the decimal from 1: 1 2 0.48 5 0.52.

Topic 6

29

Name

Reteaching

6-2

Fractions and Decimals A fraction and a decimal can both be used to represent the same value. Write 0.35 as a fraction.

3 as a decimal. Write __ 25

Write the decimal as a fraction with a denominator of 10, 100, 1000, or another power of ten.

Method 1: Write an equivalent fraction with a denominator of 10, 100, 1000, or another power of ten. Then write the decimal.

Then write the fraction in simplest form.

3 = _____ 3 × 4 = ___ 12 = 0.12 __ 25 25 × 4 100

Method 2: Divide the numerator by the denominator.

35 = ______ 35 ⫼ 5 = __ 7 ___ 100 100 ⫼ 5 20 7. So 0.35 = __

0.12 177 25 3.00 2 5 50  50 0

3 = 0.12. So __ 25

20

Write a decimal and a fraction in simplest form for each shaded portion. 1.

2.

0.6, _35

7 0.28, __ 25

Write each decimal as a fraction in simplest form.

_ 1 2 _ 1 4

3. 0.5 6. 0.25

_ 4

4.

0.8

7.

0.125

5 _ 1 8

__ 9 5. 0.36 8. 0.070

25 ___ 7 100

Convert each fraction to a decimal. 93 9. ___ 100 14 12. __ 25

0.93 0.56

10.

7 __

13.

7 __

10 40

0.7 0.175

11 11. __ 20 6 14. ___ 100

0.55 0.06

15. Geometry Draw eight congruent figures. Shade some of the figures to make a color pattern. Write a decimal and a fraction in simplest form to represent the shaded part of the set.

28

Sample answer: Four squares shaded, four squares not shaded, 0.5, _12 Topic 6

© Pearson Education, Inc. 6

Reteaching 6-2

35 0.35 = 35 hundredths = ___ 100

Name

Practice

6-3

Improper Fractions and Mixed Numbers 1. Draw a picture to show _97 .

2. Draw a picture to show 3_45.

Check students’ drawings. Write each improper fraction as a whole number or mixed number in simplest form.

5

25 3. __ 5

5_29

47 4. __ 9

52 5. __ 7

Write each mixed number as an improper fraction.

__ 55

7. 13_34

5

8. 9_58

4

__ 77

Practice 6-3

__ 24

6. 4_45

7_37 8

__ 32

9. Reasoning Write 8 as an improper fraction with a denominator of 4.

4

Which letter on the number line corresponds to each number? F 4

10. 5_25

A C

D

B 5 7 11. 4__ 10

D

E

C

6 23 12. __ 5

A

13. Which number does the picture show?

12 A __ 8

B 2_18 C 2_14 20 D __ 8

© Pearson Education, Inc. 6

14. Writing to Explain Can you express _99 as a mixed number? Why or why not?

No, _99 can be expressed only as a fraction or as a whole number (1).

Topic 6

35

Name

Reteaching

6-3

Improper Fractions and Mixed Numbers A mixed number combines a whole number with a fraction. It is greater than one. An improper fraction has a numerator that is larger than its denominator.

How to Write an Improper Fraction as a Mixed Number

The quotient is the whole number in the mixed number.

2 2 5

2 5 12 10 2

The remainder is the numerator. The denominator stays the same.

Multiply the denominator by the whole number.

3 

2 5

5  3  15 Then add the numerator. 15  2  17

17 5

Write this number for the numerator. Use the original denominator.

3

2 12 2 5 5

2 17  5 5

1. Draw a picture to show 4_23.

Write each improper fraction as a whole number or mixed number in simplest form. 60 2. __ 40

1_12

3 3__ 10

30422_T08_8-3RT1

33 3. __ 10

12 4. __ 7

Write each mixed number as an improper fraction. 5. 4_13

__ 13 3

20 6. 1__ 50

__ 70 50

8. Reasoning Write 6 as an improper fraction with a denominator of 10.

30422_T08_8-3RT-1a

34

Topic 6

7. 8_78

1_57 __ 71 8

__ 60 10

© Pearson Education, Inc. 6

Reteaching 6-3

12 Write 5 as a mixed number. Divide the numerator by the denominator.

How to Write a Mixed Number as an Improper Fraction

Name

Practice

6-4

Decimal Forms of Fractions and Mixed Numbers Write each fraction or mixed number as a decimal. 33 1. ___ 100 3 4. 1__ 16

.33 1.1875

2. _25 5. 4_79

0.4 4.7

3. _16 5 6. 6__ 11

Write each decimal as a fraction or a mixed number in simplest form.

__ 2

7. 0.08 10. 4.75

25 4_34

__ 6

8. 0.24 11. 1.06

25 3 1__ 50

9. 0.325 12. 5.15

0.16 6.45 __ 13

40 3 5__ 20

__ 1 25 oz.

14. The scale at a deli counter shows 2.54 lb. What is the mixed number equivalent for the number shown?

27 lb. 2__ 50

Practice 6-4

13. The label on a cosmetic bottle says 0.04 oz. What is the fraction equivalent for this amount?

15. Reasoning What is a situation in which you would use fractions to express a number less than one? What is a situation in which decimals seem to work better?

Sample answers: Only _13 of the cars are red; Sara’s batting average is .324.

16. Which decimal is equivalent to 4_45? A 4.4 B 4.45 C 4.5 D 4.8 17. Writing to Explain How do you know where to place the bar when a decimal is a repeating decimal?

© Pearson Education, Inc. 6

Sample answer: Place the bar over the number or numbers that repeat.

Topic 6

41

Name

Reteaching

6-4

Decimal Forms of Fractions And Mixed Numbers How to Convert Fractions to Decimals

How to Convert Decimals to Fractions

Write _59 as a decimal.

Write 0.65 as a fraction.

Divide the numerator by the denominator. Annex zeros if necessary.

65 0.65 ⫽ 65 hundredths ⫽ ___ 100 65 in simplest form. Write ___ 100 65 ⫽ ______ 65 ⫼ 5 ⫽ __ 13 ___ 100 100 ⫼ 5 20 13 __ So, 0.65 ⫽

.

20

Write 3.375 as a mixed number. 3.375 ⫽ 3 ⫹ 0.375 375 ⫽ _________ 375 ⫼ 125 ⫽ _ 3 ____ 1,000 1000 ⫼ 125 8 3 3 _ _ 3⫹ ⫽3

The decimal 0.555 is a repeating decimal. Place a bar over the repeating digit.

8

8

So, 3.375 ⫽ 3_38 .

So, _59 ⫽ 0.5.

Write each fraction or mixed number as a decimal. 1. _13 4. 2_14

0.3 2.25

20 2. ___ 100

5. 5_18

0.2 5.125

6 3. __ 10

6. 1_49

Write each decimal as a fraction or a mixed number in simplest form.

_ 2

7. 0.4 10. 3.2

_ 5

5

3_1 5

8. 0.625 11. 2.18

8

9 2__ 50

9. 0.45 12. 4.68

0.6 1.4 __ 9

20 17 4__ 25

13. Number Sense The Lady Bug trail in Sequoia National Forest is 5.1 miles long. How does it compare to a trail that is 5_25 miles long?

Sample answer: 5_25 converts to 5.4, so the Lady Bug trail is the shorter of the two trails.

© Pearson Education, Inc. 6

Reteaching 6-4

375 0.375 ⫽ 375 thousandths ⫽ ____ 1,000

40

Topic 6

Name

Practice

6-5

Problem Solving: Draw a Picture 1. A community swimming pool places buoys every 1.5 feet across the pool to mark off swimming areas. Use your ruler and the number line to show where each buoy is placed.

0

1.5 3 4.5

6

7.5 9 10.5 12 13.5 15 16.5 18 feet

2. A trail is marked every 0.6 mile. Use the number line below to show the start of the trail if the trail is 5.4 miles long. 30422_T08_8-6PR-1a

30422_T08_8-6PR-1

1.8

Start of trail

End of trail miles

30422_T08_8-6PR-2 30422_T08_8-6PR-2a

0 0.75

2.25

feet

Practice 6-5

3. A conveyer belt at a factory moves parts from station to station. The stations are 0.75 feet apart. Draw and label a number line that shows stops at 0.75, 2.25, and 4.5 feet.

4.5

4. Kayla drew the number line to show the distance between Fontana and Rialto. If Fontana is 0, what is the label at Rialto?

Fontana

1.2

2

30422_T08_8-6PR-3aRialto

miles

A 4.2 B 4.4 C 4.8

30422_T08_8-6PR-4

© Pearson Education, Inc. 6

D 5.2 5. Writing to Explain Maggie is planting bushes every 1.5 feet along the side of a fence. The fence is 22.5 feet long. Explain how Maggie can draw a picture to show where each bush is planted.

Sample answer: She can draw a number line starting at 0 and ending at 22.5 with each unit on the number line representing 1.5 feet, for a total of 15 units. Topic 6

47

Name

Reteaching

6-5

Problem Solving: Draw a Picture Sometimes you need to draw a picture to solve a problem. Jasmine is making a charm bracelet. She wants to put a charm every 0.5 inch on the bracelet. The bracelet is 6 inches long. Use a ruler and the number line below to mark and label the place for each charm. 0

2

6 inches

Read and Understand You know the length of the bracelet and where to place each charm. You know the length of the number line.

Measure the number line to divide it into equal units of 0.5. 0

Plan and Solve

0.5

1 1.5

2

Divide the line from 0 to 2 into fourths to show 0.5, 1, and 1.5. Use each unit of 0.5 to mark and label the rest of the number line.

0

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.56 inches

Draw a picture to solve the problems. 1. A neighborhood has speed bumps every 0.25 miles along the main road. Use your ruler and the number line to mark and label the place of each speed bump. 0

0.25

0.5

0.75

1

1.25

1.5

miles

2. A path between neighborhoods is 0.7 miles long. Mark and label the end of the path on the number line below. Path starts

0.2 miles

46

Topic 6

Path ends

© Pearson Education, Inc. 6

Reteaching 6-5

You need to mark and label each 0.5 unit on the number line.

bracelet = 6 inches charm = every 0.5 inches number line = labels at 0, 2, and 6