Understanding Division of Fractions - Weebly

Name

Reteaching

9-1

Divide a fraction by a whole number.

Find _18 4 4.

Use a model to show _18 .

Divide each eighth into 4 equal parts.

1

1.

5 __

Each section shows _____

32

(8 3 4)

1 4 4 5 __

1.

_

8

32

1 1 1 1 1 1 1 1

8 8 8 8 8 8 8 8

1

32

Divide a fraction by a fraction.

Find _34 4 _14.

Use a number line.

Count the number of _14s in _34.

0

1

4

2

4

3

4

Use repeated subtraction.

Subtract _14 from _34 until the difference

is 0.

3 2_

1 5_

2

_

4

4

4

2 2_

1 5_

1

_

1

4

4

4

1 2_

1 50

_

4

4

Count the number of times you

subtracted to find the quotient.

3 4 _

1 53

_

4

4

There are three _14s.

3 4_

1 53

_

4

4

Solve each division sentence. Use a model if you wish.

1. 3 4 _13 5

9

2. _15 4 4 5

__

1

20

Find each quotient. Simplify if possible.

3. 3 4 _12 5

3 4 __

1 5

6. __

16

16

9. 8 4 _14 5

6

3

32

9

5 4 _13 5 15

7 4 __

1 5

__

7

12

12

9 4 __

1 5

4. __

10

10

5. _15 4 3 5

7.

8. _12 4 6 5

10.

11. _67 4 _17 5

__

1

15

__

1

12

6

12. Draw a Picture The square dancing club meets for 3 hours. Every _34 hour, the

dancers change partners. How many different partners will each dancer have in one

meeting? Draw a picture to show your solution.

3 4 _34 5 4; 4 partners. Check students¡¯ drawings.

13. Writing to Explain Explain why the quotient of two fractions less

than 1 is always greater than either fraction.

The quotient is always greater than the fractions because

you are dividing by a number less than one.

26

Topic 9

? Pearson Education, Inc. 6

Reteaching 9-1

Understanding Division of

Fractions

Name

Practice

9-1

Understanding Division of

Fractions

Solve each division sentence using the models provided.

9

1. 3 ? _13 =

1

2

1

4

3

4. 8 ? _14 ?

7. _78 ? _18 ?

10. 6 ? _23 ?

1

6

0

Find each quotient. Simplify if possible.

32

7

__

1

5. _17 ? 4 ?

11 ? __

1 ?

8. __

12

12

9

11. 7 ? _13 ?

5

3. _56 ? _16 ?

24

2

6

3

6

4

6

28

6. 5 ? _12 ?

10

11

1 ?3?

9. __

12

36

21

15 ? __

1 ?

12. __

16

16

Practice 9-1

0

__

1

2. _14 ? 6 ?

5

6

__

1

15

13. Draw a Picture Olivia has a piece of ribbon _12 yard long. If she cuts it

into 6 equal pieces, what will be the length of each piece, in yards?

1 yard

Check students pictures: __

12

14. Geometry A regular polygon has a perimeter of 12 units. If each

side measures _34 unit, how many sides does the polygon have?

16

15. Which division expression is

shown by this model?

1

2

3

4

5

6

7

8

9

10

0

9 ? __

1

A __

10

10

9

1

B 1? __

10

9

D 10 ? __

10

9 ?1

C __

10

? Pearson Education, Inc. 6

16. Writing to Explain When you divide a whole number by a fraction

less than 1, will the quotient be greater than or less than the whole

number? Explain, and give an example.

The quotient will be greater because you are

dividing by a number less than 1. 4 ¡Â _13 = 12:

There are more fraction parts than wholes.

1

2

3

4

5

6

1

7

2

1

Each section  3

8

9

10

11

12

3

Topic 9

27

Name

Reteaching

9-2

Dividing a Whole Number by

a Fraction

Number



Reciprocal



Product

3



1

_



1

1

_





1



1

8

2

_

3

3

8

_

1

3

_

2



Find 14  _47.

Step 1

Step 2

Step 3

Rewrite the division as

multiplication using the

reciprocal of the divisor.

Divide out common factors

if possible. Then multiply.

If your answer is an

improper fraction, change it

to a mixed number.

The reciprocal of _47 is _74 .

14

__

7

1

 _74



49

__

2

49  24_

1

__

2

2

2

14 ¡Â _47 = 14 ¡Á _74

Find the reciprocal of each fraction or whole number.

_7

5

1. _57

2. 11

__

1

11

3. _92

_2

9

Find each quotient. Simplify if possible.

4. 12  _45

7. 24  _34

10. 36  _89

15

32

40_12

5. 2 ¡Â _14

8. 18  _89

11. 42  _78

8

20_14

48

8

6. 16 ¡Â __

10

10

9. 25 ¡Â __

11

12. 40 ¡Â _45

20

27_12

50

13. Karolyn makes rolls for a friend¡¯s dinner party. She uses 3 lb of

butter. Each stick of butter weighs _14 lb. How many sticks of butter

does Karolyn need to make her rolls?

12 sticks

32

Topic 9

? Pearson Education, Inc. 6

Reteaching 9-2

To divide a whole number by a fraction, you can multiply the whole

number by the reciprocal of the fraction. The reciprocal of a number

has the numerator and the denominator reversed. The product of a

number and its reciprocal is 1.

Name

Practice

9-2

Dividing a Whole Number by

a Fraction

Find the reciprocal of each fraction or whole number.

_9

1. _59

5

2. 8

_1

3. _73

8

Find each quotient. Simplify if possible.

24

42 4 _79 5 54

_

22 4 _56 5 26 2

5

15 4 _13 5 45

48

10 4 _56 5 12

_

7 4 _23 5 10 1

2

6 4 _15 5 30

4. 8 4 _25 5

5. 4 4 _16 5

6. 18 4 _38 5

7.

8.

9.

10.

13.

11.

14.

12.

15.

7

Practice 9-2

20

12 4 _12 5 24

_

20 4 _34 5 26 2

3

9 4 _18 5 72

_3

16. Writing to Explain Will the quotient of 5 4 _78 be greater than or less

than 5? Explain.

The quotient will be greater than 5 because you are

dividing by a number that is less than 1.

17. Reasoning How many times will you need to fill a _12 cup

measuring cup to measure 4 cups of flour?

8

18. Geometry The distance around a circular flower bed is 36 feet.

Jasper wants to put stakes every 8 inches ( _23 of a foot) around the

bed. How many stakes does he need?

54 stakes

19. Algebra Which expression is equal to 9 3 _32 ?

A 2 4 _39

B 3 4 _92

C 9 4 _23

? Pearson Education, Inc. 6

D 9 4 _32

Topic 9

33

Name

Reteaching

9-3

Dividing Fractions

To divide by a fraction, you can multiply by its reciprocal. The reciprocal

of a number has the numerator and the denominator reversed.

Step 1

Step 2

Step 3

Rewrite the division as

multiplication using the

reciprocal of the divisor.

Divide out common factors

if possible. Then multiply.

If your answer is an

improper fraction, change it

to a mixed number.

3 is __

10 .

The reciprocal of __

10

3

4

_

2

5

1

3 _

10

4  __

4 ¡Á __

_

5

5

10

3



10

___

3



3

Find each quotient. Simplify if possible.

4

1. _12  _14  _12 



2

8 =

2. _47  __

21

Reciprocal of _14

3. _13  _12

6. _37  3

9. _59  _12

9 _

4

12. __

5

10

_2

3

4. _25 ¡Â _23

7

7. _13  _89

_1

1_19

1_18

10. _35  _34

13. _13  _38

8  2_

2

_

3

3

8

_

_3

_4

7



__

21

8

1_12

8

Reciprocal of __

21

5

7

5. _58 ¡Â __

10

8

_4

5

_8

9

8. _56 ¡Â _18

_3



11. _34 ¡Â _56

14. _47 ¡Â _34

__

25

28

6_23

__

9

10

__

16

21

3 -gallon servings

15. Aaron has _78 gallon of bottled water. How many __

16

can he pour?

4_23 servings

16. Draw a Picture Show how Rebecca can divide _34 of a cake into

9 pieces. What fraction of the whole cake will each piece be?

1

Sample answer: Each piece is __

12 of

the cake.

? Pearson Education, Inc. 6

Reteaching 9-3

3.

Find _45 ¡Â __

10

38

Topic 9

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