Dividing Fractions and Mixed Numbers

Learn to divide fractions and mixed numbers.

Dividing Fractions and Mixed Numbers

Vocabulary

reciprocal

Look at the relationship between the

fractions and . If you switch the

numerator and denominator of a fraction,

you will find its reciprocal. Dividing by a

number is the same as multiplying by its

reciprocal.

34__ 4

3__

24 ÷ 4 = 6 24 • = 614__

Reciprocal

Check It Out: Example 1B

Find the reciprocal.

45__

45__ • = 1 Think: of what number is 1?

45__

54__4

5__ • = = 1

2020__ of is 1.

45__ 5

4__

The reciprocal of is .45__ 5

4__

Additional Example 2A: Using Reciprocals to Divide Fractions and Mixed Numbers

Divide. Write each answer in simplest form.

÷ 7 87__

87__ ÷ 7 = •

Rewrite as multiplication using the

reciprocal of 7, . 17__

Multiply by the reciprocal.

87

__ 17__

8 • 17 • 7____ =

The answer is in simplest form.

=

849__

Additional Example 2B: Using Reciprocals to Divide Fractions and Mixed Numbers

÷ 56__

56__ ÷ = •

Rewrite as multiplication using the

reciprocal of , . 32__

Simplify before multiplying.

56

__ 32__

5 • 36 • 2____ =

You can write the answer as a mixed number.

=

54__

23__

23__

23__

1

2

Multiply.

= 1

14__

Additional Example 2C: Using Reciprocals to Divide Fractions and Mixed Numbers

2 ÷ 1 34__

Write the mixed numbers as

improper fractions. 2 =

and 1 = 1312__

Rewrite as multiplication.

11 • 12

4 • 13______

=

You can write the answer as a mixed number.

=

3313__

112__

34__

1

3Simplify before multiplying.

= 2

713__

2 ÷ 1 = ÷3

4__ 1

12__ 11

4__ 13

12__ 11

4__

112__

11

4__ 12

13__ •

Multiply. =

Check It Out: Example 2A

Divide. Write each answer in simplest form.

÷ 3 23__

23__ ÷ 3 = •

Rewrite as multiplication using the

reciprocal of 3, . 13__

Multiply by the reciprocal.

23

__ 13__

2 • 13 • 3____ =

The answer is in simplest form.

=

29__

Check It Out: Example 2B

÷ 710__

710__ ÷ = •

Rewrite as multiplication using the

reciprocal of , . 51__

Simplify before multiplying.

710__ 5

1__

7 • 510 • 1____ =

You can write the answer as a mixed number.

=

72__

15__

15__

15__

1

2

Multiply.

= 3 12__

Check It Out: Example 2C

3 ÷ 1 23__

Write the mixed numbers as

improper fractions. 3 =

and 1 = . 109__

Rewrite as multiplication.

11 • 9

3 • 10______

=

You can write the answer as a mixed number.

=

3310__

19__

23__

1

3Simplify before multiplying.

= 3

310__

3 ÷ 1 = ÷2

3__ 1

9__ 11

3__ 10

9__ 11

3__

19__

11

3__ 9

10__ •

Multiply. =

Lesson Quiz

Find the reciprocal.

1. 2.

Divide. Write each answer in simplest form.

3. ÷ 20 4. 3 ÷ 2

5. Rhonda put 2 pounds of pecans into a -pound

bag. How many bags did Rhonda fill?

111__ 8

13__

47__ 1

2__ 1

2__

34__ 1

4__

111__ 13

8__

135__ 7

5 __ 2

5__, or 1

11 bags