Basic Mathematics for College Students

These observations suggest the following rule for dividing two fractions.

Dividing Fractions

To divide two fractions, multiply the first fraction by the reciprocal of the

second fraction. Simplify the result, if possible.

For example, to find  we multiply by the reciprocal of

Change the

division to

multiplication.

The reciprocal

of is.

Thus,  We say that the quotientof and is

20

21

.

3

4

5

7

20

21

.

3

4

5

7



20

21

Multiply the numerators.

 (^) Multiply the denominators.
5 # 4
7 # 3
4
3
3
4


5

7



3

4



5

7



4

3



3

4.

5

7

3

4 ,

5

7

3.3 Dividing Fractions 235

Self Check 2

Divide: 

Now TryProblem 17

7

8

2

3

Self Check 3

Divide and simplify: 

Now TryProblem 21

8

25

4

5

EXAMPLE 2

Divide: 

StrategyWe will multiply the first fraction, by the reciprocal of the second
fraction, Then, if possible, we will simplify the result.

WHYThis is the rule for dividing two fractions.

Solution

Multiply by the reciprocal of , which is

Since 5 and 12 have no common factors other than 1, the result is in simplest form.



5

12

Multiply the numerators.

Multiply the denominators.



1  5

3  4

5

4.

4

5

1

(^3)

1

3



4

5



1

3



5

4

4

5.

13 ,

4

5

1

3

EXAMPLE 3

Divide and simplify: 

StrategyWe will multiply the first fraction, by the reciprocal of the second
fraction, Then, if possible, we will simplify the result.

WHYThis is the rule for dividing two fractions.

3

20.

9

16 ,

3

20

9

16