Basic Mathematics for College Students

Because of the relationship between multiplication and division, the sign rules for

dividingfractions are the same as those for multiplyingfractions.

236 Chapter 3 Fractions and Mixed Numbers

Self Check 5

Divide and simplify:



Now TryProblem 29

a

7

6

b

2

3

Solution

Multiply by the reciprocal of which is

Multiply the remaining factors in the numerator: 1 3  1  5  15

 (^) Multiply the remaining factors in the denominator: 1  4  1 4.

15

4

To simplify, factor 9 as 3 3, factor 20 as 4 5, and factor

16 as 4 4. Then remove out the common factors of 3 and 4

from the numerator and denominator.



3

1

 3  4

1

 5

4

1

 4  3

1

Multiply the numerators.

 (^) Multiply the denominators.

9  20

16  3

20

3.

3

20 ,

9

(^16)

9

16



3

20



9

16



20

3

EXAMPLE 4

Divide and simplify:

StrategyWe will write 120 as a fraction and then multiply the first fraction by the

reciprocal of the second fraction.

WHYThis is the rule for dividing two fractions.

Solution

Write 120 as a fraction:

Multiply by the reciprocal of which is

 84 Any whole number divided by 1 is the same number.

Multiply the remaining factors in the numerator: 1 12  7 84.

 Multiply the remaining factors in the denominator: 1 1 1.

84

1

To simplify, factor 120 as 1012, then remove the common

 factor of 10 from the numerator and denominator.

10

1

 12  7

1  10

1

Multiply the numerators.

 Multiply the denominators.

120  7

1  10

7

10.

10

7 ,

120

 1

120

1



7

10

120  120 ^1201.

10

7



120

1



10

7

120 

10

7

Self Check 4

Divide and simplify:

Now TryProblem 27

80 

20

11

EXAMPLE 5

Divide and simplify: 

StrategyWe will multiply the first fraction, by the reciprocal of the second

fraction, To determine the sign of the result, we will use the rule for

multiplying two fractions that have different (unlike) signs.

WHYOne fraction is positive and one is negative.

 181.

1

6 ,

a

1

18

b

1

6