Basic Mathematics for College Students

Solve application problems by dividing fractions.

Problems that involve forming equal-sized groups can be solved by division.

3

3.3 Dividing Fractions 237

Self Check 6

Divide and simplify:

(7)

Now TryProblem 33



35

16

Solution

Multiply by the reciprocal of which is

  3

Multiply the remaining factors in the numerator.

  (^) Multiply the remaining factors in the denominator.

3

1

To simplify, factor 18 as 36. Then remove the common

  (^) factor of 6 from the numerator and denominator.

1  3  6

1

6

1

 1



Multiply the numerators.

Multiply the denominators.

Since the fractions have unlike signs,

make the answer negative.

 

1 # 18

6 # 1

61  181 ,  181.

1

6

a

1

18

b

1

6

a

18

1

b

EXAMPLE 6

Divide and simplify: (3)

StrategyWe will multiply the first fraction, by the reciprocal of To
determine the sign of the result, we will use the rule for multiplying two fractions
that have the same (like) signs.

WHYBoth fractions are negative.

Solution

Multiply by the reciprocal of 3, which is

Multiply the remaining factors in the numerator:

(^1)  (^7)  1 7.
Multiply the remaining factors in the denominator:
36  1 36.



7

36

To simplify, factor 21 as 37. Then remove the common

 (^) factor of 3 from the numerator and denominator.

3

1

 7  1

36  3

1

Multiply the numerators.

Multiply the denominators.



21  1

36  3

Since the product of two negative fractions is

a positive, drop both signs and continue.

1

3

 b

21

36

  3621  31.

21

36

(3)

21

36

a

1

3

b

 2136 , 3.

21

36

EXAMPLE (^7) Surfboard Designs Most surfboards are made of a foam
core covered with several layers of fiberglass to keep them water-tight. How many
layers are needed to build up a finish of an inch thick if each layer of fiberglass
has a thickness of 161 of an inch?
3
8
Foam core
Finish:
3 – in. thick
8