Basic Mathematics for College Students

3.3 Dividing Fractions 233

We will now discuss how to divide fractions. The fraction multiplication skills that you
learned in Section 3.2 will also be useful in this section.

Find the reciprocal of a fraction.

Division with fractions involves working with reciprocals.To present the concept of
reciprocal, we consider the problem

Any whole number divided by 1 is equal to that number.

The product of and is 1.
Whenever the product of two numbers is 1, we say that those numbers are
reciprocals.Therefore, and are reciprocals. To find the reciprocal of a fraction,we
invert the numerator and the denominator.

Reciprocals

Two numbers are called reciprocalsif their product is 1.

Caution! Zero does not have a reciprocal, because the product of 0 and a

number can never be 1.

8

7

7

8

8

7

7

8

 1

Multiply the remaining factors in the numerator.

Multiply the remaining factors in the denominator.



1

1

To simplify, remove the common factors of

 (^) 7 and 8 from the numerator and denominator.

7

1

# 8

1

8

1

# 7

1

Multiply the numerators.

(^) Multiply the denominators.

7

8

#^8

7



7 # 8

8 # 7

7

8 

8

7.

1

SECTION 3.3

Dividing Fractions

Objectives

1 Find the reciprocal of a fraction.

2 Divide fractions.

3 Solve application problems by

dividing fractions.

EXAMPLE (^1) For each number, find its reciprocal and show that their
product is 1: a. b. c. 5
StrategyTo find each reciprocal, we will invert the numerator and denominator.
WHYThis procedure will produce a new fraction that, when multiplied by the
original fraction, gives a result of 1.
Solution
a.Fraction Reciprocal
invert
The reciprocal of is.
Check:

2

3

#^3

2



2

1

# 3

1

3

1

# 2

1

 1

3

2

2

3

3

2

2

3

3

4

2

3

Self Check 1

For each number, find its

reciprocal and show that their

product is 1.

a. b. c. 8

Now TryProblem 13

5

6

3

5