Basic Mathematics for College Students

Caution! Don’t confuse the concepts of the oppositeof a negative number

and the reciprocalof a negative number. For example:

The reciprocal of is 

The opposite of is

Divide fractions.

To develop a rule for dividing fractions, let’s consider a real-life application.

Suppose that the manager of a candy store buys large bars of chocolate and

divides each one into four equal parts to sell. How many fourths can be obtained from

5 bars?

We are asking, “How many ’ s are there in 5?” To answer the question, we need to

use the operation of division. We can represent this division as 5 

There are 20 fourths in the 5 bars of chocolate. Two observations can be made

from this result.

• This division problem involves a fraction: 5 


• Although we were asked to find 5  we solved the problem using
  multiplicationinstead ofdivision: 5  4 20. That is, division by (a fraction)
  is the same as multiplication by 4 (its reciprocal).

5 

1

4

 5 # 4

1

4

1

4 ,

1

4.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

We divide each bar

into four equal parts and

then find the total

number of fourths

5 ÷

1

• 4
  ChocolateChocolateChocolate

ChocolateChocolate

5 bars of chocolate Total number of fourths = 5 • 4 = 20

1

4.

1

4

2

9

16

.

9

16

16

9

.

9

16

234 Chapter 3 Fractions and Mixed Numbers

b.Fraction Reciprocal



invert

The reciprocal of is 

Check:

The product of two fractions with like

signs is positive.

c. Since 5  , the reciprocal of 5 is

Check: 5 #

1

5



5

1

#^1

5



5

1

# 1

1 # 5

1

 1

1

5

.

5

1



3

4

a

4

3

b

3

1

 4

1

4

1

 3

1

 1

4

3

.

3

4

4

3

3

4