Page 221 - Basic College Mathematics with Early Integers

198 C HAPTE R 3 I FRACTIONS

Objective Dividing Fractions

Before we can divide fractions, we need to know how to find the reciprocal of a
fraction.

Reciprocal of a Fraction
the fraction is b a b a b
Two numbers are reciprocals of each other if their product is 1.The reciprocal of
#
a
#
#
b a because b a = b a = 1.
For example,
2 5 2 5 10
The reciprocal of is because # = = 1.
5 2 5 2 10
1 1 5 1 5
The reciprocal of 5 is because 5 # = # = = 1.
5 5 1 5 5
7 11 7 11 77
The reciprocal of - is - because - # - = = 1.
11 7 11 7 77

Every number has a reciprocal except 0.The number 0 has no reciprocal because
#
there is no number such that 0 a = 1.
Division of fractions has the same meaning as division of whole numbers. For
example,

10 , 5 means: How many 5s are there in 10?
10
There are two 5s in 10, so
10 , 5 = . 2
5 5
3 1 1 3
, means: How many s are there in ?
4 8 8 4
!

1 3 3 1
There are six s in , so , = . 6
8 4 4 8
ΩΩΩΩΩΩ

We use reciprocals to divide fractions.

Dividing Fractions
To divide two fractions, multiply the first fraction by the reciprocal of the sec-
ond fraction.
If a, b, c, and d represent numbers, and b, c, and d are not 0, then

#
a c a d a d Copyright 2012 Pearson Education, Inc.
, = # =
#
b d b c b c
c
reciprocal