Page 257 - Basic College Mathematics with Early Integers

234 C HAPTE R 3 I FRACTIONS

Thus,

1 3 7
+
2 8 8
=
3 1 7
-
4 6 12
7 7
= , Rewrite the quotient using the , sign.
8 12
7 12
= # Multiply by the reciprocal.
8 7
1 1
# #
7 3 4
= Multiply.
# #
2 4 7
1 1
3
= Simplify.
2
Work Practice 2

Method 2 for Simplifying Complex Fractions
The second method for simplifying complex fractions is to multiply the numerator
and the denominator of the complex fraction by the LCD of all the fractions in its
numerator and its denominator.This has the effect of leaving sums and differences of
integers in the numerator and the denominator, as we shall see in the example below.
Let’s use this second method to simplify the complex fraction in Example 2 again.
1 3
+
2 8
PRACTICE 3 Example 3 Simplify:
3 1
Use Method 2 to simplify: -
4 6
1 1
+ Solution: The complex fraction contains fractions with denominators 2, 8, 4, and
2 6
6.The LCD is 24. By what we can call the fundamental property of fractions, recall
3 2
- that we can multiply the numerator and the denominator of the complex fraction
4 3 by 24. Notice below that by the distributive property, this means that we multiply
each term in the numerator and denominator by 24.
1 3 1 3
+ 24a + b
2 8 2 8
=
3 1 3 1
- 24a - b
4 6 4 6
12 1 3 3
a 24 # b + a24 # b
2 1 8 1 Apply the distributive property.Then divide out
=
6 3 4 1 common factors to aid in multiplying.
a24 # b - a24 # b
4 6
1 1
12 + 9
= Multiply.
18 - 4
21
=
14
1
#
7 3 3
= = Simplify.
#
7 2 2 Copyright 2012 Pearson Education, Inc.
1
Answer Work Practice 3
8
3. or 8 The simplified result is the same, of course, no matter which method is used.
1