Page 256 - Basic College Mathematics with Early Integers

COMPLEX FRACTIONS, ORDER OF OPERATIONS, AND Objectives
3.6 MIXED NUMBERS
Simplify Complex Fractions.

Objective Simplifying Complex Fractions Review the Order of Operations.

Thus far, we have studied operations on fractions.We now practice simplifying frac- Evaluate Expressions Given
tions whose numerators or denominators themselves contain fractions. These frac- Replacement Values.
tions are called complex fractions.
Write Mixed Numbers as
Improper Fractions.
Complex Fraction
Write Improper Fractions as
A fraction whose numerator or denominator or both numerator and denomi- Mixed Numbers or Whole
nator contain fractions is called a complex fraction. Numbers.

Examples of complex fractions are

1 1 3 4
+ - 2
4 2 8 5

3 3 1 3
-
2 4 6 10
Method 1 for Simplifying Complex Fractions
Two methods are presented to simplify complex fractions. The first method makes
use of the fact that a fraction bar means division.
1
4
Example 1 Simplify: PRACTICE 1
3
7
2
1 10
Simplify:
4 1
Solution: Since a fraction bar means division, the complex fraction can be
1 3 3 5
written as , . Then divide as usual to simplify. 2
4 2
1 3 1 2
, = # Multiply by the reciprocal.
4 2 4 3
1
#
1 2
=
# #
2 2 3
1
1
=
6
Work Practice 1
1 3
+
2 8
Example 2 Simplify: PRACTICE 2
3 1
- 1 1
4 6 +
2 6
Solution: Recall the order of operations. Since the fraction bar is considered a Simplify: 3 2
grouping symbol, we simplify the numerator and the denominator of the complex -
4 3
fraction separately.Then we divide.
#
1 3 1 4 3 4 3 7
+ + +
#
2 8 2 4 8 8 8 8
= = = Answers
#
#
3 1 3 3 1 2 9 2 7 7 8
- - - 1. 2. or 8
#
#
4 6 4 3 6 2 12 12 12 Continued on next page 2 1
233