Page 258 - Basic College Mathematics with Early Integers

S E C T I O N 3.6 I COMPLEX FRACTIONS, ORDER OF OPERATIONS, AND MIXED NUMBERS 235
4
- 2
5
Example 4 Simplify: PRACTICE 4
3
3
10
Solution: Use the second method and multiply the numerator and the Simplify: 4
denominator of the complex fraction by the LCD of all fractions. Recall that 3
2 5 - 1
2 = . The LCD of the denominators 5, 1, and 10 is 10.
1
4 2 4 2
- 10a - b Don’t forget to
5 1 5 1
= Multiply the numerator and denominator by 10. multiply the numerator and
3 3 the denominator of the com-
10a b
10 10 plex fraction by the same
number—the LCD.
2 4 2
a10 # b - a10 # b
5 1 1 Apply the distributive property.Then divide
=
1 3 out common factors to aid in multiplying.
10 #
10
1
8 - 20
= Multiply.
3
-12
= =-4 Simplify.
3
Work Practice 4

Objective Reviewing the Order of Operations

At this time, it is probably a good idea to review the order of operations on expres-
sions containing fractions. Before we do so, let’s review how we perform operations
on fractions.
Review of Operations on Fractions
Operation Procedure Example
Multiply Multiply the numerators and 5 1 5 # 1 5
#
multiply the denominators. 9 2 = 9 2 = 18
#
Divide Multiply the first fraction by the 2 11 2 13 2 # 13 26
#
reciprocal of the second fraction. 3 , 13 = # = 3 11 = 33
3 11
Add or 1. Write each fraction as an equivalent
Subtract fraction whose denominator is the LCD. 3 1 3 2 1 6 1 7
#
+ = + = + =
2. Add or subtract numerators and write the 4 8 4 2 8 8 8 8
result over the common denominator.
Now let’s review the order of operations.
Order of Operations
1. Perform all operations within parentheses ( ), brackets [ ], or other grouping
symbols such as fraction bars or square roots, starting with the innermost set.
2. Evaluate any expressions with exponents.
3. Multiply or divide in order from left to right.
4. Add or subtract in order from left to right.

4 2
Example 5 Simplify: a b - 1 PRACTICE 5
5
2 3
4 2 Simplify: a b - 2
Solution: According to the order of operations, first evaluate a b . 3
5
Answers
4 2 16 4 2 16 15 46
a b - 1 = - 1 Write a b as . 4. - 5. -
5 25 5 25 Continued on next page 8 27