Page 173 - Basic College Mathematics with Early Integers

Objectives 2.6 ORDER OF OPERATIONS

Simplify Expressions by Using the
Order of Operations.
Objective Simplifying Expressions
Evaluate an Algebraic Expression.
We first discussed the order of operations in Chapter 1. In this section, you are
Find the Average of a List of given an opportunity to practice using the order of operations when expressions
Numbers. contain signed numbers. The rules for the order of operations from Section 1.9 are
repeated here.

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.

Before simplifying other expressions, make sure you are confident simplifying
Examples 1 through 3.

PRACTICE 1–3 Examples Find the value of each expression.
Find the value of each 2
expression. 1. 1-32 = 1-321-32 = 9 The base of the exponent is -3.
4
2
1. 1-22 2. –3 =–(3)(3)=–9 The base of the exponent is 3.
2. -2 4 3. 2 5 = 2 15 52 = 2 25 = 50 The base of the exponent is 5.
# #
2
#
#
#
3. 3 6 2
Work Practice 1–3

When simplifying expressions with exponents, remember that parentheses make
an important difference.
2
2
1-32 and -3 do not mean the same thing.
2
1-32 means 1-321-32 = 9.
#
2
-3 means the opposite of 3 3, or -9.
Only with parentheses around it is the -3 squared.

-6122
PRACTICE 4 Example 4 Simplify:
-3
-25
Simplify: Solution: First we multiply -6 and 2.Then we divide.
5(-1)
-6122 -12
= Copyright 2012 Pearson Education, Inc.
-3 -3
= 4
Answers
Work Practice 4
1. 16 2. -16 3. 108 4. 5
150