1.3
Order of Operations
Goals p Use the order of operations to evaluate algebraic
expressions.
p Use a calculator to evaluate real-life expressions.
VOCABULARY
Order of operations
The rules established to evaluate an expression involving
more than one operation
Example 1
Evaluating Without Grouping Symbols
Evaluate the expression 4x2 3 when x 3.
Solution
4x2 3 4 p 3 2 3
Operations that
have the same
priority, such as
multiplication and
division or addition
and subtraction, are
performed using the
left-to-right rule, as
shown in Example 2.
Example 2
Substitute 3 for x.
4p 9 3
Evaluate power.
36 3
Evaluate product.
39
Evaluate sum.
Using the Left-to-Right Rule
a. 28 7 4 (28 7) 4
Work from left to right.
21 4
17
b. 15 9 3 4 15 (9 3) 4
Divide first.
15 3 4
(15 3 ) 4
Work from left to right.
18 4
14
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Chapter 1 • Notetaking Guide
6
ORDER OF OPERATIONS
1. First do operations that occur within grouping symbols .
2. Then evaluate powers .
3. Then do multiplications and divisions from left to right.
4. Then do additions and subtractions from left to right.
Example 3
Using a Fraction Bar
5p3
5p3
13 62 4
13 36 4
Evaluate power.
15
Simplify the numerator.
13 36 4
15
Work from left to right.
49 4
15
45
Subtract.
1
3
Simplify.
Checkpoint Evaluate the expression for the given value of
the variable.
1. 29 4b when b 6
5
42
2. 18 when c 7
c
12
Evaluate the expression.
4
3. 2 p 32 7
4
18
7
Copyright © McDougal Littell/Houghton Mifflin Company All rights reserved.
4. [22 (43 8)] p 3
42
Chapter 1 • Notetaking Guide
7
Using a Calculator
Example 4
When you enter the following in your calculator, does the calculator
display 8.7 or 4.3?
6.4
12.8
3.2
1.7
ENTER
Solution
a. If your calculator uses order of operations, it will display 8.7.
6.4 12.8 3.2 1.7 6.4 (12.8 3.2) 1.7
6.4 4 1.7
10.4 1.7
8.7
b. If your calculator displays 4.3, it performs the operations as they
are entered.
[(6.4 12.8) 3.2] 1.7 ( 19.2 3.2) 1.7
6 1.7
4.3
Checkpoint Two calculators were used to evaluate an
expression. The calculators gave different results. Which
calculator used the established order of operations? Rewrite
the expression with grouping symbols so that both calculators
give the correct result.
5. 6
12
4
4
ENTER
Calculator A: 0.5
Calculator B: 5
Calculator B; 6 (12 4) 4
6. 14
6
2
3
ENTER
Calculator A: 5
Calculator B: 12
Calculator A; 14 (6 2 3)
7. 4
6
24
3
ENTER
Calculator A: 0
Calculator B: 16
Calculator B; (4 6) (24 3)
Copyright © McDougal Littell/Houghton Mifflin Company All rights reserved.
Chapter 1 • Notetaking Guide
8