1.3 Order of Operations

GOAL 1Use the order of operations to evaluate algebraic expressions.

GOAL 2 Use a calculator to evaluate real-life expressions such as calculating sales tax.

What you should learn

To solve real-life problems, such as calculating the cost of admission for a family to a state fair.

Why you should learn it

GOAL 1 USING THE ORDER OF OPERATIONS

WHAT IS THE ORDER OF OPERATIONS?

It’s the method we use to evaluate an expression involving more than one operation:

1.

2.

3.

4.

1.3 Order of Operations

Grouping symbols (innermost first, work to the outermost)

Powers

Multiplication and division

Addition and subtraction

left to right

left to right

Extra Example 1

Evaluate the expression when x = 3.

1. 2. 227 3x 24 8x 24(3) 8

4(9) 8

36 828

227 3 3

27 9 3 3 3

6

EXAMPLE 2

What happens when operations that have the same priority appear in the same expression, such as 5 – 4 +1?

Perform the operations fromleft to right!

5 – 4 + 1

1 + 1

2

5 – 4 + 1

5 – 5

0

Which is correct?

1. Perform operations within grouping symbols, beginning with the innermost first.

2. Simplify powers.

3. Multiply and divide from left to right.

4. Add and subtract from left to right.

ORDER OF OPERATIONS

Summary

EXAMPLE 3

Extra Example 3

24 3

5 9 2

72

5 9 2

72

14 2

72

12

6

Simplify the expression. Click to see each step.

2

24 3

5 3 2

Simplify the power.

Simplify the numerator.

Work from left to right.

Subtract.

Simplify.

Hint: The fraction bar serves as a grouping symbol. Simplify the numerator and denominator separately before the final step.

Checkpoint1. Evaluate the expression when x = 5.

a. 2x2 + 8 b. 100 ÷ x2 + 6

2. Simplify the expression.

a. 25 + 10 – 8 b. 24 ÷ 2 • 3 c. 36 – 6 ÷ 3 + 3

3. Simplify the expression.

2

16 2 8

10 2 4

58 10

27 36 37

4

GOAL 2 EVALUATING EXPRESSIONS WITH A CALCULATOR

EXAMPLE 5

The point: YOU must know how your calculator works. Be sure you work through the examples and understand

YOUR calculator.

1.3 Order of Operations

EXAMPLE 4

Checkpoint

Simplify each expression using your calculator. Identify the order in which the operations are performed.

1.

2.

3.

10.5 4.2 1.4 3.5

(10.5 4.2) 1.4 3.5

(10.5 4.2) (1.4 3.5)

11; division, subtraction, addition

8; subtraction, division, addition

≈1.29; subtraction, addition, division

QUESTIONS?