1. 1.3 What you should learn Why you should learn it Order of Operations
GOAL 1
Use the order of operations to evaluate algebraic expressions.
GOAL 2
Use a calculator to evaluate real-life expressions such as calculating sales tax.
Why you should learn it
To solve real-life problems, such as calculating the cost of admission for a family to a state fair.

2. 1.3 Order of Operations 1 GOAL 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.
Grouping symbols (innermost first, work to the outermost)
Powers
Multiplication and division
Addition and subtraction
left to right
left to right

3. Extra Example 1
Evaluate the expression when x = 3.

4. Perform the operations from
What happens when operations that have the same priority appear in the same expression, such as 5 – 4 +1?
5 – 4 + 1
1 + 1 2
5 – 4 + 1
5 – 5
Which is correct?
Perform the operations from
left to right!
EXAMPLE 2

5. Summary ORDER OF OPERATIONS
Perform operations within grouping symbols, beginning with the innermost first.
Simplify powers.
Multiply and divide from left to right.
Add and subtract from left to right.
EXAMPLE 3

6. Extra Example 3 Simplify the expression. Click to see each step.
Hint: The fraction bar serves as a grouping symbol. Simplify the numerator and denominator separately before the final step.
Simplify the power.
Simplify the numerator.
Work from left to right.
Subtract.
Simplify.

7. Checkpoint 1. Evaluate the expression when x = 5.
a. 2x b ÷ x2 + 6 58 10
Simplify the expression.
a – b. 24 ÷ 2 • c. 36 – 6 ÷ 3 + 3 27 36 37
Simplify the expression. 4

8. 1.3 Order of Operations 2 EVALUATING EXPRESSIONS WITH A CALCULATOR
GOAL 2
EVALUATING EXPRESSIONS WITH A CALCULATOR
The point: YOU must know how your calculator works. Be sure you work through the examples and understand YOUR calculator.
EXAMPLE 4
EXAMPLE 5

9. Checkpoint
Simplify each expression using your calculator. Identify the order in which the operations are performed. 1. 2. 3.
11; division, subtraction, addition
8; subtraction, division, addition
≈1.29; subtraction, addition, division

10. QUESTIONS?