1. Objective
Use the order of operations to simplify expressions.

2. When a numerical or algebraic expression contains
more than one operation symbol, the order of
operations tells which operation to perform first.
Order of Operations
Perform operations inside parentheses.
First:
Second:
Evaluate powers/exponents.
Third:
Perform multiplication and division
from left to right.
Perform addition and subtraction from
left to right.
Fourth:

3. Helpful Hint The first letter of these words can help you
remember the order of operations.
Please
Excuse My
Dear
Aunt
Sally
Parentheses
Exponents
Multiply
Divide
Add
Subtract

4. Example 1: Translating from Algebra to Words
Simplify each expression.
A. 15 – 2 · 3 + 1
There are no parentheses or exponents.
15 – 2 · 3 + 1
15 – 6 + 1
Multiply before you add/subtract.
9 + 1 = 10
Subtract and add from left to right.
B ÷ 2
÷ 2
There are no parentheses.
÷ 2
Do exponents. Only to the 3.
Divide before you add/subtract.
21 – 5 = 16
Add and subtract from left to right.

5. Check It Out! Example 1c
Simplify the expression.
There are two sets of parentheses
–20 ÷ [–2(4 + 1)]
Do what is in the innermost parentheses first
Next do what is in the remaining set of parentheses
–20 ÷ [–2(4 + 1)]
–20 ÷ [–2(5)]
–20 ÷ –10
Divide. 2

6. Example 3A: Simplifying Expressions with Other Grouping Symbols
When there is a fraction bar, do everything on the top and then everything on the bottom.
2(–4) + 22
42 – 9
2(–4) + 22
42 – 9
Multiply, then add to simplify the numerator.
–8 + 22
42 – 9 14
42 – 9
Do the exponent, then subtract to simplify the numerator. 14
16 – 9 14 7
= 2
Divide.

7. Check It Out! Example 3b
Simplify.
|4 – 7|2 ÷ –3
The absolute-value symbols act like parentheses (do what is inside them first).
|4 – 7|2 ÷ –3
|–3|2 ÷ –3
Now perform the operation of absolute value.
32 ÷ –3
Next do the exponent
9 ÷ –3
Divide. –3

8. Check It Out! Example 3c
Simplify.
Square roots act like parentheses too (Do what is inside it first)
Then find the square root.
3 · 7
Multiply. 21

9. Example 5: Retail Application
A store offers gift-wrapping at three price levels.
The amount of money made from wrapping gifts each day can be found using 2B + 4S + 7D.
On Friday the store wrapped 10 Basic (B) packages, 6 Super (S) packages, and 5 Deluxe (D) packages.
Use the expression to find how much money the store made from gift wrapping on Friday.
(Plug in the values for B, S, and D to solve.)

10. Example 5 Continued
2B + 4S + 7D
First substitute the value for each variable.
2(10) + 4(6) + 7(5)
Multiply the three pieces.
Add from left to right. 79
The store made $79 from gift wrapping on Friday.