1. Purpose
Students will be able to use the order of operations to simplify expressions.

2. PEMDAS 1. Parentheses and grouping symbols. 2. Exponents.
Order of Operations
1. Parentheses and grouping symbols.
2. Exponents.
3. Multiply and Divide from left to right.
4. Add and Subtract from left to right.

3. Grouping Symbols parentheses ( ) fraction bar —
brackets [ ] absolute value | |
braces { } radical symbol
If an expression contains more than one set of grouping symbols, evaluate the expression from the innermost set first.
Example: (4+(5-4)-1)
(4 + 1 – 1) = 4

4. Please Parentheses Excuse Exponents My Multiply Dear Divide Aunt Add
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

5. Example 1: Translating from Algebra to Words
Simplify each expression.
A. 15 – 2 · 3 + 1
15 – 2 · 3 + 1
There are no grouping symbols.
15 – 6 + 1
Multiply. 10
Subtract and add from left to right.
B. 12 – ÷ 2
12 – ÷ 2
There are no grouping symbols.
12 – ÷ 2
Evaluate powers. The exponent applies only to the 3.
12 – 9 + 5
Divide.
Subtract and add from left to
right. 8

6. You try! Simplify the expression. 8 ÷ · 3 8 ÷ · 3
1 2
8 ÷ · 3
8 ÷ · 3
1 2
There are no grouping
symbols.
16 · 3
Divide. 48
Multiply.

7. You Try! Simplify the expression. 5.4 – 32 + 6.2 There are no grouping
symbols.
5.4 –
5.4 –
Simplify powers. –
Subtract
2.6
Add.

8. You Try! Simplify the expression. –20 ÷ [–2(4 + 1)]
There are two sets of grouping
symbols.
–20 ÷ [–2(4 + 1)]
Perform the operations in the
innermost set.
–20 ÷ [–2(5)]
Perform the operation inside
the brackets.
–20 ÷ –10 2
Divide.

9. Example 2B: Evaluating Algebraic Expressions
Evaluate the expression for the given value of x.
42(x + 3) for x = –2
42(x + 3)
First substitute –2 for x.
42(–2 + 3)
Perform the operation inside the parentheses.
42(1)
16(1)
Evaluate powers. 16
Multiply.

10. You Try! Evaluate the expression for the given value of x.
(x · 22) ÷ (2 + 6) for x = 6
(x · 22) ÷ (2 + 6)
(6 · 22) ÷ (2 + 6)
First substitute 6 for x.
(6 · 4) ÷ (2 + 6)
Square two.
(24) ÷ (8)
Perform the operations inside the parentheses. 3
Divide.

11. Example 3: Simplifying Expressions with Other Grouping Symbols
2(–4) + 22
42 – 9
The fraction bar acts as a grouping symbol. Simplify the numerator and the denominator before dividing.
2(–4) + 22
42 – 9
–8 + 22
42 – 9
Multiply to simplify the numerator.
–8 + 22
16 – 9
Evaluate the power in the denominator.
Add to simplify the numerator. Subtract to simplify the denominator. 14 7 2
Divide.

12. Example 3: Simplifying Expressions with Other Grouping Symbols
3| ÷ 2|
The absolute-value symbols act as grouping symbols.
3| ÷ 2|
Evaluate the power.
3| ÷ 2|
Divide within the absolute-value symbols.
3|16 + 4|
3|20|
Add within the absolute-symbols.
3 · 20
Write the absolute value of 20. 60
Multiply.

13. You Try! Simplify. The radical symbol acts as a grouping symbol.
Subtract.
3 · 7
Take the square root of 49. 21
Multiply.

14. Look for words that imply mathematical operations.
You may need grouping symbols when translating from words to numerical expressions.
Remember!
Look for words that imply mathematical operations.
difference subtract
sum add
product multiply
quotient divide

15. Example 4: Translating from Words to Math
Translate each word phrase into a numerical or algebraic expression.
A. the sum of the quotient of 12 and –3 and the square root of 25
Show the quotient being added to
B. the difference of y and the product of 4
and
Use parentheses so that the product is evaluated first.

16. Example 5: Retail Application
A shop offers gift-wrapping services at three price levels. The amount of money collected for wrapping gifts on a given day can be found by using the expression 2B + 4S + 7D. On Friday the shop wrapped 10 Basic packages B, 6 Super packages S, and 5 Deluxe packages D. Use the expression to find the amount of money collected for gift wrapping on Friday.

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

18. Exit Task Simply each expression. 2. 52 – (5 + 4) |4 – 8|
1. 2[5 ÷ (–6 – 4)] –1 4
3. 5  8 – ÷ 22 40
Translate each word phrase into a numerical or algebraic expression.
4. 3 three times the sum of –5 and n
3(–5 + n)
5. the quotient of the difference of 34 and 9 and the square root of 25
6. the volume of a storage box can be found using the expression l · w(w + 2). Find the volume of the box if l = 3 feet and w = 2 feet.
24 cubic feet