Order of Operations for Equations
When equations have more than one operation, there are rules that determine in what
order we should do each operation. The following lists these rules
called order of operations:
1. First do all operations that lie inside parentheses.
example: 8 + 3² - 2 x (5 + 2)
8 + 3² - 2 x 7
2. Next, do any work with exponents.
example : 8 + 3² - 2 x 7
8 + 9 -2 x 7
3. Moving from left to right, do all multiplication and division.
example : 8 + 9 - 2 x 7
8 + 9 - 14
4. Again working from left to right, do all addition and subtraction.
example : 8 + 9 - 14
17 - 14 = 3
A simple way to recall each step is to remember the letters 'PEMDAS', and the
phrase "Please Excuse My Dear Aunt
Sally."
P = Parenthesis
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
In the examples below, without the parentheses, the problems are solved by working problems from left to right and performing all multiplication, division, addition and subtraction. When parentheses are used, you first perform the operations inside the parentheses; the answer will be different!
Example: Parenthesis
Without Parenthesis
With Parenthesis
9 - 7 + 4 =
9 - (7 + 4) =
2 + 4 =
9 - 11 =
6
-2
Example: Parenthesis & Exponents
Without Parenthesis
With Parenthesis
10 + 2 x 5 x 3³ ÷ 10
(10 + 2) x 5 x 3³ ÷ 10
10 + 2 x 5 x 27 ÷ 10
12 x 5 x 3³ ÷ 10
10 + 270 ÷ 10 12 x 5 x 27 ÷ 10
=37 60 x 27 ÷ 10
1620 ÷ 10
= 162