Order of Operati ns
Rules
I. Grouping Symbols (both
explicit and implicit)
Examples
implicit
explicit
A “division bar”
4 8 7
23 5
II. Exponents and Square
Roots
III. Multiply and Divide (in
either order) always
complete left to right
exponents
square roots
48
6 2
8
2
16
IV. Add and Subtract (again,
in either order) always
complete left to right
15
3
5
12
5
17
Order of Operations
Mathematical operations involving addition, subtraction, division, multiplication, and
exponents are performed according to a preferred order.
If the preferred order in which the operation is to be performed is not followed, a wrong
answer will be obtained.
This means that any wrong way you choose to perform an operation can give you an
answer (even though it may be wrong).
The preferred order of mathematical operations is given by the acronym:
P-E-M-D-A-S
Please
1. First, work with parenthesis, brackets, or other
grouping symbols.
Excuse
2. Second, work with exponents.
My
Dear
3. Third, work with Multiplication or Division
in order from left to right.
Aunt
Sally
4. Last, work with Addition or Subtraction
in order from left to right.
1. Start by simplify numbers in parenthesis first, followed by brackets. Within the
parenthesis or brackets:
a. Simplify exponents first
b. Then multiplication or division from left to right
c. Finally addition or subtraction from left to right
2. After parenthesis and brackets, simplify exponents.
3. Then, simplify multiplication/division, from left to right.
4. Finally, simplify addition/subtraction from left to right.