Try this helpful device when simplifying an expression or equation:
"P" for
"E" for
Parentheses
Exponents
"M" for
Multiply
"D" for
"A" for
"S" for
Divide
Add
Subtract
VERY IMPORTANT:
Always work your problems from left to right.
Parentheses and exponents are of equal importance, and whichever comes first, going from left to right, must be
addressed before all other operations.
Multiplication and division are the next two operations in line, and are of equal importance. At this point, perform
whichever of these operations comes first going from left to right.
Finally, you may add or subtract, depending upon which of these operations appears first, going from left to right.
Note: Parentheses are grouping symbols. Other grouping symbols include brackets, braces, radical signs and
absolute value bars. These are all included under the category of parentheses when performing order of operations.
The Academic Support Center at Daytona State College (Math 17 pg 1 of 2)
P E M D A S ( Please Excuse My Dear Aunt Sally )
Parentheses / Exponents
(
)
Multiplication / Division
Addition / Subtraction
Parentheses
Examples:
[ ]
Brackets
{ }
Braces
2-8  4 6
=2-26
= 2 - 12

Radical Sign
= -10
Check first for parentheses and / or exponents. Since
there are none, you then looking for multiplication or
division. Both operations are present, and because
division comes first, going from left to right, you will
do the division first (- 8  4). Multiplication comes
next (-2  6), and then subtraction (2 - 12).
2.
32 + 7 - 5 (9 - 1)
= 9 + 7 - 5 (8)
= 9 + 7 - 40
= 16 - 40
= - 24
This problem has parentheses and an exponent. Since
the exponent appears first, going from left to right, you
must work it first ( 32). Next, you will do the arithmetic
inside of the parentheses (9 - 1). The next operation to
address is multiplication -5 (8). The parentheses in this
situation signify multiplication. Addition precedes
subtraction (9 + 7), then (16 - 40).
3.
4 + 2 [8 - (5 + 2)]
= 4 + 2 [8 - (7)]
= 4 + 2 (8 - 7)
= 4 + 2 (1)
=4+2
=6
Here we have parentheses within brackets. Start
working the problem from the inside out; in other
words, begin with the computation inside of the
parentheses ( 5 + 2 ), then, remembering that there is an
understood 1 by the parentheses - 1 ( 7 ), multiply to
obtain - 7.
Do the computation inside of the
parentheses (8 - 7), and then follow with the next
operation of importance, multiplication 2 (1).
Finish up with the addition (4 + 2).
1.
 
Absolute Value Bars
Note:
If you have parentheses within
parentheses or brackets, work
From the inside out. (See example 3)
Caution!
Do not attempt to do these problems
in your head. Take the time to
rewrite each step after completing an
operation.
JCM
The Academic Support Center at Daytona State College (Math 17 pg 2 of 2)