Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 3: Order of Operations and Integers 33

• MD: Multiply and Divide, moving from left to right


• AS: Add and Subtract, moving from left to right

DEFINITION

PEMDAS is a mnemonic, or memory device, to help you

remember that the order of operations is parentheses,

exponents, multiplication and division, addition and

subtraction.

Some people use a sentence, like Please Excuse My Dear Aunt Sally,
to help remember the letters in PEMDAS, and others use an image of
a house. The house reminds you that multiplication and division are
done together, and so are addition and subtraction.

P

E

M D

A S

MATH TRAP

Multiplication and division have the same priority. Don’t do all the multiplication

and then all the division. Do multiplication or division as you meet them as you work

across the line. The same is true for addition and subtraction. Do them as you come to

them.

Here are some examples of the order of operations at work. Look at each example first, and think
about what you would do. Then read the explanation to see if you had all the rules in order.

Example 1: Simplify (4 v 52 – 8) v 3

There are parentheses here, so work on what’s inside them first. It’s a little problem

of its own, so follow the order of operations. First is the exponent. The exponent of 2

on the 5 tells you to multiply 5 v 5. That makes the problem (4 v 25 – 8) v 3. Do the

multiplication inside the parentheses, and you have (100 – 8) v 3. Then you can

subtract to get 92 v 3. That gives you 276.

There are a lot of memory devices to help you remember the order, and one of them, PEMDAS,
is so common many people use it in place of order of operations, as if it were a name. The letters
in PEMDAS are meant to help us remember to:

• P: Simplify expressions inside Parentheses


• E: Evaluate powers, or numbers with Exponents