When working with numerical or algebraic expressions containing two or more operations, there is a conventional order in which operations are performed. If an ordering precedence did not exist, operations could potentially yield more than one correct answer.

Does 9 - 3 x 2 = 3 ?
OR
Does 9 - 3 x 2 = 12 ?
This one is correct!
 
This one is NOT correct!

You need to know and remember this ordering:
bullet Order of Operations: Proceed in this order:
 
1. Parentheses are done first
2.
Exponents are done next
3.
Multiplication and Division (done as they are encountered left to right)
4. Addition and Subtraction (done as they are encountered left to right)


An acronym that is used to help remember this order is
PEMDAS.

Parentheses, Exponents, (Multiplication/Division), (Add/Subtract).

Common Mnemonic Phrase:
"Please Excuse My Dear Aunt Sally".

There are also other phrases that can be used, or you can make up your own.

AuntSallly
caution1

While PEMDAS lists M before D, remember that multiplication and division are done as they are read from left to right. It may not always be the case that multiplication is done "before" division.
The expression
16 ÷ 4 x 2 = 8 (not 2).
The same is true of addition and subtraction: 8 - 4 + 2 = 6 (not 2).


You will need to follow "order of operations" when working with a variety of mathematical topics: evaluating formulas, solving equations, evaluating algebraic expressions, and simplifying monomials and polynomials. Let's look at simplifying some numerical expressions.

expin1
Simplify 40 - 2(6 - 4)2
 
40 - 2(2)2
 
Parentheses
40 - 2(4)
 
Exponent
40 - 8
 
Multiply
32
 
Subtract

 

expin2
Simplify 30 - (8 - 15 ÷ 3) x 2
 
30 - (8 - 5) x 2
 
Parentheses/Divide
30 - (3) x 2
 
Parentheses/Subtract
30 - 6
 
Multiply
24
 
Subtract

 

expin3
Simplify 2(20 - 32 + 1) - (42 ÷ 2 x 3)
 
2(20 - 9 + 1) - (42 ÷ 2 x 3)
 
Parentheses/Exponent
2(20 - 9 + 1) - (21 x 3)
 
Parentheses/Divide
2(12) - (21 x 3)
 
Parentheses/Subtract/Add
2(12) - (63)
 
Parentheses/Multiply
24 - (63)
 
Multiply
-39
 
Subtract

 

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