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:
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. 


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.

Simplify: 6 + 5 x 4 

6 + 20 

Multiply 
26 

Add 

Simplify: 8 + ½ x 12 + 15 ÷ 5 

8 + 6 + 15 ÷ 5 

Multiply 
8 + 6 + 3 

Divide 
17 

Add 

Simplify: 3(8 + 1)  4(8  5) 

3(9)  4(3) 

Parentheses 
27  12 

Multiply 
15 

Subtract 

When working with a fraction bar (the bar meaning "division"), it is implied that a set of parentheses surrounds everything in the numerator (top) and a set of parentheses surrounds everything in the denominator (bottom).
Simplify the top, simplify the bottom, then deal with the fraction bar.
Consider the example below as if it was written (6^{2} + 5  3^{2}) / (8  4).



Simplify:




Exponents (top) 


Add/Subtract (top); Subtract (bottom) 
8 

Divide (fraction bar = divide) 

Simplify: 2^{3} + (3 + 2)(6  3) 

2^{3} + (5)(3) 

Parentheses 
8 + (5)(3) 

Exponent 
8 + 15 

Multiply 
23 

Add 
Now, let's try a couple of more challenging situations:

Simplify: 30  (8  15 ÷ 3) x 2 

30  (8  5) x 2 

Parentheses; Divide first 
30  (3) x 2 

Parentheses; Subtract 
30  6 

Multiply 
24 

Subtract 

Simplify: 2(20  3^{2 } + 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 
