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! 

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 abbreviation 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".

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). 

Simplify 40  2(6  4)^{2} 

40  2(2)^{2} 

Parentheses 
40  2(4) 

Exponent 
40  8 

Multiply 
32 

Subtract 

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 

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 
