Refresher Topic

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!

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 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".

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).



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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