Order of Operations


Order of Operations is a sequence of steps used to find answers to mathematical sentences.  With this standard we can be sure that people all over the world will get the same answers.

Please Excuse My Dear Aunt Sally
(parentheses - exponents - multiplication & division - addition & subtraction)


Do what's inside the parentheses first.  If there are nested parentheses (several sets), work inside-out.  Continue working until you remove all parentheses (or other grouping symbols).  Each time you start with a new set of parentheses, you must start at the beginning of PEMDAS.
Calculate all exponents next.  Be sure that you've done parentheses first!
Then do all multiplication & division from LEFT TO RIGHT.  These are considered "undoing" or "opposite" operations.
Finally, do all addition & subtraction from LEFT TO RIGHT.  These are considered "undoing" or "opposite" operations.

 

GROUPING SYMBOLS
 
   (    )     [    ]     <    >     {    } 

The fraction bar is also considered to be a grouping symbol because it implies division.  However, everything on the top of the fraction must be simplified, and everything on the bottom of the fraction must be simplified before division can be performed.
 
 
 

EXAMPLES
 

10 (8+122)
10 (8+122)
10 (8 + 144)
10 (152)
1,520
2 + 4 - 5 x 6 + 8 ÷ 2
2 + 4 - 5 x 6 + 8 ÷ 2
2 + 4 - 30 + 4
6 - 30 + 4
-24 + 4
-20
20 + 4(2+1)3 - 2(5-7)2 + 8(3+7) x 6
20 + 4(2+1)3 - 2(5-7)2 + 8(3+7) x 6
20 + 4(3)3 - 2(-2)2 + 8(10) x 6
20 + 4(27) - 2(4) + 8(10) x 6
20 + 108 - 8 + 80 x 6
20 + 108 - 8 + 480
128 - 8 +480
120 + 480
600
5 [ 2 + (32 - 2  x 4) -6 + (8-8)] - 5
5 [ 2 + (32- 2  x 4) -6 + (8-8)] - 5
5 [ 2 + (9- 2  x 4) -6 + (8-8)] - 5
5 [ 2 + (9- 8) -6 + (8-8)] - 5
5 [ 2 + 1 - 6 + 0] - 5
5 [ 3 - 6 + 0] - 5
5 [ -3 + 0] - 5
5 [ -3] - 5
- 15 - 5
-20

 

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