Order of operations


The order of operations is an order mathematicians have agreed upon to perform operations to simplify mathematical expressions.

This order is as follows:

First, do all operations within parentheses or other grouping symbols.

Second, simplify mathematical expressions involving exponents.

Third, multiply and divide in order from left to right.

Lastly, add and subtract in order from left to right.


Example #1

52 + (10 - 3 × 2) - 7

Simplify the expression inside the parentheses. Notice though that inside the parentheses, there are two operations (- and × )

Inside the parentheses, perform the multiplication first.

52 + (10 - 6) - 7

52 + 4 - 7

Simplify the exponent

25 + 4 - 7

Add and subtract from left to right

29 - 7 

22

Example #2

4  ÷ 4 × 5 - 1 + 23  ( Do exponent )

4  ÷ 4 × 5 - 1 + 8   ( Do division )

1 × 5 - 1 + 8       ( Do multiplication )

5 - 1 + 8           ( Do subtraction )

4 + 8               ( Do addition ) 

12

Something that can help you remember the order of operations is the mnemonic " Please Excuse My Dear Aunt Sally"

Please is for parentheses

Excuse is for Exponent

My Dear is for multiply and divide from left to right

Aunt Sally is for add and subtract from left to right

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