Order of Operations

by: Rorie Brownfield

Explanation of the popular mnemonic for remembering the Order of Operations.

Parentheses

The first step of the Order of Operations is to solve anything inside of parentheses.  This is represented with the word "Please" in the popular mnemonic "Please Excuse My Dear Aunt Sally." Sometimes, there won't be anything in parentheses. In that case, you will skip this step.

4 × 7 + (108 ÷ 9)5 - 7² + 11

4 × 7 + (12)5 - 7² + 11

Exponents

The next step in the Order of Operations is to solve any exponents.  In the mnemonic, this step is represented by the word "Excuse."  Like the step of Parentheses, there may not be any exponents within the expression, and you will skip this step.

4 × 7 + (12)5 - 7² + 11

4 * 7 + (12)5 - 49 + 11

Multiply and Divide

The next step in the Order of Operations to solve any multiplication or division problems within the expression or equation.  The word "My" represents "Multiply" and the word "Dear" represents "Division" in the mnemonic.  The reason that multiplication and division are together in this presentation is because you must do both from left to right.  If there isn't any multiplication or division in the expression, you will skip this step.

4 × 7 + (12)5 - 49 + 11

28 + (12)5 - 49 + 11

28 + 60 - 49 + 11

Addition and Subtraction

The last steps of the Order of Operations is to solve any addition or subtraction problems.  You must do these from left to right, like the step "Multiply and Divide."  "Addition" is represented by the word "Aunt" in the mnemonic and "Subtraction" is represented by "Sally."  If there isn't any addition or subtraction in the expression, then you have obviously already solved it.

28 + 60 - 49 + 11

88 - 49 + 11

39 + 11

50

Example Problems

(48 - 34) ÷ 7 × 20 - 10 + 70 × 2²

6² × 2 + 72 ÷ (84 ÷ 7)

Comment Stream