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Order of Operations

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When an expression contains more than one operation, you can get different answers depending on the order in which you solve the expression.

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**Here are some examples…**

Problem Without Order of Operations Following Order of Operations x 2 48 x 2 96 84 32 + 8 112 121 9 + 8 17 (4 + 5) x 7 4 + 35 39 9 x 7 63

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Mathematicians have agreed on a certain order for evaluating expressions, so we all arrive at the same answers. We often use grouping symbols, like parentheses, to help us organize complicated expressions into simpler ones.

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**“Please Excuse My Dear Aunt Sally”**

is a helpful way to remember these rules for the order of operations.

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**First, do all operations that lie inside parentheses.**

“Please” First, do all operations that lie inside parentheses. Example: (3 + 12)2 + 3 x 9 (15)2 + 3 x 9

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**Next, do any work with exponents or roots.**

“Excuse” Next, do any work with exponents or roots. Example: (15)2 + 3 x 9 x 9

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**Working from left to right, do all multiplication and division.**

“My Dear” Working from left to right, do all multiplication and division. Example: x 9

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**Finally, working from left to right, do all addition and subtraction.**

“Aunt Sally” Finally, working from left to right, do all addition and subtraction. Example: 252

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**Be sure to follow the order of operations within the parentheses.**

Important Note: Be sure to follow the order of operations within the parentheses.

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**“Please Excuse My Dear Aunt Sally”**

Remember… “Please Excuse My Dear Aunt Sally” Parentheses, Exponents, Multiplication & Division, Addition & Subtraction

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**Some examples…. 8 x 22 + 7 x 5 67 (4 + 3 x 2)2 - 5 55 *Exponents***

*Multiplication* * Addition* 67 (4 + 3 x 2)2 - 5 (4 + 3 x 2) - 5 *Parentheses - Multiplication* (4 + 6) - 5 (4 + 6) -5 *Parentheses – Addition* 10 - 5 *Subtraction* 55

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