Order of Operations

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

Here are some examples… Problem Without Order of Operations Following Order of Operations 12 + 36 x 2 48 x 2 96 12 + 72 84 32 + 8 112 121 9 + 8 17 (4 + 5) x 7 4 + 35 39 9 x 7 63

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.

“Please Excuse My Dear Aunt Sally” is a helpful way to remember these rules for the order of operations.

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

Next, do any work with exponents or roots. “Excuse” Next, do any work with exponents or roots. Example: (15)2 + 3 x 9 225 + 3 x 9

Working from left to right, do all multiplication and division. “My Dear” Working from left to right, do all multiplication and division. Example: 225 + 3 x 9 225 + 27

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: 225 + 27 252

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

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

Some examples…. 8 x 22 + 7 x 5 67 (4 + 3 x 2)2 - 5 55 *Exponents* *Multiplication* 32 + 35 * 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