Concept

Order of Operations

The order of operations is the order to follow when evaluating an expression that has more than one operation. The order of operations can be described as a series of steps.

Consider this expression to see the steps in action. (1+2)* 3^2-5+5/2 = ? The example expression contains a set of parentheses, an exponent, multiplication, division, addition, and subtraction. The expression is evaluated following the order of operations.

Expression	Simplified	Operation
(1+2)* 3^2-5+5/2	3* 3^2-10/2	Evaluating Parentheses and Grouping Symbols
3* 3^2-10/2	3* 9-10/2	Exponents
3* 9-10/2	27-5	Multiplication and Division
27-5	22	Subtraction

There are a few things to note about this evaluation.

The addition in the numerator of 5+52 was evaluated at the same time as the expression between parentheses (1+2). This is because fraction bars are grouping symbols like parentheses.
The order of operations must be followed when evaluating expressions in grouping symbols.
Operations that are inverse and at the same level must be evaluated from left to right. This rule applies for multiplication and division and for addition and subtraction.

To remember the order of operations, it is useful to memorize the acronym PEMDAS. Each letter of PEMDAS indicates a set of operations. A fun sentence to remember this acronym is Please Excuse My Dear Aunt Sally.