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Teaching Guides

## Order of Operations in Mathematics

Posted by scott-locklear on September 11, 2013

The order of operations is the set of rules that tells you which parts of an equation to work on in what order so you will get the correct result when solving it. The order you do things in is critical in order to get the right results—work in the wrong order and you will likely get an incorrect answer.

Mastering the order of operations is one of the most important and often used skills you will acquire in solving mathematical equations consistently and successfully. With practice, it will become second nature, so don’t worry if it seems a little confusing at first.

How to Remember the Order of Operations

You may have learned the mnemonic device “PEMDAS” to help you remember what operations to complete first. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition and Subtraction. Remember to start with the innermost brackets and parentheses first and work outward. Multiplication and division can be done at the same time—multiplication does not necessarily come first. The same goes for addition and subtraction—addition does not necessarily come first.

Key Points

• Remember that multiplication and division, though notated with their own separate “signs,” are really two parts of the same mathematical operation. Think of division as multiplication by a reciprocal or a multiplicative inverse.
• Addition and subtraction are part of the same mathematical operation as well. It might help to think of subtraction as simply the addition of a negative number.
• The elements of an equation under the horizontal “bar” of a radicand in the square root function should be treated like they’re surrounded by brackets or parentheses.

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