Order of Operations

I'm starting off with the order of operations because I feel that this is the beginning of math. Yes, there are the actual operations of addition, subtraction, multiplication, division, and exponents. Those are what I consider pre-math.

The purpose of the order of operations is to simplify an expression (hint, if you ever come across a question on a homework or test that says "simplify" or "simplify the expression," this is what it is talking about). In other words, we want to make something ugly into something pretty.

In order to do that, we use the order of operations, which is:

Parentheses

Exponents

Multiplication/Division

Addition/Subtraction

Hint, Multiplication and Division are done at the same time, from right to left across the expression. Addition and Subtraction are done at the same time, from right to left across the expression.

Just remember, P E MD AS. You can memorize this as just what it sounds like (the made-up word "pemdas") or as the sentence "Please Excuse My Dear Aunt Sally."

All of this probably doesn't make any sense yet. Now let's do two examples to give this nonsense some context.

Clearly, order of operations matters. Two expressions that may look very similar may simplify very differently. Let's do one more, slightly harder, example.