# Intermediate 2 Mathematics/Algebraic Operations

### Order of Operations

The order of operations tells you what to do first when you see a problem. This is something that you will keep for all levels of math. The order of operations is fundamental even past Calculus.

An acronym that helps memorize this order is P.E.M.D.A.S.
Another way to memorize it is by saying:

Parentheses

Excuse

Exponents

My

Multiplication

Dear

Division

Aunt

Sally

Subtraction

Here are some examples of how this works:

Ex.1

${\displaystyle (2+5)*3^{2}}$

Solution

${\displaystyle =(7)*3^{2}}$
${\displaystyle =(7)*9}$

${\displaystyle =63}$

Before we start the next example let's take a look on how this problem would look if we hadn't had the parentheses.
${\displaystyle 2+5*3^{2}}$

${\displaystyle =2+5*9}$

${\displaystyle =2+45}$

${\displaystyle =47}$

As you can see doing things in a certain order really does change the outcome of the and equation.

Ex.2

${\displaystyle (2+2)^{2}+(3-2)*5}$

Solution

${\displaystyle (4)^{2}+(1)*5}$

${\displaystyle 16+1*5}$

${\displaystyle 16+5}$

${\displaystyle 21}$