# Basic Operations

### Topics

## Introduction to :

The order in which we complete a mathematical equation or expression is essential. Doing the steps of a problem out of order can lead to a totally different answer, even if you do the calculations correctly. So, for everyone to get the same answer, the **order of operations** was developed. You will be using these almost every day of your mathematical careers from now on.

All equations and expressions must be completed in the following order...

## PEMDAS

**P**arentheses - simplify everything inside the parentheses

**E**xponents - simplify any exponents (*See Powers and Roots)*

**M**ultiplication &**D**ivision - multiply and divide from left to right

**A**ddition &**S**ubtraction - add and subtract from left to right

PEMDAS will be your friend for life. If you have trouble remembering your new BFF's name, try out this memory trick... "**P**lease **E**xcuse **M**y **D**ear **A**unt **S**ally".

**Look Out**: even though M comes before D, multiplication and division are equals; you'll need to complete these operations from left to right. The same is true for addition and subtraction. Think of them as equal partners.

#### Order of Operations Example 1

Since there are no parentheses or exponents, division is our first step. |

#### Order of Operations Example 2

First, simplify the parentheses. Since there are many operations in the parentheses, follow the order of operations inside them, too. In this problem, division would come first. |

#### Order of Operations Example 3

In this problem, treat the numerator and denominator like they are in separate parentheses, and the fraction bar as a division sign. You could rewrite this problem as: . Now simplify each set of parentheses using the correct order of operations. |

#### Order of Operations Example 4

Here, we have two sets of parentheses, the regular ones and the brackets. Simplify the innermost set first. |