## Order of Operations:

### Introduction

Look at and evaluate the following expression:How many different ways can we interpret this problem, and how many different answers could someone possibly find for it?

The

*simplest*way to evaluate the expression is simply to start at the left and work your way across:

This is the answer you would get if you entered the
expression into an ordinary calculator. But if you entered the
expression into a scientific calculator or a graphing calculator you
would probably get 29 as the answer.

In mathematics, the order in which we perform the various

**operations**(such as adding, multiplying, etc.) is important. In the expression above, the operation of**multiplication**takes precedence over**addition**, so we evaluate it first. Let’s re-write the expression, but put the multiplication in brackets to show that it is to be evaluated first.
First evaluate the brackets: . Our expression becomes:

When we have only addition and subtraction, we start at the left and work across:

Algebra students often use the word

**“PEMDAS”**to help remember the order in which we evaluate the mathematical expressions:**P**arentheses,**E**xponents,**M**ultiplication,**D**ivision,**A**ddition and**S**ubtraction.### Order of Operations

- Evaluate expressions within
**P**arentheses (also all brackets and braces { }) first. - Evaluate all
**E**xponents (terms such as or ) next. **M**ultiplication*and***D**ivision is next - work from left to right completing**both**multiplication and division in the order that they appear.- Finally, evaluate
**A**ddition*and***S**ubtraction - work from left to right completing**both**addition and subtraction in the order that they appear

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