# Arithmetic

This module provides an opportunity to revise the order in which operations are performed when carrying out arithmetic calculations. The questions in this module have been designed so they can be answered without the use of a calculator.

### Introduction

Arithmetic is about working with numbers, particularly addition, subtraction, multiplication and division.

Combining these operations involves the use of some rules so that there is no misunderstanding in how to perform the calculations. We need to ensure there is only one way to interpret a written arithmetic statement.  So, the rules provide an order of operations that everyone follows.

### Order of Operations

Rules for the order in which operations are performed is important in ensuring there is only one way to interpret an arithmetic statement.

#### BODMAS

There are several acronyms used to help remember the order of operations. The one you are most likely to have seen before is BODMAS.

B:         Brackets first

O:        Orders (numbers involving powers or square roots) are done next

DM:     Division and Multiplication are next and are done left to right

AS:       Addition and Subtraction are calculated last and are done left to right.

Note

Division and multiplication have the same importance.  Whichever operation comes first when you read left to right is done first.

Addition and subtraction have the same importance. Whichever operation comes first when you read left to right is done first.

Alternate acronyms include:

BIDMAS, where I stands for indices .

BEDMAS, where E is for exponents.

PEMDAS, where P is for parentheses.

It does not matter which acronym you use the order is still the same.

You may know how to use these rules. The following questions will give you an idea of those rules you can apply correctly and those that need some more work.

##### What do you know?
 $3+9\div 3 =$
 $20-8\times 2 +6=$
 $25-(3+7)=$
 $29-(8-7)-3\times 4=$
 $10-(10-(2+3))=$
 $\left( 20-2^3\right)\times 5=$
 $\left( 5-3\right)^4-2\times 4=$
 $\sqrt{36+64}+21=$
 $4+16\div 4-(3+2)=$
 $25-\left(15-(6+2)+4\right)=$