## Why Do We Need the Order of Operations?

Imagine we wanted to find the answer to the calculation below:This calculation contains two operations: adding and multiplying. There are two orders to doing this calculation and two answers. Do we add then multiply, or multiply then add?

## Order 1

Add the first two numbers, then multiply the result with the third number.**1 + 2**× 3 =

**3**× 3 = 9

## Order 2

Multiply the last two numbers, then add the result to the first number.
1 +

Which answer is the correct one?
It turns out the second order of operations is the correct one.
Luckily, there is a simple way to use the correct order.
**2 × 3**= 1 +**6**= 7## BODMAS

**BODMAS**is an acronym for the order of operations. It stands for:

The order of operations is read from top to bottom. The operations with a curly bracket (

**{**) are on the same level, and can be performed in any order.

**B**rackets. Evaluate brackets first.**O**rder. Evaluate exponents (such as squares and square roots) second.**D**ivision and**M**ultiplication. Evaluate numbers that are divided and multiplied third.**A**ddition and**S**ubtraction. Evaluate numbers that are added and subtracted fourth.

## How to Use the Order of Operations

Using the order of operations is easy.## Question

Find**2 + 3**.

^{2}− (8 × 2) ÷ 2## Step-by-Step:

## 1

**B**rackets. Evaluate expressions within brackets first. In our example, there is one pair of brackets:

**(8 × 2)**= 16.

2 + 3^{2} − **(8 × 2)** ÷ 2

= 2 + 3^{2} − **16** ÷ 2

## 2

**O**rder. Evaluate numbers with exponents second. In our example, there is one exponent:

**3**= 9.

^{2}2 + **3 ^{2}** − 16 ÷ 2

= 2 + **9** − 16 ÷ 2

## 3

**D**ivision and

**M**ultiplication. Evaluate numbers that are divided and multiplied third. In our example, there is one division:

**16 ÷ 2**= 8.

2 + 9 − **16 ÷ 2**

= 2 + 9 − **8**

## 4

**A**ddition and

**S**ubtraction. Evaluate numbers that are added and subtracted fourth. In our example, there is one

**+**'s and one

**−**. Addition and subtraction take the same precedence, so it does not matter which order we do them in. We will do them left to right.

2 + 9 − 8 |
= 11 − 8 \(\:\:\:\:\:\:\:\:\:\:\:\:\) as 2 + 9 = 11 |

11 − 8 |
= 3 |

## Answer:

2 + 3^{2}− (8 × 2) ÷ 2 =

**3**

## Top Tip

## BODMAS, BIDMAS, BEDMAS, PEMDAS

BODMAS is one acronym used to remember the order of operations, but different parts of the world will use different ones.**BODMAS**is used in the United Kingdom and Australia. Sometimes**BIDMAS**is used, where**I**is for**I**ndices rather than**O**for**O**rder.**BEDMAS**is used in Canada, where**E**is for**E**xponent. The words (Order, Indices, Exponents) are all different words for the same thing.**PEMDAS**is used in the United States of America:**P**arentheses,**E**xponent,**M**ultiplication,**D**ivision,**A**ddition,**S**ubtraction. Parentheses is another word for brackets. A useful memory device for**PEMDAS**is "**P**lease**E**xcuse**M**y**D**ear**A**unt**S**ally."

## Note

## What Is an Operation?

An operation takes values and calculates a new value from them.- The numbers operated upon are called
**operands**. - The symbol which shows what type of operation is taking place is called the
**operator**.

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