The order of operations tells us what order to perform operations in.
A calculation may have several operations, such as: adding, subtracting, multiplying, dividing and squaring.

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?

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

Please tell us using

## 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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