# Precedence in Mathematical Operators

## What comes first?

We are going to introduce a simple set of rules here that can be remembered to solve that age old problem.

Which do we do first?

# Prerequisites:

- none

# Terminology

BODMAS: Brackets first then Other then Division then Multiplication then Addition and finally Subtraction

Formulae: A group of mathematical symbols that make a result

Infix: The notation commonly used in mathematical formulae

# The Problem

What is the answer to

3 + 2 x 4?

There are **two** possible solutions. You can either calculate the **3 + 2** part first (which we can show in by forcing this with brackets as **brackets go first**)

(3 + 2) x 4 = (5) x 4 = 20

But, if we calculate the **2 x 4** part first we would calculate the following

3 + (2 x 4) = 3 + (12) = 15

now (don’t be too confused); 20 is not the same as 15. Shocking.

Now **brackets** have been used above to make it clear which order the calculation should be taken in.

This is clearly not *acceptable* as we need to have brackets all over the place. Wouldn’t it be better if we had a set of rules to see what should be calculated first? That is where `BODMAS`

comes in.

# BODMAS

`BODMAS`

tells us which order to perform a calculation in. Brackets first then Other then Division then Multiplication then Addition and finally Subtraction.

Since multiplication is ahead of addition in the order of `BODMAS`

,

3 + 2 x 4

this is therefore calculated as

15

*Problem solved*

# Conclusion:

When you perform a calculation you need to know which order of precedence a calculation might have. In order to do so, people have developed an anacronym to help them out. `BODMAS`

is an easy to remember order, meaning Brackets first then Other then Division then Multiplication then Addition and finally Subtraction and stopping eternal confusion when calculating answers.

Not bad. Not bad at all.

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