# Order of operations: BIDMAS

## In a nutshell

The order of operations is a rule that states which operation must be performed first. It is very helpful when having to solve multi-step equations.

## Order of operations: BIDMAS

BIDMAS is the acronym for the order of equations. It stands for:

**B**rackets**I**ndices**D**ivision/**M**ultiplication**A**ddition/**S**ubtraction

**Note: **Division/Multiplication and Addition/Subtraction are written on the same line because it depends what comes first when reading the equation from *left to right**. *

##### Example 1

*What is $30-3\times(8 -1)$?*

*First, using **BIDMAS**, simplify any **Brackets**:*

$8-1=7$

*The equation is now:*

$30-3\times7$

*There are no** Indices**, so move on to **Division/Multiplication**:*

$3\times7=21$

*The equation is now:*

$30-21$

*Finally, go through any **Addition/Subtraction:*

$30-21=9$

__$\underline{30-3\times(8-1)=9}$__

##### Example 2

*Two variables $y$ and $x$ are connected through the formula $y=3x^2-x+5$. What is $y$ when $x=4$?*

*Substituting in $x=4$ into the equation gives:*

*$y=3(4)^2-4+5$*

*Going through **BIDMAS**, there are no **Brackets **to simplify. So, move onto **Indices**:*

$4^2=16$

*The equation then becomes:*

$y=3\times16-4+5$

*Now, move onto ***Division/Multiplication**:

$3\times16=48$

*The equation then becomes:*

$y=48-4+5$

*Finally, move onto **Addition/Subtraction**:*

*Note that even though the addition comes first in **BIDMAS**, you perform the subtraction first as it comes first when reading the equation from left to right. *

*$48-4=44$*

*$44+5=49$*

__$\underline{y=49}$__