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:

Brackets
Indices
Division/Multiplication
Addition/Subtraction

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.

$48-4=44$ 

$44+5=49$ 

$\underline{y=49}$ 