3.10

# Using BIDMAS

Below we look at each of the BIDMAS rules in turn.

## Brackets

The convention states that any calculations which are in brackets are performed first. It is important to note that any calculations within these brackets must also follow the rules of BIDMAS.

## Indices

Indices is another word for powers. For example $2^{3}$ which is $2 \times 2 \times 2$.

If we have a calculation such as $4 \times 2^{3}$ we evaluate $2^{3}$ first.

$2^{3}$ is 8 so we re-write the calculation as $4 \times 8$ which gives an answer of 32.

Note that if we did $4 \times 2$ first giving 8 and then cube, we get $8^{3}$ which is 512. A very different result to 32!

## Division and multiplication

Division and multiplication have equal weighting as they are the same operation.

Dividing by 2 is the same as multiplying by $\frac{1}{2}$. Once the indices have been dealt with then any multiplications and divisions are performed next. If there is more than one multiplication or division in the calculation we perform them in the order they appear in the calculation working from left to right.

$6 \times 4 \times 2^{3} \div 12$
$= 6 \times 4 \times 8 \div 12$ (performing the indices first)
$= 24 \times 8 \div 12$
$= 192 \div 12$
$= 16$.

Addition and subtraction have equal weighting as they are the same operation. Subtracting 2 is the same as adding -2. Once the multiplication and divisions have been dealt with then any additions and subtractions are performed. If there is more than one addition or subtraction in the calculation we perform them in the order they appear in the calculation working from left to right.

$6 + 4 \times 2^{3} - 12$
$= 6 + 4 \times 8 - 12$ (evaluating the indices first)
$= 6 + 32 – 12$ (evaluating the $4 \times 8$)
$= 38 – 12$ (working from left to right)
$= 26$.

In the previous step we considered these two calculations:

a) $6 \div 2(1+2)$
b) $9 – 3 \div \frac{1}{3} + 1$

Use a calculator and input these calculations. Does your calculator obey the rules of BIDMAS? Share your findings in the comments below.

## Problem sheet

Now complete questions 4 and 5 from this week’s worksheet.

## Teaching resources

• Two games: Connect 4 and Whodunnit: these require students to choose a question and use their knowledge of order of operations to evaluate the statement.
• Priority of Operations (BIDMAS): this resource contains ten instant maths ideas covering a whole range of suggestions that may be used as starter questions, extension questions or probing questions to assess understanding.