# BODMAS?

Every time the Daily Mail runs a ‘maths quiz’, they usually include a problem which must be solved using ‘order of operations’, for example:

Without any rules, there would be two possible answers to this problem: ‘9’ or ‘7’. ‘Order of operation’ is important, because it tells us which operations (addition, subtraction, multiplication, division) take precedence. If we ignore the order of operation, and simply work from left to right, then we obtain the following answer:

$1+2×3=9$

But this is the wrong answer! Why? Because if we follow the correct ‘order of operation’, we must always multiply before we add, so the correct answer is:

$1+2×3=7$

To help us remember the correct order of operation, we can use a mnemonic. In the UK, this mnemonic is generally ‘BODMAS‘ (or, if you prefer, ‘BIDMAS‘; more on that, later). So, what does this represent?

BODMAS: Brackets, followed by Orders (i.e. powers or indices), then Multiplication OR division and, finally, Addition OR Subtraction.

Important, it’s NOT ‘Multiplication’ THEN Division’ and it’s NOT ‘Addition THEN Subtraction’.

ALL these operations don’t have to be present in an equation. If there are no ‘brackets’, for example, then we simply ignore the ‘B’ in BODMAS and move on to the next operation.

In our example, following BODMAS, we must perform multiplication BEFORE addition, as follows:

$1+{\mathbf{2}}{\mathbf{×}}{\mathbf{3}}=1+6=7$

Now let’s look at another example:

$\left(1+2\right)×3=?$

This time, we have brackets and, if we follow BODMAS, then we must solve what’s inside the brackets first:

${\mathbf{\left(}}{\mathbf{1}}{\mathbf{+}}{\mathbf{2}}{\mathbf{\right)}}×3=3×3=9$