mathsGrade 6-82 min read

BODMAS: the order operations actually happen in

Why 2 + 3 × 4 is 14 and not 20. The order maths is done in isn't a suggestion — it's a fixed rule, and one line of the rule trips up almost everyone.

Type $2 + 3 \times 4$ into a calculator and it says $14$ , not $20$ . That's not the calculator being clever — it's following the order of operations, the agreed sequence every calculation is done in. Without it, the same sum would give different answers to different people, which would make maths useless.

The order: BODMAS

Work through an expression in this order, top to bottom:

Letter	Meaning	Example
B	Brackets	$(2 + 3)$ first
O	Orders (powers, roots)	$4^2$ , $\sqrt{9}$
DM	Division and Multiplication	$\times$ and $\div$
AS	Addition and Subtraction	$+$ and $-$

So in $2 + 3 \times 4$ , the multiplication outranks the addition: do $3 \times 4 = 12$ first, then $2 + 12 = 14$ .

The line everyone gets wrong

Division and multiplication are equal rank — and so are addition and subtraction. When two operations of the same rank sit together, you work left to right, not "all multiplication before all division."

12 \div 2 \times 3 = (12 \div 2) \times 3 = 6 \times 3 = 18

Doing the multiplication first here ( $2 \times 3 = 6$ , then $12 \div 6 = 2$ ) gives the wrong answer. Same rank means left to right.

Worked example

5 + 2 \times (8 - 3)^2

Brackets: $8 - 3 = 5 \Rightarrow 5 + 2 \times 5^2$
Orders: $5^2 = 25 \Rightarrow 5 + 2 \times 25$
Multiply: $2 \times 25 = 50 \Rightarrow 5 + 50$
Add: $55$

When in doubt, add brackets of your own. Writing $2 + (3 \times 4)$ changes nothing about the answer but makes the order impossible to misread. Examiners never penalise brackets that make your intention clear.

Last revised 28 August 2024.