Most sums use a single operation at a time. But what should you do with an expression that mixes them, like 2 + 3 \times 4?

One person adds first — 2 + 3 = 5, then 5 \times 4 = 20. Another multiplies first — 3 \times 4 = 12, then 2 + 12 = 14. They can't both be right! So that everyone gets the same answer, mathematicians agreed on an order of operations: a fixed order for the four operations — addition (+), subtraction (-), multiplication (\times), and division (\div).

Strong operations go first

The rule sorts the four operations into two tiers. Multiplication and division are the "strong" pair — they happen first. Addition and subtraction come after.

So 2 + 3 \times 4 = 14, not 20. Press play to watch it unfold (a fresh expression each time):

Same tier? Left to right

When the operations are on the same tier, just work left to right, like reading a sentence.

(Not 10 - 7 = 3 — the subtraction is further left, so it goes first.) Multiplication and division share their tier the same way:

Parentheses jump the queue

What if you really do want to add first? Wrap it in parentheses (round brackets). Whatever sits inside parentheses is worked out before anything else:

Same numbers, same operations — but the parentheses flip the answer from 14 to 20. That is exactly what they are for.

The whole rule, in order

1. Parentheses — innermost first.
2. Multiplication and division — then these, left to right.
3. Addition and subtraction — last of all, left to right.

A handy way to remember it is the word BODMAS: Brackets, Orders (powers), Division, Multiplication, Addition, Subtraction. "Brackets" are the parentheses, and "Orders" are powers — a lesson for later.

One trap to watch: DM is a single tier and so is AS. Do each pair left to right — don't always do division before multiplication, or addition before subtraction. (Some countries spell the very same rule PEMDAS.)