What is the order of operations?

Work out brackets first, then powers, then multiplication and division from left to right, then addition and subtraction from left to right. So 2 + 3 x 4 is 2 + 12 = 14, because the multiplication happens before the addition regardless of which comes first in the line.

Why does multiplication come before addition?

Because 3 x 4 is shorthand for a group - three fours already added together. In 2 + 3 x 4 the multiplication is a package deal: you are adding 2 to a group of three fours. Unwrapping the package first is not a convention someone chose at random; it is what the notation means.

Is PEMDAS the same as BODMAS or BIDMAS?

Yes - they are the same rule with different letters. The trap in all of them is reading the letters as six separate steps. Multiplication and division are ONE step done left to right, and addition and subtraction are one step done left to right. 8 / 2 x 4 is 16, not 1, because you go left to right through the x and / tier.

11. Addition and subtraction sit on the same tier and go left to right: 8 - 2 = 6, then 6 + 5 = 11. Doing the addition first (2 + 5 = 7, then 8 - 7 = 1) applies a priority that does not exist.

Order of Operations

Here is the argument that breaks the internet every few months: 2 + 3 × 4. Half the comments say 20, half say 14, and the half that says 14 is right — not because a committee voted, but because 3 × 4 was never two numbers. It was a package.

This guide gives you the rule as three steps, then the reason it exists, then the two traps that produce almost every wrong answer.

The rule, in three steps

Brackets first. Anything in brackets is worked out before it can touch the rest.
Then × and ÷, left to right. One tier, one sweep. (Powers like 3² sit just above this tier — square first, then multiply.)
Then + and −, left to right. Also one tier, one sweep.

That is the whole rule. PEMDAS, BODMAS and BIDMAS are all this list wearing different hats.

Why the order exists

Multiplication is compressed addition: 3 × 4 means 4 + 4 + 4. So 2 + 3 × 4 is really 2 + (4 + 4 + 4) — a two, plus a group of three fours. The group was built before the sentence was; the × sign just keeps it wrapped. Unwrapping the package before adding the 2 is not politeness to a convention. It is reading the notation for what it says.

Brackets exist for the opposite moment: when you want the addition to happen first, you say so out loud. (2 + 3) × 4 = 5 × 4 = 20. Same three numbers, different sentence.

Worked examples, one rung at a time

Step 2 beats step 3: multiply before you add

2 + 3 × 4 → 2 + 12 → 14

5 × 2 + 3 × 4 → 10 + 12 → 22 — both packages open first, then the adding.

Brackets change the sentence

(2 + 3) × 4 → 5 × 4 → 20

18 − (4 + 6) → 18 − 10 → 8

All four operations at once

Work the tiers in order: brackets, then × and ÷, then + and −.

7 + 2 × 6 − 5 → 7 + 12 − 5 → 19 − 5 → 14

With a power

3² + 4 × 5 → 9 + 20 → 29 — the square unwraps first (it is compressed multiplication, one level further up), then the ×, then the +.

The two traps worth naming

Reading the letters as six steps. The M and D in PEMDAS are one tier, left to right — and so are A and S. 8 ÷ 2 × 4 = 4 × 4 = 16, not 1. 8 − 2 + 5 = 6 + 5 = 11, not 1. Doing all multiplication before all division (or all addition before all subtraction) invents a priority that does not exist.
Sweeping right to left. Within a tier the sweep is left to right. It only matters for ÷ and −, which is exactly where people get burned.

Why left to right? Because − and ÷ are not symmetric: 8 − 2 is not 2 − 8. The convention picks one reading order so the same line means the same thing to everyone. Addition and multiplication alone would not need it — order does not change them — which is why the trap only bites when subtraction or division shows up.

Learn it properly in the app

Math Challenge teaches this as a proper lesson ladder, one idea per lesson, each with pictures and try-it problems:

Brackets First — brackets say which part to work out first.
Multiply and Divide Before Adding and Subtracting — no brackets? Do × and ÷ first, left to right.
Brackets with All Four Operations — the full rule: brackets, then × and ÷, then + and −.

All three live in the Basic Arithmetic lessons in the app's Learn tab.

Practice it in the game

The Order of Ops topic drills exactly these shapes: a + b × c, two packages like a × b + c × d, bracketed sentences like (a + b) × c, and in hard mode four-term runs and squares like 2² + 3 × 4. Difficulty rises as you get them right.

Your turn

Three to try — tap what you get.

3 + 4 × 2

(3 + 4) × 2

20 − 12 ÷ 4

Practice order of operations free →