Is 2 + 3 × 4 fourteen, or twenty? Both look reasonable — and that is exactly the problem. So everyone agrees on one fixed order for doing the maths, and suddenly there is only ever one answer.
Start hereTake 2 + 3 × 4. Read it left to right and you get 20. Do the multiplying first and you get 14. Same symbols, different answers — and a maths where the answer depends on who is reading is no use to anyone.
So mathematicians did the sensible thing: they wrote down one fixed order of operations that everybody follows. Brackets first, then indices (powers), then multiplying and dividing, then adding and subtracting. In the IB and the UK we remember it with the word BIDMAS. Follow it, and 2 + 3 × 4 is always 14 — for you, for your teacher, for a calculator in Tokyo, for a computer running a spaceship. The rule isn't there to trip you up. It's there so the whole world can read the same line of maths and land on the same number.
Imagine the sum 2 + 3 × 4 with no rules at all. You start at the left like reading a sentence: 2 plus 3 is 5, then 5 times 4 is 20. Tidy. But your friend looks at the same line, spots the multiplication, and does that first: 3 times 4 is 12, then plus 2 is 14. You can't both be right — yet nothing in the symbols says who wins. That gap is what the order of operations closes.
Here are the two paths side by side. Both are computed live, so you can trust the numbers — only one of them follows the agreed order.
Tempting, because it's how we read words. But it treats "+" and "×" as equals taken in order, and they're not — so it quietly gives the wrong answer.
Multiplying outranks adding, so it happens first — no matter where it sits in the line. This is the answer every calculator and mathematician agrees on.
The order of operations isn't a maths fact you discover — it's an agreement we keep, like driving on the same side of the road.
Why does multiplication get to jump the queue? Because 3 × 4 is really a shorthand. It means "three lots of four," a single quantity bundled up — and you can't break that bundle apart just because a "+ 2" is standing in front of it. The multiplication describes one thing (twelve), and the addition then adds two to it. Reading strictly left to right would chop the bundle in half, which is why it goes wrong. The rule simply protects the things that were always meant to stay together.
BIDMAS is six letters standing for four jobs, done strictly in order from the top of this ladder down. At each level you finish everything on that level before you drop to the next.
Anything inside ( ) first. Brackets are the boss — they let you force a part to happen before all the rest.
Powers and roots next — the little raised numbers, like the ² in 3². "Index" is just the posh word for a power.
These two share a level — equal in rank. When both appear, you take them left to right.
Last of all, and also equal in rank to each other. Again: when both appear, work left to right.
The big trap in the name: D coming before M does not mean divide before multiply, and A before S doesn't mean add before subtract. Each of those pairs sits on the same rung — we'll prove it with a live demo further down.
You may have met the same rule under a different name. In some countries it's BODMAS (the "O" stands for "Of" or "Order," another word for indices), and in the United States it's PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction). Different letters, identical rule — brackets, then powers, then the times-and-divide level, then the plus-and-minus level. So if a friend abroad swears by PEMDAS, you're both following the same ladder.
Pick an expression. The glowing piece is the one operation BIDMAS says to do next — and the note tells you why it wins. Tap Do this step to carry it out; the expression rewrites itself and the spotlight jumps to whatever comes next. Keep going until there's nothing left but the answer.
Notice the spotlight never just slides left to right. It hunts for brackets first, then powers, then the times-and-divide level, then plus-and-minus — exactly the ladder from above, turned into a moving highlight.
Run 2 + 3 × 4 and watch the multiplication light up before the plus, even though the plus is written first — there's your 14, not 20. Then try 6 + (4 − 1)² ÷ 3. The brackets glow first (4 − 1 makes 3), then the bracket vanishes because it's only holding one number, then the little ² fires (3² is 9), then the divide (9 ÷ 3 is 3), and only at the very end the add — landing on 9. Every jump of the spotlight is the ladder choosing the next rung.
Here's the rule people forget. Divide and multiply live on the same rung, and so do add and subtract. So what happens when a line has two of them, like 24 ÷ 4 × 3? There's no winner by rank — they're equals. The tie-breaker is simple: do them in the order they appear, left to right. The divide is written first, so the divide goes first.
It really matters. Tap each example to see the correct left-to-right path next to the answer you'd get by wrongly doing the second operation first. Both numbers are computed live.
See how far apart the answers land? With 24 ÷ 4 × 3, going left to right gives 18, but grabbing the multiplication first gives a stray 2. With 20 − 6 + 5, left to right gives 19, while doing the addition first gives 9. The maths didn't change — only the order did, and order is everything. That's why "DM" and "AS" share a rung: neither letter outranks its partner, so the position on the page breaks the tie.
Sometimes the natural order isn't the order you want. Suppose you need to add 5 and 3 first, then multiply by 2. Written plainly as 5 + 3 × 2, BIDMAS would do the multiply first and give 11 — not what you meant. So you reach for brackets: (5 + 3) × 2. The brackets are an override button. They shout "this part happens first, no matter what the ladder says," and the answer becomes 16.
Take the richer line 40 − (5 + 3) × 2 and walk it the BIDMAS way. Brackets first: 5 + 3 is 8, so the line becomes 40 − 8 × 2. Now the times-and-divide level: 8 × 2 is 16, giving 40 − 16. Finally the subtraction: 24. Notice the subtraction was written ages before the multiplication, yet it had to wait its turn at the very bottom of the ladder. Brackets reordered the start; rank ordered the rest.
A handy habit: when a sum looks crowded and you're unsure how someone will read it, add brackets yourself to spell out exactly what you mean. They never change a correct answer, and they wipe out any doubt. Mathematicians and programmers do this constantly — not because they've forgotten BIDMAS, but because a clear bracket is kinder than a clever one-liner.
Type 2 + 3 × 4 into different machines and you can genuinely get different answers. A cheap four-function calculator — the kind on a shop till or a basic phone app — often works strictly left to right, button by button, so it announces 20. A scientific calculator, the kind you use in class, knows BIDMAS and waits to evaluate the whole line, so it gives 14. The machine isn't broken; it's just following a different (simpler) recipe. Knowing which kind you're holding saves you from trusting the wrong number.
People slip for the same reasons. The most common is racing left to right out of habit, because that's how we read. The next is misreading the "DM" and "AS" pairs as a strict order and forcing multiply before divide, or add before subtract. And a quieter one: when an expression is written sloppily, even careful people can read it two ways. That's not really a BIDMAS failure — it's a writing failure, and the cure is the same as always: more brackets, fewer arguments.
You may even have seen a sum go viral online with thousands of people fighting over the "real" answer. Almost always, the fight isn't about whether BIDMAS is true — it's about an expression written so ambiguously that reasonable people disagree on what it even says. The lesson isn't to pick a side; it's to write maths clearly enough that the question never comes up.
True only when everything is on the same rung. The moment a × or a power shows up beside a +, left to right gives the wrong answer — that's the whole 14-versus-20 story.
No — "DM" isn't an order. Divide and multiply are equal partners; you take whichever comes first as you read left to right. Same goes for add and subtract.
The truth that replaces both myths is one sentence: climb the ladder by rank, and break ties left to right. Rank decides between different levels — a power beats a multiply, a multiply beats an add. Left-to-right only steps in when two operations are genuinely equal and you need a tie-breaker. Hold those two ideas together and you'll never be fooled by either myth, because you'll always know why the next step is the next step — not just that a rhyme told you so.
Work each one out in your head using the ladder, then tap your answer. You'll see straight away whether it's right — and the full worked steps either way. No pressure; getting one wrong is just the fastest way to spot which rung you skipped.
If a question caught you out, look at which rung the steps started on. Nearly every order-of-operations slip is really one thing: doing a lower rung before you'd finished a higher one. Slow down, find the top rung that still has work on it, and do that first — every time.
Without a fixed order, the same sum gives different answers. BIDMAS is the one rulebook everyone shares, so 2 + 3 × 4 is always 14.
Brackets, then indices, then divide-and-multiply, then add-and-subtract. Finish each level before dropping to the next.
When two operations share a rung — × with ÷, or + with − — there's no winner by rank, so do them in reading order.