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Order of Operations

Maths · Stage 2 Extension
Year 4
★ Extension · Stage 3 (Years 5–6)
Lesson Guide
Explanation
Ava and Ben both work out 2 + 3 times 4. Ava goes left to right and gets 20. Ben multiplies first and gets 14. They cannot both be right — a maths question has to have one answer, or nobody could ever agree on anything. So mathematicians agreed on an order, and everybody in the world follows it. Ben is following it. By the end of this lesson so will you.
Your Turn
Before you read on, work out 10 + 2 times 5 both ways. Check: left to right gives 60, multiplying first gives 20. Only one of those is correct.
Watch Out
Reading left to right is what your eyes want to do, and it is wrong more often than it is right. The rule beats the habit.
Explanation
Here is the order. Brackets first. Then multiplication and division. Then addition and subtraction last. There is a reason it is not random: multiplying is just repeated adding, so 3 times 4 is a bigger, tighter job than a single plus. Bigger jobs get done first, and the loose plus signs mop up at the end. So in 2 + 3 times 4, the 3 times 4 is one lump worth 12, and then you add the 2.
Your Turn
Say the three levels out loud without looking: brackets, then what, then what? Check: brackets, then multiply and divide, then add and subtract.
Watch Out
Multiply and divide are on the SAME level as each other — one is not stronger than the other. Same for add and subtract.
Explanation
What if a question has both a divide and a multiply, like 20 divided by 4 times 2? They are on the same level, so neither one gets to go first. When jobs are equally strong you just work left to right, like reading. 20 divided by 4 is 5, then 5 times 2 is 10. If you grabbed the multiply first you would get 2.5, which is wrong. The same goes for a plus and a minus together.
Your Turn
Work out 12 minus 5 + 3, left to right. Check: 12 minus 5 is 7, then 7 + 3 = 10. If you added first you would get 4, which is wrong.
Watch Out
The most common slip in the whole topic: seeing a times sign and doing it before a divide that came earlier. Equally strong means left first.
Explanation
Brackets are the override switch. Whatever is inside them gets done first, no matter what. 2 + 3 times 4 is 14, but put brackets round the 2 + 3 and it becomes 5 times 4, which is 20. Exactly the same digits and signs, and a completely different answer. That is why brackets exist: they let whoever wrote the question tell you the order they want.
Your Turn
Work out (10 minus 4) times 3, then 10 minus 4 times 3. Check: 18 and negative 2. Actually 10 minus 12, so the second one dips below zero — the brackets matter enormously.
Watch Out
Do not skip the brackets because they look small. They are the loudest thing in the question.
Explanation
Here is a full one: 6 + (8 minus 3) times 4 minus 10 divided by 5. Take it one line at a time. Brackets first, so the 8 minus 3 becomes 5. Then the strong operations: 5 times 4 is 20, and 10 divided by 5 is 2. Now only plus and minus are left, so work left to right: 6 + 20 is 26, minus 2 is 24. Writing one line per step is what stops you making mistakes — it looks slower and it is much faster in the end.
Your Turn
Try 3 times (4 + 2) minus 8 divided by 4, one line at a time. Check: brackets give 6, so 3 times 6 is 18, and 8 divided by 4 is 2, so 18 minus 2 = 16.
Watch Out
Doing two steps in your head on one line is where the marks disappear. Write every line, even the easy ones.
📌 Key Points — this lesson in a nutshell
  • Brackets first, then × and ÷, then + and −.
  • Same level? Work left to right — that covers × with ÷, and + with −.
  • Brackets overrule everything, and they change the answer on purpose.
  • One step per line. Two steps at once is where the mistakes live.
Step 1: Introduction
Step 1 of 5
Who is right? Ava works left to right 2 + 3 × 4 = 5 × 4 = 20 Ben multiplies first 2 + 3 × 4 = 2 + 12 = 14 Same question. Two different answers. Maths cannot allow that — so there is a rule about what to do first. Ben is right. Here is why.
The order everyone agrees on 1 Brackets ( ) anything inside them, first 2 Multiply × and divide ÷ the strong operations 3 Add + and subtract − the weak operations, last Multiplying is repeated adding, so it is a bigger job. Bigger jobs go first. That is the whole idea.
When two jobs are equally strong 20 ÷ 4 × 2 Left to right ✓ 20 ÷ 4 = 5 5 × 2 = 10 10 Multiply first ✗ 4 × 2 = 8 20 ÷ 8 = 2.5 2.5 Divide and multiply are equally strong. Neither wins, so you simply read them left to right, the way you read a sentence.
Brackets change the answer on purpose 2 + 3 × 4 multiply first 2 + 12 14 (2 + 3) × 4 brackets first 5 × 4 20 Same digits, same signs — different answer. Brackets are how you say "do this bit first". They are not decoration. They are an instruction, and they overrule every other rule.
One question, one line at a time 6 + (8 − 3) × 4 − 10 ÷ 5 brackets: 6 + 5 × 4 − 10 ÷ 5 multiply: 6 + 20 − 10 ÷ 5 divide: 6 + 20 − 2 left to right: 26 − 2 = 24 One step per line. Never two at once.
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