Order of operations
Which part of a sum do you do first? Brackets, then powers and roots, then multiply and divide, then add and subtract. Read one step, play with it, then tap “I understand this”.
Why the order matters
What is 4 + 6 × 2? If you work from the left, you get 20. But the right answer is 16, because multiplying comes first: 6 × 2 = 12, and 4 + 12 = 16.
Everyone in the world uses the same order, so that everyone gets the same answer.
The rule
- Brackets first ( ).
- Then multiply and divide, from left to right.
- Then add and subtract, from left to right.
Multiply and divide are equally important: do whichever comes first (on the left). The same with add and subtract.
Multiplying is a shortcut for repeated adding: 6 × 2 is a packet of 6 + 6. In 4 + 6 × 2 the packet must be finished first: 4 + 12 = 16.
Watch it step by step
The solver
Tap “Next step”. The yellow part is done first.
Practise
What is the answer?
Watch out for the left-to-right trap!
Correct: 0Brackets change the answer
Computers and some calculators follow the rule; a simple calculator might not. Always work it out yourself.
Grade 7: powers, roots and negative numbers
In Grade 7 powers and roots join in. They come after brackets, but before multiply and divide:
- Brackets
- Orders: powers and roots
- Divide and Multiply, from left to right
- Add and Subtract, from left to right
(−3)² = 9, but −32 = −9. In (−3)² the negative number itself is squared; in −32 only the 3 is squared.
A root sign works like brackets: first work out everything under the root.
A power is a short way of writing repeated multiplication: 3² is really (3 × 3). It is like a little bundle that belongs together, so we work it out first.
Check yourself
- Brackets first.
- Then multiply and divide, from left to right.
- Then add and subtract, from left to right.
- 4 + 6 × 2 = 16, not 20.
Write these points in your maths book. Read them again the night before the test.
Quick questions
Tap an answer. If you get one wrong, read why and go back to that step. You get new questions every time.
You ticked all 6 steps! Now you are ready for the quiz.- Practice sheet for this classQuestions + memo · 1 A4 pagePractice sheet
- Numbers9 pages · PDFPaperMemo
Ready for more? The Grade 7 order of operations quiz gives you new sums every time.
- One step a day is enough. Ten calm minutes work better than an hour the night before the test.
- Write a sum like 3 + 4 × 5 on paper and ask the whole family: who gets 23 and who 35? Let your child explain the rule.
- Ask your child to tell you the rule in their own words. If they can explain it, they understand it.
- The ticks (“I understand this”) are saved on this device only. We never ask for names or emails.
Follows CAPS for Grade 7 Maths. Always check your teacher’s notes and textbook too.