Year 6 Maths reasoning (SATs): Order of operations and brackets
Part of the Year 6 Maths reasoning (SATs) number reasoning chapter. Chapter overview · whole chapter on one page
Order of operations and brackets
Rule
Work out brackets first. Then do multiplication and division (left to right). Then do addition and subtraction (left to right).
Brackets change the order. (2 + 3) x 4 = 20, but 2 + 3 x 4 = 14.
Key ideas
- Brackets first, then x and divide, then add and subtract.
- Work from left to right when the operations have the same priority.
- A bracket can change the answer completely.
Method. Multiplication comes before addition and subtraction.
- Multiply first. 8 x 3 is done before adding.8 x 3 = 24
- Add and subtract from left to right. 12 + 24 = 36, then 36 - 4.12 + 24 - 4 = 32
- Write the answer. 32
Check. 12 + 24 - 4 = 32. ✓
Method. Brackets first, then divide, then multiply and subtract.
- Work out the bracket. 12 + 8 = 20.(12 + 8) = 20
- Divide and multiply. Divide 4 by 2 and multiply 20 by 3.20 x 3 = 60 and 4 / 2 = 2
- Subtract. Take 2 from 60.60 - 2 = 58
- Write the answer. 58
Check. (20 x 3) - 2 = 58. ✓
Method. Work out each group, then add.
- Work out the adults. 4 x 6 = 24 pounds.24 pounds
- Work out the children. 3 x 4 = 12 pounds.12 pounds
- Add the two totals. Add the money from both groups.24 + 12 = 36 pounds
- Write the answer. 36
Check. 4 x 6 + 3 x 4 = 36. ✓
Watch out
Watch out. 2 + 3 x 4 is 14, not 20. Multiply first, then add.
Exam tip
Practice guide. Underline the multiplication and division first, then do the sum from left to right.
Exercise 1C Practice: order of operations
Non-calculatorMethod. Multiply first.
- Multiply. 6 x 3 = 18.18
- Add. 5 + 18 = 23.23
- Write the answer. 23
Check. 5 + 18 = 23. ✓
Method. Divide first.
- Divide. 12 / 4 = 3.3
- Subtract. 20 - 3 = 17.17
- Write the answer. 17
Check. 20 - 3 = 17. ✓
Method. Brackets first.
- Work out the bracket. 7 + 5 = 12.12
- Multiply. 12 x 4 = 48.48
- Write the answer. 48
Check. 12 x 4 = 48. ✓
Method. Brackets, then multiply, then add.
- Work out the bracket. 9 - 4 = 5.5
- Multiply. 6 x 5 = 30.30
- Add. 30 + 3 = 33.33
- Write the answer. 33
Check. 30 + 3 = 33. ✓
Method. Brackets, then divide and multiply, then subtract.
- Work out the bracket. 4 + 2 = 6.6
- Divide. 48 / 6 = 8.8
- Multiply. 8 x 3 = 24.24
- Subtract. 24 - 1 = 23.23
- Write the answer. 23
Check. 48 / 6 = 8, 8 x 3 = 24, 24 - 1 = 23. ✓
Method. Brackets, then multiply, then add and subtract.
- Work out the bracket. 2 + 8 = 10.10
- Multiply. 3 x 10 = 30.30
- Subtract and add from left to right. 100 - 30 = 70, then 70 + 5 = 75.75
- Write the answer. 75
Check. 100 - 30 + 5 = 75. ✓
Method. Put the brackets around the addition, so it is worked out first.
- Work out the bracket first. Brackets come first, so 2 + 3 is worked out before the multiplication.2 + 3 = 5
- Multiply. Then multiply 5 by 4.5 x 4 = 20
- Write the answer. (2 + 3) x 4
Check. (2 + 3) x 4 = 20. ✓
Method. Try a bracket around the subtraction and the addition, then check.
- Try brackets around 10 - 4. (10 - 4) / 2 + 1 = 3 + 1 = 4, which is not 2.4
- Try brackets around 2 + 1 as well. (10 - 4) / (2 + 1) = 6 / 3 = 2.2 is the answer
- Write the answer. (10 - 4) / (2 + 1) = 2.
Check. 6 / 3 = 2. ✓
Method. Multiply and divide first, then add and subtract.
- Work out the multiplications and division. 3 x 4 = 12, 2 x 5 = 10 and 6 / 3 = 2.12 + 10 - 2
- Add and subtract. 12 + 10 = 22, then 22 - 2 = 20.20
- Write the answer. 20
Check. 12 + 10 - 2 = 20. ✓
Method. Work out the cost first, then the change.
- Work out the cost. 3 bags at 3 pounds each is 3 x 3 = 9 pounds.9 pounds
- Work out the change. 10 - 9 = 1 pound.1 pound
- Write the answer. 1
Check. 9 + 1 = 10. ✓
Method. Brackets, then multiply and divide from left to right.
- Work out the bracket. 25 - 7 = 18.18
- Multiply. 18 x 5 = 90.90
- Divide. 90 / 6 = 15.15
- Write the answer. 15
Check. 18 x 5 / 6 = 15. ✓
Method. Test each option.
- Check each option. Test each one against the rule or the calculation.
- Tick the true ones. Each ticked calculation gives 14 when the multiplication or division is done first.2 + 3 x 4, 5 x 2 + 4, 20 - 3 x 2
- Leave the others unticked. These do not match.(2 + 3) x 4, 2 + 12 / 6 are not ticked
- Write the answer. 2 + 3 x 4, 5 x 2 + 4, 20 - 3 x 2
Check. Each ticked option is true. ✓
Watch out. (2 + 3) x 4 is 20, and 2 + 12 / 6 is 4, so they are not ticked.