Year 6 Arithmetic (SATs): Order of operations and mixed problems
Part of the Year 6 Arithmetic (SATs) place value and the four operations chapter. Chapter overview · whole chapter on one page
Order of operations and mixed problems
Rule
Work out brackets first. Then do multiplication and division, working from left to right. Then do addition and subtraction, working from left to right.
So 3 + 4 × 5 is 3 + 20 = 23, not 35.
Key ideas
- Brackets first, then multiply and divide, then add and subtract.
- Multiplication and division are done before addition and subtraction.
- Work from left to right when the operations are the same.
- Check by estimating: the answer should be about right.
Method. Multiplication is done before addition.
- Multiply first. Do 4 × 5 before adding 3.4 × 5 = 20
- Add the 3. Now add 3 to 20.3 + 20 = 23
- Write the answer. 23
Check. Not (3 + 4) × 5 = 35: the brackets are missing from the question. ✓
Watch out. Without brackets, the multiplication is done first, so the answer is 23.
Method. Brackets first, then division and multiplication from left to right.
- Do the brackets. 8 + 4 = 12 inside the brackets.(8 + 4) = 12
- Divide. Then 12 ÷ 3 = 4.12 ÷ 3 = 4
- Multiply. Finally 4 × 2 = 8.4 × 2 = 8
- Write the answer. 8
Check. Working left to right after the brackets gives the same answer. ✓
Method. Multiply before you add and subtract, and then go from left to right.
- Multiply. 3 × 4 = 12 is done first.20 - 12 + 6
- Subtract. Then 20 - 12 = 8.8 + 6
- Add. Finally 8 + 6 = 14.14
- Write the answer. 14
Check. The multiplication comes before the subtraction and addition. ✓
Watch out. Doing the subtraction first gives 17 × 4 + 6 = 74, which is wrong.
Exercise 1E Practice: order of operations and problems
Non-calculatorMethod. Multiply before adding.
- Multiply. 3 × 4 = 12.6 + 12
- Add. 6 + 12 = 18.18
- Write the answer. 18
Check. Adding first would give 36, which is wrong. ✓
Method. Divide before adding.
- Divide. 20 ÷ 4 = 5.5 + 6
- Add. 5 + 6 = 11.11
- Write the answer. 11
Check. Check: 11 - 6 = 5 = 20 ÷ 4. ✓
Method. Brackets first, then multiply.
- Brackets. 9 - 3 = 6.6 × 4
- Multiply. 6 × 4 = 24.24
- Write the answer. 24
Check. Without brackets, 9 - 12 would be -3, which is wrong. ✓
Method. Divide before subtracting.
- Divide. 12 ÷ 3 = 4.18 - 4
- Subtract. 18 - 4 = 14.14
- Write the answer. 14
Check. The answer is 14, not 2. ✓
Method. Brackets, then multiply, then subtract.
- Brackets. 5 + 7 = 12.2 × 12 - 4
- Multiply. 2 × 12 = 24.24 - 4
- Subtract. 24 - 4 = 20.20
- Write the answer. 20
Check. 20 + 4 = 24, which is 2 × 12. ✓
Method. Brackets first, then divide.
- Brackets. 12 + 8 = 20.20 ÷ 5
- Divide. 20 ÷ 5 = 4.4
- Write the answer. 4
Check. 4 × 5 = 20. ✓
Method. Multiply the packs first, then add the single pencils.
- Work out the packs. 3 packs of 6 is 18 pencils.3 × 6 = 18
- Add the singles. 18 + 4 = 22.18 + 4 = 22
- Write the answer. 22
Check. Ali has 22 pencils in total. ✓
Method. Multiply the rows by the chairs in each row, then subtract the chairs taken away.
- Find all the chairs. 12 × 15 = 180.12 × 15 = 180
- Take away the chairs. 180 - 18 = 162.180 - 18 = 162
- Write the answer. 162
Check. 162 + 18 = 180. ✓
Method. Work out the cost for each group, then add.
- Adults. 5 × £4 = £20.£20
- Children. 6 × £2 = £12.£12
- Add the two totals. £20 + £12 = £32.£32
- Write the answer. £32
Check. The cost for the adults is more than half the total, so £32 is sensible. ✓
Method. Brackets change the order: the sum inside is done first.
- Try the brackets around 7 + 5. (7 + 5) × 3 = 12 × 3.(7 + 5) × 3
- Work it out. 12 × 3 = 36, which is the target.12 × 3 = 36
- Write the answer. (7 + 5) × 3 = 36
Check. Without brackets, 7 + 5 × 3 is 22. ✓
Method. Try brackets around the first sum.
- Brackets around 4 + 3. (4 + 3) = 7.(4 + 3) × 2 + 1
- Work it out. 7 × 2 = 14, then 14 + 1 = 15.14 + 1 = 15
- Write the answer. (4 + 3) × 2 + 1 = 15
Check. Without the brackets the answer is 11. ✓
Method. Subtraction is done from left to right.
- Do the first subtraction. 10 - 4 = 6.10 - 4 = 6
- Do the second subtraction. 6 - 3 = 3.6 - 3 = 3
- Write the answer. No, the answer is 3, because subtraction works from left to right.
Check. The answer is 3, not 9. ✓
Method. Test each choice against the question.
- Read what the question asks. Decide what you need to find or check.
- Test the choice. 2 + 3 × 4 means 2 + 12, which is 14.2 + 3 × 4 = 14 is right
- Reject the other choices. Adding first gives 20, and multiplying the whole thing gives 24. Both break the order of operations.2 + 3 × 4 = 20 and 2 + 3 × 4 = 24 are not right
- Write the answer. 2 + 3 × 4 = 14
Check. 2 + 3 × 4 = 14 is right. ✓