Four Operations
Addition, subtraction, long multiplication and long division, including mental maths strategies.
What is Four Operations?
The four operations – addition, subtraction, multiplication and division – are the foundation of all maths. In the 11+ exam, you will be expected to carry out these calculations quickly and accurately, often without a calculator.
Questions may involve large numbers, decimals or multi-step problems. You need to be confident with both written methods (column addition, long multiplication, short and long division) and mental strategies for simpler calculations.
Mastering these operations is essential because almost every other maths topic builds on them.
Step-by-Step Method
Line up the digits by place value
For addition and subtraction, write the numbers in columns so that ones, tens, hundreds etc. are all lined up.
Work from right to left
Start with the ones column and work leftwards. Carry or borrow as needed.
For multiplication, use the column method or grid method
Break one number into parts (e.g. 36 = 30 + 6), multiply each part, then add the results together.
For division, use short or long division
Short division (bus stop method) works well for single-digit divisors. Use long division for two-digit divisors.
Check your answer
Use the inverse operation to check. If 245 + 378 = 623, then 623 – 378 should give 245.
Worked Examples
4,567 + 2,985 = ?
Working
- Start from the right: 7 + 5 = 12. Write 2, carry 1.
- 6 + 8 + 1 = 15. Write 5, carry 1.
- 5 + 9 + 1 = 15. Write 5, carry 1.
- 4 + 2 + 1 = 7.
48 x 36 = ?
Working
- 48 x 6 = 288 (8×6=48, carry 4; 4×6=24, +4=28)
- 48 x 30 = 1,440 (48×3=144, then add a zero)
- 288 + 1,440 = 1,728
846 / 6 = ?
Working
- 8 / 6 = 1 remainder 2. Write 1, carry 2.
- 24 / 6 = 4. Write 4.
- 6 / 6 = 1. Write 1.
Common Mistakes
Forgetting to carry in addition or multiplication, leading to an answer that is too small.
Always write your carry digit clearly above the next column and remember to add it.
Misaligning columns so digits are added to the wrong place value.
Use squared paper or draw neat columns. Line up the ones digits first.
Writing the remainder as a decimal incorrectly in division (e.g. 17 / 5 = 3 r 2, then writing 3.2).
A remainder of 2 out of 5 is 2/5 = 0.4, so the answer is 3.4, not 3.2.
Top Tips
- Learn your times tables up to 12 x 12 by heart – this makes multiplication and division much faster.
- Use estimation to check your answer. Round the numbers and do a quick mental calculation to see if your answer is in the right ballpark.
- For subtraction, you can check by adding your answer to the smaller number – you should get the larger number.
- When multiplying by 5, try multiplying by 10 and halving the result.
- Write neatly and keep columns straight – most errors come from messy working.
Ready to practise?
Put these techniques into action with our free practice papers.
Practise Maths Questions