Topics / Maths
Arithmetic
Every harder maths question rests on quick, accurate arithmetic. Grammar school papers reward children who can add, subtract, multiply and divide larger numbers reliably and choose smart shortcuts instead of grinding every step.
What is tested
- Four operations with whole numbers, including 3- and 4-digit numbers
- Order of operations (brackets first)
- Mental strategies such as doubling, halving and partitioning
Worked example
Work out 347 + 586 − 129.
- Add first: 347 + 586 = 933.
- Then subtract: 933 − 129 = 804.
- Check by adding back: 804 + 129 = 933.
Answer: 804
Exam-day checklist
- Line up digits by place value for written methods.
- Estimate first so you can spot a wild answer.
- Check with the inverse operation.
- Use brackets and order of operations for mixed sums.
Common mistakes
- Forgetting to carry or borrow.
- Doing operations left to right when a multiplication should come first.
- Copying a number wrongly between lines of working.
Try it yourself
1. Work out 48 × 25.
Show answer
1,200
25 is a quarter of 100, so 48 × 100 ÷ 4 = 4,800 ÷ 4 = 1,200.
2. Work out 1,000 − 387.
Show answer
613
Count up: 387 + 13 = 400, + 600 = 1,000, so the difference is 613.
Practise arithmetic with school-style questions
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