Operations on Whole Numbers
What the exam tests
Operations on whole numbers tests addition, subtraction, multiplication and division, including long methods and word problems. It also tests the order of operations and checking answers.
Core rules
- Line up digits by place value for addition and subtraction. Carry when a column totals 10 or more; borrow from the next column when subtracting a larger digit from a smaller one.
- Long multiplication: multiply by each digit, shift one place left for tens, then add the partial products.
- Division: divide, multiply, subtract, bring down. The remainder must be less than the divisor.
- BODMAS/BIDMAS order: brackets, then powers, then multiplication and division from left to right, then addition and subtraction from left to right.
- Check with the inverse: addition with subtraction, multiplication with division.
Worked example
Calculate 36 ÷ (7 − 4) + 5 × 6. Brackets first: 7 − 4 = 3. Then division and multiplication in order: 36 ÷ 3 = 12 and 5 × 6 = 30. Finally add: 12 + 30 = 42. Working left-to-right without the bracket rule would give a different, wrong answer.
Traps that cost marks
Do not add before multiplying in an expression such as 2 + 3 × 4; multiply first to get 14. Do not ignore a remainder; write it clearly or as a fraction. When subtracting across zeros, borrow correctly. Keep columns aligned, especially in long multiplication and division.