Arithmetic and Number Operations
Arithmetic and Number Operations
This domain checks fluency with integer arithmetic, order of operations, factors and multiples, rounding, and estimation. Questions often combine several operations in one expression, so the examiner is testing procedure as much as the final value. You should be able to justify each step, not just produce an answer.
Core rules
- Apply BODMAS/PEMDAS: Brackets, Orders (powers/roots), Division and Multiplication left to right, Addition and Subtraction left to right.
- For negative numbers: adding a negative moves left; subtracting a negative moves right; a negative times a negative is positive.
- A prime has exactly two factors, 1 and itself. Use prime factorisation to find LCM and GCD: take highest powers for LCM and lowest shared powers for GCD.
- Rounding: look at the digit immediately after the required place; 5 or more rounds up. Do not round intermediate values in a multi-step calculation unless told to estimate. Estimation questions expect a sensible rounded answer, not an exact one.
Worked example
Evaluate −3 + 4 × (5 − 7)² ÷ 2. Brackets: 5 − 7 = −2. Orders: (−2)² = 4. Multiplication/division left to right: 4 × 4 = 16, 16 ÷ 2 = 8. Addition: −3 + 8 = 5. Answer: 5.
Traps
Working left to right regardless of operation; treating −2² as 4 (it is −4 without brackets); confusing LCM with GCD; rounding 0.45 to 0.5 when asked for one decimal place (it is 0.5) but rounding too early in a chain.