Number and Arithmetic
Core ideas
Number questions reward fluency with the four operations applied to integers, fractions, decimals and percentages, plus confident movement between those forms. You need place value and rounding (including significant figures), order of operations, factors and multiples, prime factorisation, HCF and LCM, ratio and proportion, powers and roots, and standard form.
Traps
- Working left to right instead of applying the order of operations: indices first, then multiplication and division, then addition and subtraction.
- Sign errors with negatives: (-3)² = 9 but -3² = -9.
- Assuming a percentage increase followed by the same percentage decrease returns to the starting value.
- Carrying a rounded value into a later step instead of the exact value.
- Comparing or combining quantities that are in different units.
Worked example
Increase 80 by 15%, then decrease the result by 15%. A 15% increase is a multiplier of 1.15, so 80 × 1.15 = 92. A 15% decrease is a multiplier of 0.85, so 92 × 0.85 = 78.2. The answer is not 80, because the second change acts on a larger base than the first.
Rule of thumb
For any percentage change of r%, use a single multiplier: 1 + r/100 for an increase, 1 - r/100 for a decrease. Chaining multipliers is faster and safer than calculating the change and adding it each time.