Number and Operations
Number and Operations
Candidates should be fluent with integers, fractions, decimals, percentages, ratios, powers, and roots. Know place value, factors and multiples, prime factorisation, the order of operations, and properties of zero and one. Move confidently between fractions, decimals, and percentages; simplify ratios; and solve proportional problems. Estimation and reasonableness checks are part of the skill, not an optional extra. Also interpret remainders in context and use inequality symbols correctly.
Traps appear with negative signs, especially when subtracting integers or distributing a negative. Cancelling terms instead of factors is a frequent error: in (x+3)/3, the 3s do not cancel. Dividing by a fraction requires multiplying by its reciprocal. In percentage questions, identify the base; a 20% increase followed by a 20% decrease does not restore the original amount. Check whether a question asks for an exact value, an estimate, or a rounded answer, and keep units consistent.
Rule of thumb: rewrite quantities in the same form before comparing or combining them. The word 'of' usually means multiply, and percentage change is (new − old) ÷ old × 100%.
Worked example: evaluate (3/4) ÷ (2/9). Multiply by the reciprocal: (3/4) × (9/2) = 27/8 = 3.375. Estimate first: 0.75 ÷ about 0.22 is a little over 3, so the result is reasonable.