Basic Number Operations and Arithmetic Fluency
Fluency with structure, not just speed
Arithmetic questions reward candidates who see numbers as relationships. Secure the order of operations (brackets, indices, multiplication and division left to right, addition and subtraction left to right), integer rules for negatives, and fluent conversion among fractions, decimals and percentages. Memorise multiplication facts to 12 × 12, squares to 15², and common equivalents such as 1/8 = 0.125 and 3/8 = 37.5%. Know divisibility tests for 2, 3, 4, 5, 9, 10 and 11; they turn “which is divisible by 3” into a digit-sum check rather than long division.
Traps that cost marks
Sign errors are the most common: subtracting a negative, or distributing a minus across brackets, changes every following term. In fraction division, multiply by the reciprocal of the divisor, not the dividend. When multiplying decimals, count total decimal places rather than aligning points; when adding, align points exactly. Watch for mixed units inside one expression and for expressions such as 12 ÷ 3 × 2, which equals 8, not 2. Do not cancel across a plus sign.
Worked example
Evaluate 36 − 4 × (7 − 2)² + 18 ÷ 3. Brackets first: 7 − 2 = 5. Indices: 5² = 25. Then 4 × 25 = 100 and 18 ÷ 3 = 6. The expression becomes 36 − 100 + 6 = −58. A quick estimate (about 40 − 100 + 6) confirms the size and sign, catching a misplaced minus.
Rule of thumb: estimate the answer before calculating, then check the final digit or sign against your estimate.