Ratio, Proportion, Percentage and Consumer Arithmetic
Ratio, proportion, percentage and consumer arithmetic
This domain links ratio notation, direct and inverse proportion, percentage change, and money calculations. You must simplify ratios, divide a quantity in a given ratio, use the unitary method, and recognise when two quantities increase together (direct proportion) or one falls as the other rises (inverse proportion). Percentage work includes increase and decrease, profit and loss, discount, VAT or sales tax, simple and compound interest, wages, currency conversion and hire purchase.
Common traps are calculating a percentage change from the new value instead of the original, adding successive percentage changes instead of multiplying multipliers, and confusing percentage points with percent. A 20% discount followed by 10% VAT is not a 10% discount: the multipliers are 0.8 and 1.1, giving 0.88, so the final price is 12% below the original. In reverse-percentage questions, divide by the multiplier rather than subtracting the stated percentage. Keep ratio units consistent and simplify before dividing.
Worked example: after a 15% increase an item costs $92. Find the original price. The multiplier is 1.15, so original = 92 / 1.15 = 80. The original price was $80. Check: 15% of 80 is 12, and 80 + 12 = 92.
Rule of thumb: for percentage changes, write the multiplying factor first; for proportion, identify which quantity is being shared or scaled before doing arithmetic.