Number and Algebra: operations, percentages, rates and linear relationships
Number and algebra is the toolkit the other three strands assume. In the numeracy Common Assessment Task (CAT) it appears through pay slips, discounts, GST invoices, recipes, fuel use and simple formulas - not as abstract manipulation, but as a decision about which operation to apply and in what order. You need fluency with integers, decimals, fractions, percentages, ratios and rates, plus the confidence to form and solve a simple linear equation from a written description.
Rules worth memorising
- Order of operations: brackets, then indices, then × and ÷ (left to right), then + and −.
- Percentage change: multiply by (1 ± r). A 25% discount means × 0.75; adding 15% GST means × 1.15.
- Reverse percentages: divide by the multiplier. Never subtract the GST percentage from a GST-inclusive total.
- Ratios: multiply every part by the same factor, and check whether the ratio is part-to-part or part-to-whole.
- Rates: reduce to ‘per 1 unit’ and convert units before calculating.
- Linear relationships: y = mx + c. Solve by applying the inverse operation to both sides, working in reverse order.
Worked example
An invoice total of $386.40 includes 15% GST. What was the amount before GST, and how much GST was charged?
The total is 115% of the pre-GST amount, so pre-GST = 386.40 ÷ 1.15 = $336.00. GST = 386.40 − 336.00 = $50.40. Check: 336.00 × 0.15 = 50.40. ✓
The common wrong answer takes 15% of 386.40 (57.96) and subtracts it, giving 328.44 - that calculates 15% of the wrong base.
Traps that cost marks
- Rounding part-way through; carry full precision and round only the final answer.
- Confusing percentage points with percent: a rise from 4% to 6% is 2 percentage points but a 50% increase.
- Dropping negative signs when subtracting a larger number from a smaller one.
- Mixing units - cents with dollars, minutes with hours - inside one calculation.