Numeracy, Proportion and Financial Mathematics
Core concepts
Essential Mathematics rewards careful reading and sensible estimation as much as calculation. You must be fluent with the four operations on whole numbers, decimals and fractions, with percentages, ratio and proportion, and with unit conversion (length, mass, capacity, time, and rates such as km/h). Financial topics build directly on these: percentage increase and decrease, profit and loss, mark-up and discount, simple and compound interest, wages and salaries, overtime, commission, taxation, and budgeting. Know the difference between simple interest, calculated only on the principal, and compound interest, calculated on the growing balance.
Traps to watch
- Percentage change on different bases. A 20% discount followed by 10% off is not 30% off.
- Percentage of what? Always identify the base before calculating.
- Rounding money too early. Keep full precision until the final step, then round to the nearest cent.
- Interest periods. A rate of 6% per annum compounded monthly uses 0.06/12 per month, not 0.06.
- Time units. Match the rate period to the time: months with a monthly rate, years with an annual rate.
- Overtime and penalty rates apply only to the hours in that category, not the whole week.
Worked example
A jacket priced at $180 is discounted by 15%, then a further 10% is taken off the sale price. Final price: first discount gives 180 × 0.85 = $153; second gives 153 × 0.90 = $137.70. The overall reduction is $42.30, which is 23.5%, not 25%. Rule of thumb: successive percentage changes multiply as decimals, so 0.85 × 0.90 = 0.765, meaning the customer pays 76.5% of the original price. Always sanity-check that your answer is plausible (a discount must be smaller than the original price).