Arithmetic: Ratio, Percentage, Averages and Number Work
What you must command
Arithmetic in a written paper rewards disciplined method more than speed. You need fluency with fractions, decimals and percentages and the ability to move between them; ratio and proportion, including dividing a quantity in a given ratio and scaling recipes or maps; averages, including the mean of a combined group; simple and compound interest; profit and loss with cost price versus selling price; speed, distance and time with unit conversion; and the rules of divisibility, factors, multiples, HCF and LCM. Approximation and estimation deserve attention too, because questions often ask for a sensible rounded answer.
Traps that catch candidates
- Percentage change is always measured against the original amount, so a 20% rise followed by a 20% fall does not return to the start.
- In profit and loss, the percentage is normally taken on cost price unless the question says otherwise.
- Compound interest must be applied to the growing balance, not the original sum each year.
- When combining groups, the overall mean is a weighted mean; averaging the two group means is wrong unless the groups are the same size.
- Ratio shares must sum to the whole: check that your parts add to the original quantity.
- Time units are not decimal: 1.5 hours is 1 hour 30 minutes, not 1 hour 50 minutes.
Worked example
A sum of 4,800 is shared between three people in the ratio 3:4:5. Total parts = 12, so one part = 400. Shares are 1,200, 1,600 and 2,000. Check: they add to 4,800.
Rule of thumb
Write down the quantity that represents 100%, then find 1% by division before scaling to the percentage you need. This single habit removes most arithmetic slips.