Percentage, Ratio & Proportion
Percentage and ratio underpin half the arithmetic paper — profit and loss, interest, data interpretation and mixtures are all percentage questions wearing different clothes. The single highest-value habit here is converting a percentage into a fraction before you calculate: 12.5% is one-eighth, and dividing by 8 beats multiplying by 0.125 every time.
Don't read this page — work through it. Each block asks you to commit to an answer before it tells you anything.
Start here: what do you already know?
Percentage & ratio — true or false?
6 statements · 10s each
The conversions to know cold
| Fraction | % | Fraction | % |
|---|---|---|---|
| 1/2 | 50% | 1/8 | 12.5% |
| 1/3 | 33⅓% | 1/9 | 11⅑% |
| 1/4 | 25% | 1/10 | 10% |
| 1/5 | 20% | 1/12 | 8⅓% |
| 1/6 | 16⅔% | 1/16 | 6.25% |
| 1/7 | 14²/₇% | 1/20 | 5% |
Reading these in both directions — "37.5% is 3/8" as readily as the reverse — is what separates a 30-second solution from a three-minute one.
Sort by which is larger
Is each value more or less than one-half?
0/63/8
Which group does it belong to?
Commit to the answer
Compute, then check
1/4What is 20% of 250?
55
Method, in order
Match the percentage to its fraction
Quick reference
Exam tip: a 10% rise followed by a 10% fall is a 1% net loss, not a return to the start. The general result is x²/100 % — memorise it and these questions take five seconds.