A single conversion table removes twenty or thirty seconds from percentage questions, ratio questions, probability questions and data interpretation questions — every one of them asks you to move between a fraction, a decimal and a percentage. Candidates who compute 5 ÷ 8 by long division on the exam lose the marks they came to collect.
There is a second, quieter win: comparing fractions correctly. The most common careless error in quantitative sections is deciding that 3 ÷ 5 is bigger than 7 ÷ 11 because 5 is smaller than 11. It is not — and a cross-multiplication takes four seconds.
A fraction is a division waiting to happen, and a percentage is just a fraction with 100 underneath. Three representations, one number:
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 1/10 | 0.1 | 10% |
Notice the structure: every entry on the right is the decimal times 100, so you only ever memorise the fraction-to-decimal half. Notice also that the list is built from halves, quarters, fifths, eighths and tenths — the denominators that appear in real questions.
| Fraction | Decimal | Percentage | Fraction | Decimal | Percentage |
|---|---|---|---|---|---|
| 1/2 | 0.5 | 50% | 1/8 | 0.125 | 12.5% |
| 1/3 | 0.333… | 33.3% | 3/8 | 0.375 | 37.5% |
| 2/3 | 0.666… | 66.7% | 5/8 | 0.625 | 62.5% |
| 1/4 | 0.25 | 25% | 7/8 | 0.875 | 87.5% |
| 3/4 | 0.75 | 75% | 1/9 | 0.111… | 11.1% |
| 1/5 | 0.2 | 20% | 1/11 | 0.0909… | 9.09% |
| 2/5 | 0.4 | 40% | 1/12 | 0.0833… | 8.33% |
| 3/5 | 0.6 | 60% | 1/16 | 0.0625 | 6.25% |
| 4/5 | 0.8 | 80% | 1/7 | 0.142857… | 14.3% |
| 1/6 | 0.166… | 16.7% | 1/20 | 0.05 | 5% |
To compare a/b with c/d, cross-multiply: if a × d exceeds c × b, the first fraction is larger. Example: 7/12 against 11/19 gives 7 × 19 = 133 and 11 × 12 = 132, so 7/12 is larger — by a margin of one part in 228, which is why this question is always designed to catch estimation.
240 ÷ 8 = 30, then 30 × 5 = 150. Dividing first keeps the numbers small; multiplying first gives 1,200 ÷ 8, which is the same answer with more to hold in your head.
Cross-multiply: 7 × 19 = 133 against 11 × 12 = 132, so 7/12 is larger, by a sliver. Options that include "cannot be determined" are wrong: the comparison is fully determined.
0.375 = 375/1000. The HCF of 375 and 1000 is 125, so divide both: 3/8. Recognising 0.375 directly from the table saves the work.
1/7 = 0.142857…, so 14.2857…%, which rounds to 14.3%. The nearby distractor is 12.5%, which is 1/8.
Which is larger, 2/3 or 5/8?
What is 3/8 expressed as a percentage?
A recipe needs 2/3 of a kilogram of flour and you are making 3/4 of the quantity. How much flour?
Express 0.272727… as a fraction in lowest terms.
Without looking back: how do you compare two fractions without a calculator, and what is 7/8 as a percentage?
The answer: cross-multiply the numerator of one by the denominator of the other; and 7/8 = 0.875, so 87.5%.
To convert a fraction to a percentage, multiply by and divide by the denominator. To compare a/b with c/d quickly, . As a percentage, 1/8 is and 7/8 is .
A question gives two ratios of students who passed a test — 5/8 of class A and 7/12 of class B — and asks which class had the higher pass rate. Solve it, then state what extra information you would need to answer "which class had more students pass".
Cross-multiply: 5 × 12 = 60 against 7 × 8 = 56, so class A's rate, 5/8, is higher. As decimals, 0.625 against 0.583 — the gap is real and visible once converted.
For the second question — which class had more students pass — you need each class's size. A rate has no size: 5/8 of a class of 40 is 25 students, while 7/12 of a class of 240 is 140, so the higher rate can belong to the class with fewer passers. This is the same trap that appears in data interpretation tables and in every "which grew faster in percentage terms" question.
Fractions are now tools rather than obstacles. The next lesson takes the most common application of them on the paper: percentages, percentage change, and the profit, loss and interest questions built on top of it.