Beyond Rankers Academy
Building Minds, Not Just Rankers
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Beyond Rankers Academy
Building Minds, Not Just Rankers
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The same value can wear four costumes — a fraction, a decimal, a percentage and a ratio. Olympiad questions mix them deliberately, so the first move is always to convert everything into one form.
Learn the common ones by heart — you will not have time to divide during the paper.
🎭 Worth memorising
| 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% |
| 1/3 | 0.333… | 33⅓% |
| 2/3 | 0.666… | 66⅔% |
Decimal to fraction. Write the digits over the matching power of ten and cancel: 0.36 = 36/100 = 9/25. And 0.125 = 125/1000 = 1/8.
You can tell without dividing at all.
🔁 The test
Reduce the fraction to its lowest terms first — this step is essential.
Factorise the denominator.
If the only primes are 2 and 5, the decimal terminates. Any other prime and it recurs.
🔁 Worked out
| Fraction | Denominator | Decimal |
|---|---|---|
| 1/8 | 2³ | 0.125 — terminates |
| 3/40 | 2³ × 5 | 0.075 — terminates |
| 5/16 | 2⁴ | 0.3125 — terminates |
| 1/6 | 2 × 3 | 0.1666… — recurs |
| 2/7 | 7 | 0.285714… — recurs |
| 7/12 | 2² × 3 | 0.5833… — recurs |
Reduce first, or you will get it wrong. 6/12 looks as if it has a 3 in the denominator, but it is really 1/2 = 0.5, which terminates.
Cross-multiplication for comparing, common denominators for adding.
Cross-multiply to compare. For 5/6 and 7/8: 5 × 8 = 40 against 7 × 6 = 42. The larger product sits above the larger fraction, so 7/8 wins.
Dividing by a fraction means multiplying by its reciprocal. 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8. There is no such flip for addition.
A fraction of a fraction means multiply. "Two-thirds of three-quarters" is 2/3 × 3/4 = 6/12 = 1/2, not 2/3 + 3/4.
12 Olympiad questions on fractions and decimals. 🍀