One half, 0.5, 50% and 2/4 are the same number wearing four different costumes. Recognising the costume is most of the work.
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Move freely between fraction, decimal and percentage and most questions become easy.
🎭 Learn the row, not the cell
| Fraction | Decimal | Percent |
|---|---|---|
| 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% |
| 1/3 | 0.333… | 33⅓% |
| 2/5 | 0.4 | 40% |
| 3/8 | 0.375 | 37.5% |
Fraction → decimal: divide the top by the bottom. Decimal → percent: multiply by 100. Percent → fraction: put it over 100 and reduce.
Every rational number, written as a decimal, either stops or repeats for ever. There is a simple test for which.
The test: reduce the fraction, then look at the denominator’s prime factors. If they are only 2s and 5s, the decimal terminates. Any other prime and it repeats. So 3/8 (8 = 2×2×2) stops at 0.375, but 1/3 and 1/6 repeat for ever.
A repeating decimal is still rational. 0.333… = 1/3 exactly. Being infinite does not make it irrational — only numbers like √2 and π, which never repeat and never stop, are irrational.
To compare fractions, make the denominators the same — or turn them all into decimals.
Which is bigger, 3/5 or 5/8? Common denominator 40: 3/5 = 24/40 and 5/8 = 25/40, so 5/8 wins. As decimals, 0.6 against 0.625 — same answer, sometimes faster.
A bigger denominator does not mean a bigger fraction. 1/3 is larger than 1/8, even though 8 > 3, because the whole is cut into fewer pieces.
12 questions on fractions, decimals and comparing values. 🍀
