Expressing one quantity as a fraction of another
This is the foundation skill behind ratio, percentages and probability. Once you can write "A as a fraction of B", everything else falls into place.
The basic idea
If you want to express A as a fraction of B, write A on top and B on the bottom: A / B, then simplify. The two quantities must be in the same unit.
Worked example: express 30p as a fraction of £2.
- Convert: £2 = 200 p (same unit needed).
- 30 / 200 = 3/20.
- Answer: 3/20.
When the fraction exceeds 1
It's perfectly fine — it just means A is bigger than B.
Worked example: express 5 hours as a fraction of 2 hours. 5/2 = 2½ (or 250%).
Linking fraction, decimal, percent
Once you've expressed A/B, converting to decimal (divide) or percent (× 100) is easy.
Worked example: 18 boys out of 30 students.
- Fraction: 18/30 = 3/5.
- Decimal: 0.6.
- Percent: 60%.
Worded contexts
Read carefully — the order matters. "20 as a fraction of 50" is 20/50, not 50/20.
Worked example: in a class of 25, 4 students walk to school. Express the walkers as a fraction of the class: 4/25.
Reverse — finding the original from a fraction
If A is 3/8 of B, and A = 24, then B = 24 × 8/3 = 64.
⚠Common mistakes
- Different units — 30 cm out of 2 m must be 30 cm out of 200 cm = 3/20, not 30/2.
- Reading order wrong — "X as a fraction of Y" puts X on top.
- Forgetting to simplify — leave the answer in lowest terms unless asked otherwise.
- Treating mixed numbers like simple fractions — 5/2 = 2½, not 2.5/1.
- Mixing up part vs whole in word problems — re-read which quantity is the "of".
➜Try this— Quick check
A bag has 12 red and 8 blue beads. What fraction of the bag is blue? Answer: 8 / (12+8) = 8/20 = 2/5.
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