Multiplicative relationships: ratio ↔ fraction
Edexcel 1MA1 expects fluent translation between three equivalent representations of a part-to-part or part-to-whole relationship: ratio, fraction, and percentage.
Three forms of the same relationship
If 3 people share a pizza in the ratio 2 : 1:
- Ratio (part : part) — 2 : 1.
- Fraction (part / whole) — first person gets 2/3 of the pizza, second gets 1/3.
- Percentage — first ≈ 66.7%, second ≈ 33.3%.
The total parts (sum of ratio terms) becomes the denominator of the fraction.
Going from ratio to fraction
ratio a : b → fraction a / (a + b) and b / (a + b).
Example: 5 : 3 → 5/8 and 3/8.
Going from fraction to ratio
If A gets 3/5 and B gets 2/5, ratio A : B = 3 : 2.
Multiplicative relationship between two quantities
"y is 3/4 of x" is equivalent to:
- y = (3/4)x.
- y : x = 3 : 4.
- y is 75% of x.
- The scale factor from x to y is 3/4 (= 0.75).
✦Worked example— Worked example (Higher)
In a class, the ratio of girls to boys is 4 : 5.
(a) What fraction of the class are girls? Answer: 4/9. (b) If there are 27 students, how many are girls? Answer: 27 × 4/9 = 12. (c) The ratio of left-handed to right-handed students is 1 : 8. How many left-handed students? Answer: 27 × 1/9 = 3.
Common Edexcel exam tip
When a question gives "the ratio of A to B is 3 : 2 and there are 30 of A", students often divide 30 by 5 (treating it as part of total). The correct approach: 30 ÷ 3 = 10 (one part), then B = 10 × 2 = 20.
For "fraction of remaining" wording, set up the total carefully. Example: 1/3 spent on rent, then 2/5 of the remainder spent on food. Remainder after rent = 2/3. Food = 2/5 × 2/3 = 4/15 of original.
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