Ratio and fraction — two ways to say the same thing
OCR J560 questions often switch between "ratio" and "fraction" forms in a single multi-part question. Knowing the conversion both ways is essential.
From ratio to fraction
If two quantities are in ratio a : b, then:
- First as a fraction of the total: a / (a + b).
- Second as a fraction of the total: b / (a + b).
- First as a fraction of the second: a / b.
Example: "Boys to girls = 3 : 2."
- Boys are 3/5 of the class.
- Girls are 2/5 of the class.
- Boys are 3/2 (= 1½) times the number of girls.
From fraction to ratio
If a fraction p/q is given (e.g. 2/7 of the students wear glasses), then:
- Glasses : no glasses = 2 : 5 (because 7 − 2 = 5 don't).
- Glasses : whole class = 2 : 7.
Always check whether the fraction is "of the whole" or "of the rest".
Simplifying ratios
Divide both parts by their HCF.
- 12 : 18 = 2 : 3 (HCF = 6).
- 0.5 : 1.5 = 1 : 3 (multiply both by 2 to clear the decimal).
- 1/2 : 1/3 = 3 : 2 (multiply both by 6 to clear fractions).
Ratios with three parts
a : b : c. The same total-fraction logic extends:
- First as fraction of total = a / (a + b + c).
Example: "Profits shared 2 : 3 : 5 between three partners. Total profit £8000." Each receives:
- 2/10 × 8000 = £1600
- 3/10 × 8000 = £2400
- 5/10 × 8000 = £4000
OCR mark scheme conventions
- B1 for the correct simplified ratio or fraction.
- M1 for setting up the right multiplier (e.g. total ÷ sum of parts).
- A1 for the final value(s).
- Marks lost for un-simplified ratios when "give in simplest form" is asked.
⚠Common mistakes
- Writing 3/2 (boys per girl) when the question wants 3/5 (boys per total).
- Forgetting to add up all parts when finding the "total".
- Inverting the order in mixed problems ("ratio of A to B" ≠ "ratio of B to A").
- Not simplifying when asked for "simplest form".
AI-generated · claude-opus-4-7 · v3-ocr-maths-leaves