Expressing one quantity as a fraction of another
OCR J560 Foundation papers (J560/01, /02, /03) frequently set "Express A as a fraction of B" — a fundamental ratio/proportion skill that bridges into percentages and ratios.
The basic recipe
Quantity A as a fraction of quantity B = A/B (then simplify).
Always same units! If A is in cm and B is in m, convert one to the other first.
✦Worked example— Example 1 — same units
In a class of 30, 12 are boys.
- Boys as a fraction of class = 12/30 = 2/5 (simplified).
✦Worked example— Example 2 — converting units
A 250 ml drink contains 50 ml of orange juice.
- Orange juice as fraction of drink = 50/250 = 1/5.
✦Worked example— Example 3 — needs conversion
A pencil 18 cm long is part of a pencil case 60 cm long. (Same units already — fine.)
But: a piece of string is 45 mm long, attached to a kite cord 1.5 m long. Convert to common units:
- 1.5 m = 1500 mm.
- String as fraction of cord = 45/1500 = 3/100.
Linking to percentages
To convert a fraction to a percentage, multiply by 100:
- 12/30 as a percentage = 12/30 × 100 = 40%.
Or with calculator: 12 ÷ 30 × 100 = 40.
Linking to ratios
A : B as a fraction = A/(A+B) of the total. E.g. 2 : 3 ratio means A is 2/5 of total, B is 3/5.
Multi-step questions
OCR often combines this with other operations:
- "Find what fraction A is of B and convert to %."
- "Increase A by 20% and find the new fraction."
- "If C is 1/4 of B, what fraction is A of C?"
For (3): if A/B = p and C/B = q, then A/C = (A/B) ÷ (C/B) = p/q.
OCR mark scheme conventions
- M1 for the correct fraction (before simplification).
- A1 for simplified fraction or correct decimal/percentage.
- B1 for unit conversion when required.
- Fraction in simplest form expected unless question states otherwise.
⚠Common mistakes
- Mixed units — most common error.
- Inverting: writing B/A instead of A/B.
- Failing to simplify the fraction.
- Adding 100 instead of multiplying when converting to percentage.
AI-generated · claude-opus-4-7 · v3-ocr-maths-leaves