Quantity as a Ratio or a Fraction

Quantity as a Ratio or a Fraction

Basic, GCSE(F),

A fraction shows the relationship between an amount and its whole. A ratio shows the relationship between two amounts as parts of a whole

Yellow and red paints are mixed together in the ratio 3 : 1 to make an orange paint. The yellow paint therefore consists of 3 cans out of 4, or `frac(3)(4)`.


1. Wages are paid to Jack and Oliver. Jack worked for 3 hours and received £30, while Oliver received £50. What was the ratio for the amount paid out between Jack and Oliver? Give the ratio in its simplest form.

Answer: 3:5

The amount paid out was in the ratio 30:50, which simplifies to 3:5 (divide both by 10).

2. What fraction of the work was done by Oliver, in hours? Assume that both Jack and Oliver are paid at the same rate.

Answer: `frac(5)(8)`

The money earned by Oliver was £50. The total amount paid for both is £30 + £50 = £80.

The fraction earned by Oliver was `frac(50)(80)` which simplifies to `frac(5)(8)`