Working with Fractions and Ratios

# Working with Fractions and Ratios

GCSE(F),

A ratio can be worked out if the fraction of the whole is known. Consider a group of 7 dogs, of which 3 are spaniels. The fraction of the group of dogs that are spaniels is frac(3)(7).

There are 4 remaining dogs. The ratio of spaniels : other dogs is 3 : 4.

When working with fractions, ratios are derived from the numerators. The fraction for the spaniels is frac(3)(7); the fraction of the other dogs is frac(4)(7); the ratio uses the numerators to obtain 3 : 4.

## Examples

1. In a class of 32 students, frac(1)(4) of them wear glasses. What is the ratio of wearers : non-wearers?

Answer: 1:3

The fractions of wearers frac(1)(4). the fraction of non-wearers is frac(3)(4). Compare the numerators the ratio is 1 : 3.

2. There are 24 cars in a car park. frac(1)(4) are red, and frac(1)(6) are silver. The remaining cars are blue. What is the ratio of red : silver : blue cars in the car park?

Answer: 3 : 2 : 7

Red cars: frac(1)(4) = frac(6)(24)

Silver cars: frac(1)(6) = frac(4)(24)

There are 14 cars remaining (= 24 - 6 - 4) = frac(14)(24)

Compare the numerators 6 : 4 : 14, and simplify to 3 : 2 : 7.