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.

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