Working with Fractions and Ratios

## Working with Fractions and Ratios

A ratio can be worked out if the fraction of the whole is known.

The denominator gives the total amount. The numerator gives the amount of each part.

## Example 1

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

The fractions of wearers frac(1)(4).

The fraction of non-wearers is 1 - frac(1)frac(4) = frac(3)(4).

Compare the numerators for the ratio 1:3.

## Example 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?

Find equivalent fractions with the same denominator.

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.

(Note that there could be more than 24 cars, but the number of cars must be a multiple of 24 and the fractions and ratios would remain the same)

Answer: 3 : 2 : 7