Working with Fractions and Ratios

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.

Answer: 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