A ratio compares two quantities of the same kind.
Before simplifying a ratio, each quantity should be in the same units. e.g. $5 to $3 or 60 minutes to 30 minutes.
A ratio can be expressed in several forms. e.g. A ratio of 1 to 2 can be written 1 : 2 or ^{1}⁄_{2} or 50%.
Ratios can be simplified like fractions. e.g. 50 : 25 can be reduced to 2 : 1.
1. Write the ratio 15 : 20 as: 

(a) A fraction 
(a)^{15}⁄_{20} = ^{3}⁄_{4} 
(b) A percentage 
(b)^{15}⁄_{20} = ^{75}⁄_{100} = 75% 
2. Two people divide $80 in the ratio 3 : 7 How much does each person get? 
2. The ratio 3 : 7 means a total of 10 parts. Each part is $80 ÷ 10 = $8 The first person gets: 3 × $8 = $24 
Proportion
Two sets of numbers are in direct proportion when the ratio between corresponding members of the sets is the same.
e.g. A = {3, 6, 9} is in proportion to B = {12, 24, 36} because members of set B are 4 times the size of the corresponding members of set A.
Problems involving Proportion
Problems involving proportion can be solved in two ways:
Method 1

Method 2

Find the value of one of the units being used. 
Form an equation involving corresponding ratios. 
A driver uses 10 litres of petrol to cover 80 km. How much petrol would be used to cover 200 km? 
A driver uses 10 litres of petrol to cover 80 km. How much petrol would be used to cover 200 km? 
80 km would require 10 litres. 1 km would require 10⁄80 litres. 200 km would require 10⁄80 × 200 litres. 25 litres would be required. 
Let x be the amount of petrol needed. 
Rates
A rate compares two quantities of a different kind.
Rates can be shown on graphs. See Topic 40.
e.g. Speed = kilometre per hour
For exciting and fun practice with speed, distance, time and bearings −
Wage rate = Dollars per week
A woman earns $425 in 50 hours. 
Rate of pay = ^{425}⁄_{50} = $8.5/hour 
A motorist travels 85 km in 2 hours. 
Speed = ^{85}⁄_{2} = 42.5 km/hr
