## Rates, Ratio and Proportion 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 12 or 50%.

Ratios can be simplified like fractions. e.g. 50 : 25 can be reduced to 2 : 1.

 Examples Answers 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 = \$24The second person gets: 7 × \$8 = \$56

### 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. 25 litres would be required.

### 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 Example 1 Answer A woman earns \$425 in 50 hours.What is her hourly rate of pay? Rate of pay = 425⁄50 = \$8.5/hour Example 2 Answer A motorist travels 85 km in 2 hours.What is his speed? Speed = 85⁄2 = 42.5 km/hr