## Ratio and Proportion

### Ratio

A ratio compares two quantities of the same kind.

Example

In my class there are 8 girls and 12 boys. The ratio of girls to boys is 8 : 12. This ratio simplifies to 2 : 3

Before simplifying a ratio, each quantity should be in the same units.

e.g. \$5 to \$3

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 or 50%

Ratios can be simplified like fractions.

e.g. 20 : 40 = 10 : 20

10 : 20 = 5 : 10

5 : 10 = 1 : 2

 Examples Answers 1. Write the ratio 15 : 20 as: (a) A fraction (a) (b) A percentage (b) 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 The 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 can be solved in two ways:

Method 1. Find the value of one of the units being used.

Method 2. Form an equation involving corresponding ratios.

 Example 1     Method 1 Method 2 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 requires 10 litres. 1 km would require litres. 200 km would require . 25 litres would be required. Let x be the amount of petrol needed. 25 litres would be required.