FractionsA 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)1520 = 34

(b) A percentage

(b)1520 = 75100 = 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
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

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.

Y9_Rates_Ratio_and_Proportion_05.gif

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 Y9_Rates_Ratio_and_Proportion_08.gif

For exciting and fun practice with speed, distance, time and bearings − Y9_Rates_Ratio_and_Proportion_09.gif

Wage rate = Dollars per week Y9_Rates_Ratio_and_Proportion_10.gif

 

Example 1
Answer

A woman earns $425 in 50 hours.
What is her hourly rate of pay?

Rate of pay = 42550 = $8.5/hour

Example 2
Answer

A motorist travels 85 km in 2 hours.
What is his speed?

Speed = 852 = 42.5 km/hr