A proportion is used to describe the relationship of some part of a whole to the whole itself and is usually given as a fraction.
Example
In a class there are 20 girls and 10 boys. The ratio of girls to boys is 20:10, or 2:1, and the proportion of girls in the class is 20 out of 30 or 20/30 = 2/3.
Worked examples
Example one
An infant school has 180 pupils, of whom 35 go home for lunch. What proportion of pupils have lunch at school?
35 out of 180 go home.
So 180 - 35 = 145 stay at school for lunch.
As a proportion this is represented as 145 out of 180
145/180 = 29/36 (dividing top and bottom by 5)
So the proportion that stays at school for lunch is 29/36.
Example two
Three schools have the same proportion of children receiving free school meals, 8/75. If the numbers of children receiving free school meals in each of the three schools are 16, 40 and 56 respectively, how many children in each school do not receive free school meals?
The proportion of pupils receiving free school meals is 8 out of every 75, or 8/75.
To work out the number of children in each of the three schools who do not receive free school meals, you need to find out the total number of pupils in each school. You can do this using the proportion 8/75 by relating the 16, 40, 56 to the 8 out of every 75 proportion given.
8 out of 75
is 16 out of 150 (the 8 has been doubled. To maintain the same proportion the 75 must also be doubled, giving 150)
is 40 out of 375 (the 8 has been multiplied by 5; 75 x 5 = 375)
is 56 out of 525 (the 8 has been multiplied by 7; 75 x 7 = 525)
So the total number of pupils in each school is 150, 375 and 525 respectively.
To find the numbers of pupils who do not have free school meals in each school, simply subtract the number of pupils getting free school meals from the total number of pupils.
School one
150 pupils of which 16 receive free school meals, so 150 - 16 = 134 pupils do not receive free school meals.
School two
375 pupils of which 40 receive free school meals, so 375 - 40 = 335 pupils do not receive free school meals.
School three
525 pupils of which 56 receive free school meals, so 525 - 56 = 469 pupils do not receive free school meals.
Avoiding common errors
Most common errors can be avoided by remembering that proportion can be scaled by multiplying or dividing both parts by the same number.