1.1 Finding a percentage of a value
Suppose that residents in a town are asked for their views on the proposed development of a nearby wind farm. The local paper says that 450 people voted, with 54 per cent in favour of the proposal, 36 per cent against and 10 per cent undecided. How can you find out how many people were in favour of the proposal?
To find the number of people who were in favour, you need to find 54 per cent of 450. There are two ways to work this out. You can either start by converting the percentage to a fraction, or alternatively to a decimal number.
- As a fraction: .
- As a decimal: 54 % = 54 ÷ 100 = 0.54.
Now remember that when ‘of’ is used in maths, it is usually an instruction to multiply.
Using the fraction conversion, write the calculation as:
So 243 people were in favour of the proposal.
So to calculate a percentage of a number, first convert the percentage to either a fraction or a decimal, and then multiply it by the given number. Have a go at this in the next activity.
Activity 2 Finding percentages of values
Find the number of people who were against the proposed wind farm, and then find the number of people who were undecided about the proposal. (Try this calculation without using the calculator.)
Since 36 per cent of the 450 people were against the proposal, you want to calculate 36 per cent of 450 to find the actual number. Here’s two methods you could have used.
- Percentage against: .
- Using a decimal instead of a fraction: .
So 162 people were against the proposal.
You know that 10 per cent of the 450 people were undecided, so you need to find 10 per cent of 450. You should be able to do this calculation without the calculator: 10 per cent is one-tenth, and one-tenth of 450 is 45. So, 45 people were undecided. The calculator should give you the same answer, but do watch for easy calculations that you can do in your head – it’s good practice!
As a final check, the three numbers you have calculated should add up to 450. The number in favour was 243, the number against was 162 and the number undecided was 45, and these do add up to 450. So, you can feel confident with the answers!
You will do some work with money and percentages in the next section.