Most people use fractions in their everyday life when they talk about time (a quarter past ten), parts of pizzas and cakes (halves and quarters), or when shopping (two-thirds off marked prices). You may also see fractions in news reports or on the internet. How often do you think about what these fractions really mean? If you can explain to somebody else what a fraction means then you are already on your way to having a good understanding of fractions.
To get going this week, look at this example and ask yourself some questions about the meaning of the fraction. This headline appeared in a press release from the British Wind Energy Association in June 2005.
Three-quarters of people in Wales believe wind farms are necessary, says new poll.
What did you think when you read the headline? Do a majority of Welsh people support this view? Do you know how many people actually think in this way?
No, you don’t actually know the number of people who think this way – the headline just tells you the proportion in favour. In other words, the headline tells you how many people support wind farms compared with the whole group. If you gathered together all the people who were polled, you could arrange them into four equal groups, so that the people in three of the groups would have supported this view and those in the fourth would not.
If only four people had been interviewed, three would have agreed that wind farms are necessary. If 4000 people were interviewed, then 3000 would have agreed, and so on. How much notice you should take of the headline would probably depend on both the number of people who were surveyed and how they were selected.
Interviewing a lot of people who had been selected at random may give a better indication of the views of the general population than would polling just a few people who lived a long way from any wind farm.
This starts to show you just what a fraction is – it tells you a proportion rather than what the actual numbers were that enabled this fraction to be written.
Activity 1 In the news
Fortunately, some information on who was interviewed was provided in the press release: 500 Welsh people were surveyed.
By dividing this group into quarters, work out how many of the people agreed with the view in the headline. How many did not agree?
If you want to divide a group into quarters that is the same as asking: what is that number divided by 4?
Remember three-quarters of the 500 people agreed.
First, split the group into quarters by dividing 500 by 4:
people – one-quarter of the people surveyed.
Three-quarters of the group means you need three sets of 125 people.
So, 375 people agreed with the statement and 125 did not. (You can check your arithmetic by noting that 375 + 125 = 500.)
In a similar way to the method used in Activity 1, you can often make sense of most everyday fractions by:
- dividing the amount or number into the desired number of equal parts
- considering how many of these parts you need.
One way to help with understanding fractions is to use diagrams or physical objects. A large cake would be nice but you’re going to use a piece of paper instead. So, before you start the next section find a piece of paper – some scrap will do.