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Succeed with maths: part 1
Succeed with maths: part 1

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1 Fractions

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 appeared in the Yorkshire Post in April 2021.

Three quarters of Yorkshire’s residents plan to holiday in the region this year.

(Snowdon, 2021)

What did you think when you read the headline? Do a majority of Yorkshire people want to holiday in their home county? Do you know how many people actually think in this way?

No, you don’t actually know the number of people who want to do this – the headline just tells you the proportion who do. In other words, the headline tells you how many people plan to holiday in Yorkshire 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 planned to holiday in Yorkshire and those in the fourth would not.

If only four people had been interviewed, three would have said they intended to holiday in Yorkshire. If 4000 people were interviewed, then 3000 would have said that, 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 intentions of the general population than would polling just a few people.

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.

  • Suppose that for this article 500 Yorkshire residents were surveyed.

    By dividing this group into quarters, work out how many of the people had the intention to holiday in Yorkshire. How many did not agree?

  • Remember three-quarters of the 500 people were going to holiday in Yorkshire.

    First, split the group into quarters by dividing 500 by 4: 125 people is equivalent to one-quarter of the people surveyed.

    To find three-quarters of the group means you need three sets of 125 people. So, 375 people intended to holiday in Yorkshire and 125 did not. (You can check your arithmetic by noting that 375 + 125 = 500.)

In a similar way to the method used here, 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 in the next section you’re going to use a piece of paper instead. So, before you start find a piece of paper – some scrap will do.