Succeed with maths – Part 1
Succeed with maths – Part 1

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

Free course

Succeed with maths – Part 1

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 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.

(BWEA, 2005)

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

Timing: Allow approximately 10 minutes

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?

Comment

If you want to divide a group into quarters that is the same as asking: what is that number divided by 4?

Answer

Remember three-quarters of the 500 people agreed.

First, split the group into quarters by dividing 500 by 4:

500 division four equals 125 people – one-quarter of the people surveyed.

Three-quarters of the group means you need three sets of 125 people.

three multiplication 125 equals 375

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.

Skip Your course resources
SWMB_1

Take your learning further

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has 50 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses.

If you are new to University-level study, we offer two introductory routes to our qualifications. You could either choose to start with an Access module, or a module which allows you to count your previous learning towards an Open University qualification. Read our guide on Where to take your learning next for more information.

Not ready for formal University study? Then browse over 1000 free courses on OpenLearn and sign up to our newsletter to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus371