1.2 Young people and debt
Activity 2 illustrates how fractions can be used to report results from a survey. Think about why fractions are useful rather than reporting the actual numbers.
Activity 2 Young people and debt
In 2001, the New Policy Institute (whose mission is to advance social justice in a market economy) published a report titled Young People, Financial Responsibilities and Social Exclusion. The report summarised the results of a survey of 210 young people, two-thirds of whom lived in rooms at the YMCA. Of the young people who were surveyed, one-half were in debt and of these, one-third owed more than £1000.
- a.How many of the people surveyed lived in rooms at the YMCA?
Two out of every three people surveyed lived in the YMCA. Into how many parts do you need to divide your group of people?
- a.One-third of the group indicates that the group is evenly divided into three parts, which is people. So, of the group will be two sets of 70 people each, which is 140 people.
- b.How many of the young people were in debt?
What’s the quickest way to find half of a given amount?
- b.If you want half of the group, that’s the same as dividing it by 2. So, , which means that 105 of the young people interviewed were in debt.
- c.Use your answer from part (b) to work out how many of these young people with debt owed more than £1000.
If you want to find a third of a number, how many equal parts do you want to divide it into? Notice the wording of the original survey results: one-third of the people who were in debt owed more than £1000. So, it’s not one-third of all of the survey participants.
- c.One-third of the group of 105 people owed more than £1000. Since , you know that 35 people owed more than £1000.
- d.What fraction of the total number of young people surveyed owed more than £1000?
How many people owe more than £1000? You found this in part (c). How many people were interviewed in all?
- d.Since 210 people were surveyed, the fraction who owed more than £1000 is which simplifies to . Hence one-third of one-half equals one-sixth.
You may not realise it but by completing this activity you have already multiplied using fractions – well done! In the next section you’ll find out more.