6.2.5 Activity: Young People and Debt

[ Why do you think the authors used fractions of the group (rather than the numbers of people) to report their results? ] The next activity illustrates how fractions are used to report results from a survey.

Activity symbol Activity: 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 summarized the results of a survey on 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, a one-third owed more than $1,600.

(a) How many of the people surveyed lived in rooms at the YMCA?

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Discussion

Two out of every three people surveyed lived in the YMCA. Into how many parts do you need to divide your group of people?

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Answer

(a) One-third of the group indicates that the group is evenly divided into 3 parts, which is 210 division three equals 70 people. So, two divided by threeof the group will be two sets of 70 people each, which is 140 people.

(b) How many of the young people were in debt?

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Discussion

What’s the quickest way to find half of a given amount?

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Answer

(b) If we want half of the group, that’s the same as dividing it by 2. So, 210 division two equals 105, 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 $1,600.

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Discussion

If we want to find a third of a number, how many equal parts do we want to break it into? Notice the wording of the original survey results: One-third of the people who were in debt owed more than $1,600. So, it’s not one-third of all of the survey participants.

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Answer

(c) One-third of the group of 105 people owed more than $1,600. Since 105 division three equals 35, we know that 35 people owed more than $1,600.

(d) What fraction of the total number of young people surveyed owed more than $1,600?

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Discussion

How many people owe more than $1,600? You found this in part (c). How many people were interviewed in all?

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Answer

(d) Since 210 people were surveyed, the fraction who owed more than $1,600 is 35 divided by 210, which reduces to one divided by six. Hence one-third of one-half equals one-sixth.

Reference:

New Policy Unit (2001) Young People, Financial Responsibilities and Social Exclusion. Available online at http://www.npi.org.uk/ files/ New%20Policy%20Institute/ More%20than%20PIN.pdf [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] [accessed 24 Sept 2011]

6.2.4 Adding and Subtracting Fractions Challenge

6.3 Multiplying Fractions