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Video: Comparing Fractions in a Real-World Context

Tim Burnham

A school conducted a survey to find out how students usually travel to school. The results are shown in the table. Which is the most popular mode of transport?

03:15

Video Transcript

The school conducted a survey to find out how students usually travel to school. The results are shown in the table. And for modes of transport, some of them walk, some travel on the school bus, some travel with parents, and some travel with friends. We’re then shown the fraction of students that fit into each of those categories. Five sixteenth walk, thirteen thirty-twoths go by bus, one eighth go with their parents, and five thirty-twoths go with friends. Which is the most popular mode of transport?

Now to answer this question, we need to compare all of those fractions and find out which one represents the largest number. Now comparing fractions is quite easy, if they’ve all got the same numerator or the same denominator. But unfortunately, these have all got different numerators and denominators. So we’ve got to try to find a common denominator.

Now remember, the word numerator has got a U in it, so it represents the upstairs part of the number. And denominator has got a D in it, so it represents the downstairs part of the number. So if we check out all of our denominators, we’ve got sixteen, thirty-two, eight, and thirty-two. And when we think about that, two times sixteen is thirty-two and four times eight is thirty-two. So we could convert all of these fractions into numbers which have a denominator of thirty-two.

So for five sixteenths, for walking, I could multiply the numerator by two and I could multiply the denominator by two, to get an equivalent fraction. And five times two is ten and sixteen times two is thirty-two. So five sixteenths or ten thirty-twoths are equivalent fractions. So I’m just gonna write that down in my table.

Now the fraction of students who take the bus is thirteen over thirty-two, so that’s already got thirty-two as a denominator. So now let’s see if we can convert one-eighth into an equivalent fraction with a denominator of thirty-two. Well we said eight times four is thirty-two. So if I multiply the denominator by four, I need to multiply the numerator by four. And one times four is four, and eight times four is thirty-two. So four over thirty-two is the same as, or it’s equivalent to, one over eight.

Well now we can look at the table and we’ve got fractions which all have the same denominator. So ten thirty-twoths, thirteen thirty-twoths, four thirty-twoths, or five thirty-twoths. Well thirteen thirty-twoths is the biggest number of thirty-twoths, so that represents the largest fraction. And that means, that the bus would be the most popular mode of transport.

So the answer is: Bus, because thirteen over thirty-two represents the largest fraction of students.

Think of it like this, if you had a cake and you cut it into thirty-two equal pieces, bus would have thirteen of these pieces, walking would only have ten of these pieces, travelling with friends would only have five of these pieces, and travelling with parents would only have four of these pieces. So the category that gets the largest chunk of that cake would be bus.