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
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.