Video Transcript
Arrange one-fifth, one-third,
one-seventh, and one-ninth in ascending order.
In this question, we’re given four
fractions and we’re told to arrange them or put them in a certain order, ascending
order. Now, when a balloon ascends in the
sky, it goes up and up. And so if we want to put these
fractions in ascending order, we need to arrange them from lower to higher. In other words, we need to start
with the smaller fraction and get greater and greater as we go along. Now what can we use to help us
compare these fractions? Perhaps you can put them in order
without using a model to help. But fraction strips can be
helpful. Let’s use some of those. We have four fractions and we’re
going to need four fraction strips. Our strips need to all be the same
length for us to compare them.
If we look at our fractions, we can
see that they’re all what we call unit fractions. They all have a numerator of
one. This means that although we’re
going to split the whole strip into lots of different parts, we’re only thinking
about one of those parts each time. Now we know that the bottom number
in a fraction tells us how many equal parts to split the whole amount into. To show one-fifth, we need to split
the whole strip into five equal parts and then shade one of those five. Now, three is a lower number than
five. But this doesn’t mean that the
fraction is smaller. We know that it means that we split
the whole amount into less equal pieces, three equal pieces. And because we’re thinking of
one-third, we simply need to shade one of these parts again.
Now we’ve modeled two fractions; we
can start to compare them. We can see that one-fifth is less
than one-third. So if we want to arrange our
fractions starting with the smallest, let’s write one-fifth before one-third. Of course, we haven’t looked at the
other fractions yet. So we don’t know where we need to
put those. One-seventh means one out of a
possible seven equal parts. This is interesting. Although it’s a larger denominator
than the other two fractions, we can see that one-seventh is actually a smaller
fraction. Of course it is. A larger denominator means more
parts, and more parts means smaller parts. We can see that one-seventh is our
smallest fraction so far, so we’re going to have to shuffle our fractions along a
bit. Our final fraction has the largest
denominator of the lot.
Let’s make a prediction. Because it has the largest
denominator, this means that the whole of the fraction strip is going to be split
into more parts. And so each of those parts is going
to be smaller. Do you think one-ninth might be our
smallest fraction? Nine equal parts and we’ll shade
one of them. We were right; the more parts we
split the whole amount into, the smaller they’ll be. Because all of the numerators in
our fractions are the same, if we want our fractions to go from the smallest to the
largest, our denominators need to go from the largest to the smallest. Look at how they do, nine, seven,
five, three. But by drawing these fraction
strips, we know why this is. And it’s all to do with what each
number in a fraction means. These fractions in ascending order
are one-ninth, one-seventh, one-fifth, and one-third.
