### Video Transcript

How much is one-quarter of
one-third?

We know that when we find a quarter
of something, we divide it into four equal parts. So another way we could write this
question is what is one-third divided by four? This would give us a quarter of
one-third. And to help us answer the problem,
we’ve been given a diagram. In fact, it’s so helpful; we could
actually just look at it and see what the answer is. But it’s very important that we
understand what the diagram represents, what does it show, and how has it been built
up? So let’s slowly build up the
diagram from the beginning and see why it represents the answer to the problem.

To begin with, we have a
rectangle. And this rectangle represents one
whole. And we’re being asked to find a
quarter of one-third. So the first thing we can do is to
divide our whole shape, our rectangle, into thirds. That’s three equal parts. There we go. Each one of these parts is worth
one-third. Now, as we’ve said already, we’re
being asked to find one-quarter of a third and that’s the same as dividing one of
these thirds into four equal parts. Let’s divide the third on the left
into four. One, two, three, four. So one-quarter of one-third is this
amount here. But what’s it worth?

Well, at the moment are rectangle
isn’t split into equal parts. And to find out the value of this
part at the top, we need to divide the rectangle so that all of the parts are
equal. So if you remember the three lines
that we drew to divide our third into quarters, we need to extend these lines all
the way across the rectangle. You can see by doing this. What we’re doing is dividing the
rectangle into parts of equal size. And then once we’ve done this, we
can find out what fraction the top part is worth.

Let’s just extend the final line
across. Now, if we count the number of
parts that we have, we can see that there are 12 equal parts. We’ve got three columns of
four. There are four in the first column,
eight in the first two columns, and then 12 altogether. So the fraction that we’ve shaded,
one-quarter of one-third, is one out of 12 possible parts. The fraction is one-twelveth. Hopefully, you can see now where
that diagram came from and how we were able to build it up to find the answer.

First, we found one-third of the
whole amount. Then we divided that third into
four equal parts to find one-quarter of a third. Then we just made sure that we
divided all of the shape in the same way so that we could work out the exact
fraction. The shape has been divided into 12
equal parts and one of those parts is a quarter of a third. And so we can say that a quarter of
a third is one-twelveth.