Video: Using an Area Model to Multiply Two Fractions

How much is 1/4 of 1/3?

03:21

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.

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