### Video Transcript

Use the diagram to find four-sevenths divided by two-fifths, i.e., the number that four-sevenths is two-fifths of.

So in the diagram, we can see that, colored in green, we have four-sevenths of an amount. So that amount is seven of our squares because that means the bit next to it that, which is shaded in green, would be three-sevenths. But what we want to see is what four-sevenths would be two-fifths of. Well, if we take a look at the diagram, we can see that in fact we have each section, so each of the little squares, being worth a seventh. So therefore, what we’ve got is a total of ten-sevenths. So therefore, we can say that it’s equal to ten-sevenths. So we can say that the number that four-sevenths is two-fifths of is ten-sevenths. We’ve done that using the diagram.

However, this is a top-heavy or improper fraction. And we’d probably want to leave it as a mixed number. So let’s do that now. Well, that would be equal to one and three-sevenths. But that’s our mixed number answer. But have we got there?

Well, if we think of ten-sevenths or 10 over seven as seven over seven or seven-sevenths plus three-sevenths, well, seven-sevenths or seven over seven is equal to a whole one. So therefore, this is gonna be equal to one whole one and three-sevenths. So that’s how we converted our top-heavy or improper fraction into a mixed number.

Now, we got the answer to this question using a diagram. But we can also double check it using our division of fraction rule. And if we remember, if we’re dividing one fraction by another, we use KCF. And that stands for keep it, change it, flip it. So we keep the first fraction, we change the sign to multiply, and then we flip the second fraction. So it gives us five over two.

So then what we do to multiply fractions is multiply the numerators then multiply the denominators. So four by five is 20. Seven by two is 14. So we get twenty fourteenths, which if we simplify is the same as ten-sevenths. So therefore, as we’ve already worked out, we know this is one and three over seven. So we’ve got the same answer as we got using the diagram.