Use the model to calculate one-fifth divided by three.
This problem asks us to divide a fraction by a whole number. And it’s a sort of a calculation that looks tricky when we first see it. A fraction is a whole number split up into parts. So how can we then divide that into more parts? And what are those parts worth? This is why using models can be a really good way to help us find the answer. It can help us visualise what’s going on. And we’ve been given a model to help us calculate one-fifth divided by three. And rather than just looking at the model, let’s draw it again as we go along. And perhaps this will help us to understand it even better.
The first number in our division, or the dividend, is one-fifth. So the first thing our model has to do is represent one-fifth. First, we can draw a strip that represents one whole. And then by dividing the strip into five equal parts, we’ve divided it into fifths. And so we can represent our dividend of one-fifth by shading in one of our fifths. This should explain where the first bar comes from. It shows us one-fifth.
Now the question asks us to divide that one-fifth into three. Well, that’s easy enough. We could draw a strip the same size as one-fifth and then simply split it into three equal parts. One of those parts is what we get when we split one-fifth into three.
If we left the model at this point, it wouldn’t be correct because it looks like the answer might be one-third. We’ve only shaded one out of three. If you remember, the whole amount was the whole of the long strip. And so to work out what our shaded part is worth, we need to split all of the fifths into three. So there are two lots of three, three lots of three, four lots of three, five lots of three in one whole. And this should explain why our second strip looks the way it does.
Each of our fifths has been split into three. That’s five groups of three. Five threes are 15. And so the whole strip has been split into fifteenths. One of those parts has been shaded. And so we can say that one fifteenth has been shaded.
We found the answer to one-fifth divided by three by first drawing a strip and splitting it into five equal parts. By shading one of those parts, this represented the one-fifth in our question. We then divided that fifth into three. And to work out the fraction that the shaded part represented, we had to continue this all the way along the strip, dividing all of the fifths into threes. This meant we divided the strip into 15 equal parts. One of those parts was shaded. And so one-fifth divided by three equals one fifteenth.