Video Transcript
There is one-quarter of a cake left. Noah eats two-thirds of it. What fraction of the cake does Noah eat?
We might think by reading the question quickly that Noah eats two-thirds of the cake; the answer must be two-thirds. But this isn’t true. We’re told that there’s one-quarter of a cake to start with. And so, Noah eats two-thirds of this amount. In other words, he eats two-thirds of one-quarter. In other words, we need to calculate the answer to two-thirds multiplied by one-quarter.
Now, when we multiply two fractions together, we simply need to multiply the numerator and then the denominator. Two lots of one equals two. And three lots of four equals 12. So, we could say that the fraction of the cake that Noah eats is two twelfths. Now, we can simplify this fraction. To do so, we need to divide both the numerator and the denominator by the same amount. And apart from one, the only number that we can divide two and 12 by is two. Two divided by two equals one. And 12 divided by two equals six. So, although Noah has eaten two twelfths of the cake, we could also say he’s eaten one-sixth of the cake.
Well, that’s how to work out the answer using calculations. But we can also use models to help work out a calculation like this. And sometimes seeing a model can help us understand why the answer is one-sixth. So, let’s go through a model, too. We’ll start off by picturing the whole cake. Here we are. This is what the cake looked like to begin with.
Now, we’re told in the first sentence that there’s only a quarter of this cake left. So, the first thing that we need to do is to divide our cake into quarters. This way we can show the quarter of the cake that’s left. So, the amount of cake that we start our problem with. It’s this quarter here. Next, we’re told that Noah eat two-thirds of it. And remember, as we’ve already discussed, this is not two-thirds of the whole cake. This is two-thirds of the quarter that there is left.
So, if we divide our quarter into thirds, three equal parts, Noah is going to eat two out of these three parts, which is the same as two-thirds of one-quarter. But what is this piece of cake worth? At the moment, the whole cake isn’t split up into parts of an equal size. So, to work out the fraction that Noah has eaten, we need to extend our lines so that they do show parts of an equal size. So, we can extend our lines that show thirds all the way across the whole cake. Of course, there’s no cake to cut, but at least it shows us what fraction we’re looking at.
We’ve divided the whole shape into 12 equal parts. And we can see that Noah has eaten two of them. So, that’s where we get the answer two twelfths from. And how does our models show one-sixth? Well, if we think of our two twelfths as being a rectangle that looks like this, we can count how many rectangles like this there are in the whole shape. One, two, one and its side down the bottom, that’s three, four, five. And another one on its side at the bottom. That’s six altogether. This is where we get the answer one-sixth from.
If there’s one-quarter of a cake left, and Noah eats two-thirds of it, the fraction of the cake that Noah eats is found by multiplying two-thirds by one-quarter. We’ve done this using calculation and also using a model. And we can say that the fraction of the cake that Noah eats is one-sixth.
