Video: Unit Fractions of Shapes in Real World Contexts

Olivia made a cake for a party and cut it into 12 equal pieces. What could the cake look like after 1/4 of it has been eaten?

03:45

Video Transcript

Olivia made a cake for a party and cut it into 12 equal pieces. What could the cake look like after one-quarter of it has been eaten?

There’re some pictures in this question that help us to understand the problem and also to help us to give our answer. We can see that the shape of the cake that Olivia’s made is a rectangle. We know that Olivia’s cut the cake into 12 equal pieces. And we can see this in the picture. There are two rows of six. And the question asks us what could the cake look like after one-quarter of it’s been eaten.

Only one of the four possible answers is correct. So, to solve the problem, we need to think carefully about what one-quarter of 12 might look like. Perhaps the easiest way to solve the problem is to actually draw lines on the cake and to split it into half and then half again. This is the same as splitting it into quarters. We know one-half of 12 equals six and half of six is three. So, one-quarter of 12 equals three. This means that three squares out of the 12 have been eaten.

We could find the same answer using numbers. To find a quarter of a number, we simply divide it by four. 12 divided by four equals three. So, we could either use the diagram or numbers to find out that one-quarter of the cake is three pieces.

The question asks us what could the cake look like after one-quarter of it has been eaten, or, in other words, after the three pieces have been eaten. The word could is important here because it could be any three pieces. And so, there isn’t one particular answer that’s always correct. But we’re given four choices. And only one of them has had one-quarter eaten.

The cake was cut into 12 equal pieces. One-quarter, or three pieces, have been eaten. And this leaves us with nine pieces. So, we need to ask ourselves, which of the cakes that we’re given as a possible answer has got nine pieces left in it?

The first cake has two rows of five, which equals 10. Our second cake has a row of five with a row of two on top. That’s seven. Our third cake has a row of six with a row of three on top. Six and three equals nine. This looks like it might be the cake we’re looking for. And our final cake has two rows of four pieces, which is eight. So, we’ve found what the cake could look like after one-quarter of it has been eaten.

Interestingly, we could’ve worked out the answer just by looking at the picture. Can you see how one-quarter of the shape has been taken away? But as we’ve said already, a much more reliable way to find the answers is to use numbers. The people at Olivia’s party could have eaten any three pieces of cake. And then, the shape would’ve looked very different.

So, the best way to find the answer is to take away three from 12 and look for a shape that has nine pieces of cake left in it. If Olivia cuts her cake into 12 equal pieces and one-quarter of them have been eaten, the answer that shows what the cake might look like is the cake that has nine pieces left in it. And that’s this one.

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