Question Video: Shading Equal Parts of Shapes to Match a Description Mathematics

Pick the rectangle that matches Jacob’s description.


Video Transcript

Pick the rectangle that matches Jacob’s description. One-third is colored blue. Two-thirds are colored yellow.

In this question, we can see four different rectangles. And we’re told to pick the rectangle that matches Jacob’s description. So perhaps we’d better read his description carefully. In his description, Jacob mentions two fractions. He tells us that one-third of the rectangle is colored blue. And then he mentions another fraction. Two-thirds are colored yellow. Now, what is this word “third” that he mentions?

A third is a type of fraction. It’s when one whole has been split into three equal parts. Now, there are two things that are really important about that definition. Firstly, we’re looking for something that’s been split into three parts. And then they need to be three equal parts too. So to begin with, let’s look at our rectangles and see which ones have been split into thirds.

If we look at our first rectangle, we can see that it has been split into three parts, but they’re not all the same size, are they? This part over here is a lot bigger than the other two. These parts are not equal. So we can’t say that this rectangle’s been split into thirds. It’s really important to understand why this rectangle is not correct because it might be quite easy to choose it as the correct answer. It does have one out of three parts colored blue and two out of three parts colored yellow. But they’re not equal parts, and so they’re not thirds. Don’t be caught out by this rectangle.

Now, if we look at our second rectangle, again, we can see one part blue, two parts yellow, and they are all equal parts. But there’s a part that’s colored white too. There are four equal parts. This rectangle doesn’t show thirds either; it shows quarters. So this doesn’t match Jacob’s description.

Now, if we look at our final two rectangles, we can see that each one has been split into three parts. And each of those three parts is equal. These have both been split into what we call thirds. But only one of our rectangles is correct. Jacob says that one-third is colored blue, in other words, one out of three equal parts. Looks like the correct rectangle might be this one, doesn’t it? This has one out of three equal parts that’s blue.

Now, when Jacob tells us that two-thirds are colored yellow, he’s telling us that two out of three equal parts are colored yellow. And we can see these in the first rectangle too. Notice that these two parts aren’t right next to each other. When we show a fraction, it doesn’t have to be that we color the parts side by side. As long as any two of the three parts are shaded, then two-thirds are shaded. We knew we were looking for a rectangle that had been divided into three equal parts, where one of those parts was colored blue and the other two parts were colored yellow. The correct rectangle is this one here. One-third is blue, and two-thirds are yellow.

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