# Lesson Video: Nonunit Fractions for Halves, Thirds, and Quarters Mathematics

In this video, we will learn how to write and model non-unit fractions with denominator 2, 3, or 4.

17:43

### Video Transcript

Nonunit Fractions for Halves, Thirds, and Quarters

In this video, we’re going to learn how to write and model nonunit fractions. And we’re especially going to be thinking about fractions that have denominators of two, three, or four.

Let’s start with a hungry mouse. What she needs is a nice, big piece of cheese. Now, if we look carefully at this cheese, we can see that it’s already been cut into mouse-sized pieces already. The whole has been split into four equal parts. We can see quarters. And depending on where you’re from, you might call these fourths. Now, if our mouse decides to eat one of these slices of cheese, we can say she’s eaten one-quarter. Now, so far, when we’ve been learning about fractions, we’ve always talked about one part. This is the same as the one slice of cheese that this mouse has eaten, one out of four equal parts.

I’m sure you know this already. Fractions that have a one as their numerator, in other words, when we’re talking about one part, are called unit fractions. But as you can see, our piece of cheese is made up of more than one part. So that’s why in this video we’re going to be thinking about fractions that have other numbers as a numerator too. These are what we call nonunit fractions. And the only way we’re going to find them is if we start eating this cheese up.

Oh! Here’s another hungry mouse looking longingly at this piece of cheese. Now, what happens if this mouse eats one of the four pieces? He’s eaten one-quarter too. It might be hard to see this because we’re slowly getting rid of the slices of cheese, aren’t we? So let’s draw dotted lines to show where they once were.

So if our first mouse ate one-quarter and our second mouse ate one-quarter, we can say that they’ve both eaten two-quarters. Watch how we write this as a fraction, two out of a possible four equal parts. And because we’re not talking about one-quarter anymore — we’re talking about two-quarters — this is one of those nonunit fractions that we mentioned. These mice have eaten two-quarters of the whole cheese.

In fact, you might know another fraction you could describe this as. It’s the same as a half, isn’t it? Half of the cheese has gone. Not for long, looks like we’ve got another hungry mouth to feed. And if this mouse eats another of our slices of cheese — remember, this is another one of the original four — then three out of the four pieces have been eaten. Three-quarters have been eaten. And this nonunit fraction is going to have a numerator of three. Remember that the numerator or the top number in a fraction shows us the number of parts that we’re talking about. So it’s three parts. And then it’s going to have a denominator of four. And remember, the denominator shows us the number of equal parts that there are altogether, three out of a possible four, three-quarters.

We’ve only got one slice or one-quarter left. Now, we can’t let a good cheese go to waste, can we? Now, the whole cheese has been eaten, four-quarters. Now, watch what happens when we write this as a fraction, four parts out of a total of four equal parts. Four-quarters is the same as one whole. Can you see that both the numerator and the denominator are the same? Whenever we see this when we’re talking about fractions, we know we’re talking about one whole.

Let’s give you a quick example, two halves, same number on the top and the bottom of this fraction. So we know it must be the same as one whole. And we know this is true, don’t we? One-half, two-halves or one whole.

Now, we did say at the start of this video that we were going to be working with nonunit fractions that have denominators of two, three, and four. In other words, we’re going to be thinking about whole amounts that have been split into two equal parts, three equal parts, or four equal parts. And that’s why in the title of our video it mentioned halves, thirds, and quarters.

Let’s try answering some questions now where we have to put into practice everything we’ve learned about nonunit fractions, in other words, those fractions where we’re talking about more than one part.

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.

Pick the shape with three-quarters shaded.

In this question, we’re thinking about quarters. Now, we know that quarters are part of a whole amount, when one whole has been split into four equal parts. Now, if we look at the circles that are in this picture, we can see that each one of them has been split into four equal parts. There’s a quick way to find quarters. And that’s to split a circle once down the middle to show halves and then dividing each of those halves into half with a line across the middle, four equal parts or quarters.

Can you see that each of the circles has got black lines to show that it’s been divided in this way? So the first thing that we can say about our possible answers is that they all show quarters. But we’re looking for a shape that has three-quarters that are shaded. Our first shape has one, two parts shaded. This has two-quarters shaded, not three-quarters. Our second shape has one, two, three parts shaded red. Looks like these are the three-quarters we’re looking for.

Let’s just quickly look at the other two shapes because they’re interesting. Our third shape has one out of four equal parts shaded. This is the one you might recognize. It has one-quarter shaded. And our final shape has four parts shaded. That’s four out of the possible four. Four-quarters are shaded. And we know that four-quarters are the same as one whole. We know that when we divide a circle into four equal parts, they’re called quarters. And so the shape that has three-quarters shaded is this circle here. It’s the one where three out of four equal parts are shaded red.

The word fraction in this question means part of a whole. And if we look at this triangle, we can see that only part of the whole amount has been shaded. And we can write down this part as a fraction. Now, what do we know about fractions? We know we can write them by drawing a line, a number above it, and a number below it. The bottom number in a fraction or the denominator shows us the total number of equal parts that the whole amount has been split into.

In this example, the whole amount is this triangle here. And it’s been split into one, two, three equal parts. And if you’re wondering whether they really are equal parts, turn your head. It might help you to see that they are. They’re all exactly the same size. And because the whole triangle has been split into three equal parts, we can write three as the denominator in our fraction.

We’re talking about thirds. So now we need to ask ourselves, how many thirds are shaded? Now, this is where the top number or the numerator in our fraction comes in. The numerator represents the number of selected parts, the number of parts that we’re talking about. And in this example, we’re talking about the number of parts that are shaded. Now, when we first introduced the fractions, we usually look at one part on its own: one-half, one-third, one-quarter, and so on. But the numerator doesn’t have to be one.

In this picture, we can see one, two parts are shaded. The numerator in our fraction is going to be two. Two out of a possible three parts have been shaded blue. And so we can say that the fraction of this shape that’s been shaded is two-thirds.

In the picture, we can see a rectangle. It’s this long strip of a rectangle here. And we can see that part of this rectangle has been shaded orange, but not all of it. If all of the rectangle had been shaded orange, we might say one rectangle is orange or one whole rectangle is orange. But this is only part of a whole rectangle. And we can use fractions to represent part of a whole.

What fraction of this long rectangle is shaded? Well, we know how to write fractions, don’t we? We need a line, a number on the top, and then a number on the bottom. To remember what each number represents, the denominator or the bottom number in a fraction shows us the number of equal parts that the whole amount has been split into. Firstly, we can look at our long strip of a rectangle. And we can see that each of the parts that it’s been split into they are all equal, aren’t they? And there are one, two, three, four parts. We call these quarters. Each of these separate parts is worth one-quarter. And because we’re talking about quarters, we know our denominator must be four, just like all those quarters that we’ve labeled our parts with.

Scarlett has shaded parts of the given whole. Complete the sentences. What out of four equal parts are shaded? What quarters of the whole is shaded?

In the picture, we can see a whole amount, and we’re told that Scarlett has shaded some parts of it. So what do you think the whole amount is that’s being talked about? It’s this whole rectangle here, isn’t it? And we can see that the whole of this long rectangle has been divided into one, two, three, four smaller rectangles. And they’re all the same size, aren’t they? They’re equal parts.

Now, we’ve got some sentences about these parts that we need to complete. But before we do that, let’s take a moment to look carefully what we’re being asked because we can make a prediction here. Our last missing number is the top number in a fraction. Now, we know that the top number in a fraction is called the numerator. Do you remember what this represents? It’s the number of parts that have been selected.

Well, in this particular question, we’re talking about shaded parts. So why don’t we change our definition? The numerator is the number of shaded parts. Now, if we come back up and look at our first missing number, we also need to write down the number of shaded parts, this time as a sentence. So even if we’d never seen this diagram, we’d be able to predict one thing. Our two missing numbers are going to be exactly the same, aren’t they?

Alright, let’s get answering this question. So our first sentence says, what out of four equal parts are shaded? One, two out of four equal parts are shaded. Now, because the whole amount has been divided into four equal parts, we know we’re talking about quarters. And that’s why the denominator or the bottom number in this fraction is four. Did you notice when we read the question we said “what quarters”? As we’ve said already, the missing number then is the numerator. The number of shaded parts is two. So we can say two-quarters of the whole is shaded. Two out of four equal parts are shaded. Two-quarters of the whole is shaded.

What have we learned in this video? We’ve learned how to write and model nonunit fractions that have denominators of two, three, or four.