Lesson Video: Unit Fractions of a Quantity | Nagwa Lesson Video: Unit Fractions of a Quantity | Nagwa

Lesson Video: Unit Fractions of a Quantity Mathematics • 3rd Grade

In this video, we will learn how to find unit fractions of an amount or a quantity using visual models and explain how this relates to division by the denominator.


Video Transcript

Unit Fractions of a Quantity

In this video, we’re going to learn how to find unit fractions of an amount or a quantity using visual models to help. And we’re going to explain what this has got to do with dividing by the denominator.

Let’s start with 12 bananas and a very hungry monkey. Now, what happens if he decides to eat a quarter of the bananas? We know there are 12 bananas, so this is just like asking, what is one-quarter of 12?

Now, if you remember, our video was called unit fractions of a quantity, and one-quarter is an example of a unit fraction. This is a fraction where we’re only thinking of one of something. This has one as the top number or the numerator. So all the way through this video, we’re only going to be thinking about fractions like one-quarter, one-half, one-fifth, one-third, and so on. And the number 12 here is the quantity of bananas. One-quarter of 12 is a unit fraction of a quantity. So how many bananas is this? Let’s draw a bar model to help us.

This bar represents our 12 bananas. Now we know when a shape, a number, or a quantity is divided into quarters, it’s split up into four equal parts. And you know a quick way to do this is to split into half and then half again because half of a half is the same as a quarter. Let’s divide another bar to show quarters then, half and then half again. We’ve divided our bar into four equal parts. Can you see which part of the fraction tells us that we need to do this? It’s the bottom number, or the denominator. This shows us the number of equal parts that we need or the number we need to divide by.

So if we were being asked to find one-half of 12, we’d need to divide by two. To find one-third of 12, we’d need to divide by three and so on. The denominator is a clue that tells us what we need to do here. Now, how many bananas is each of our quarters worth? We know that half of 12 is six. And if we split each half in half, this gives us three. And this is where our times tables facts come in useful. We know that four times three equals 12. And so 12 divided by our denominator, four, equals three. And so we can say that one-quarter of 12 bananas is three bananas. This monkey has eaten three bananas.

Here’s another monkey. She’s full of energy. And can you see why? She’s already had her lunch. She’s eaten some bananas out of this group. What fraction of the bananas has she eaten? To begin with, let’s draw a ring around the bananas that she’s eaten. This is a group of three; our monkey has eaten three bananas. But what fraction is this out of the whole amount? Don’t forget when we’re thinking about fractions, we’re thinking about dividing a whole amount into parts that are the same size or equal. Let’s split up the whole amount of bananas so that they’re in groups of the same size.

Here’s another group of three bananas, a third group, a fourth group, and one more. We’ve split the whole amount into five equal groups. And we know that when we divide something into five equal parts, each part is one-fifth. The fraction of bananas that the monkey’s eaten is one-fifth. Let’s show this is a fraction of a quantity. One-fifth of the whole amount of bananas, which we haven’t counted yet but we can do so in a moment, equals three bananas.

Let’s count in threes to find out what our missing number is. There are three, six, nine, 12, 15 bananas in the whole amount. One-fifth of 15 is three. And remember, we can check this because we can take the whole amount, which is 15, and divide it by the denominator in our unit fraction. 15 divided by five equals three. All of this tells us that the fraction of the bananas that the monkey’s eaten is one-fifth.

Do you think you’re ready to answer some questions now where you put into practice what you’ve learned? Let’s give it a go.

What fraction of the circles is shaded?

In the picture, we can see a group of circles, but only part of the whole group has been shaded. Let’s draw a box around the shaded part. Now if our question asked us, “how many of the circles are shaded?,” we could answer two. But we’re not asked this. We need to compare the group that is shaded with the whole amount because we’re being asked what fraction of the circles is shaded. In other words, if we use this bar to represent all of the circles, we’re being asked, what fraction is this part here worth? Remember, the important thing whenever we talk about fractions is that we’re talking about equal parts.

Let’s split up the rest of our group so that everything’s in equal parts. Here’s another group of two, so that’s two equal parts, three, four, five, six, seven. We’ve divided the whole amount into seven equal parts. We know this because each part contains two circles. And because there are seven equal parts, we can say each part is worth one-seventh. And because only one of our parts is shaded, we can say one-seventh is shaded. There are two, four, six, eight, 10, 12, 14 circles altogether. And we can use this to check our answer is correct.

To find one-seventh of 14, we can start with 14 and divide by the denominator, which is seven. We know there are two sevens in 14, so 14 divided by seven equals two. One-seventh of 14 circles is two circles. And of course, this matches the two circles that are shaded. It looks like our fraction is correct. The fraction of the circles that’s shaded is one-seventh.

Fill in the blank: one-quarter of 20 equals what.

In the picture, we can see a group of 20 cakes. And to answer the problem, we need to find a fraction of this quantity. We need to find one-quarter of 20. What do we know about the fraction one-quarter? Well, firstly, the numerator is one. This means it’s what we call a unit fraction. In other words, we only need to find one-quarter. We don’t need to find two-quarters or three-quarters, only one. And the bottom number or the denominator in one-quarter is a four. This tells us that we need to split the whole amount into four equal parts. That’s what a quarter is; it’s one out of four equal parts. So to find out what one-quarter of 20 is, we’re going to have to split up 20 into four equal parts.

Now, there are two ways we could do this. Firstly, we could think about the number 20 itself, and we could work out the answer to 20 divided by four. Or we could use the picture of the cakes to help. We could divide this into four equal groups. Let’s try both ways, and if we get the same answer, we know we’ve got it right. Now there’s a quick way we can split things into four. We start by finding a half, and then if we find half again, that gives us four equal parts. We know that half of 20 is 10 and then half of 10 is five. There are four fives in 20. 20 divided by four equals five. It looks like one-quarter of 20 is five, but let’s just check using the picture.

First, we can split the group in half. Now, if we split each half in half by going down the middle, we can see we’re going to end up with some half cupcakes, which we don’t really want. It makes it a bit more tricky to count. So let’s just split each half in half by drawing lines across. There we go. We’ve split the whole amount into four equal groups, and there are one, two, three, four, five cupcakes in each group. We were right. One-quarter of 20 equals five.

Fill in the blank: one-half of eight equals what.

In this question, we need to find a fraction of an amount, one-half of eight. Now we’ve got a picture to help us. There are eight cupcakes. Now, how do we find half of an amount? The clue is in the fraction itself. The top number or the numerator tells us how many parts we’re looking for. And in this case, it’s one. We’re looking for one-half. And the bottom number or the denominator shows us how many equal parts the whole has been split into. And from what we know about fractions already, we know this is true, don’t we? If we divide a shape or a number or a quantity by two, we split it into two equal parts or half. So half of the whole amount, eight, is the same as eight divided by two.

What do we get if we split eight into two equal parts? We get four and another four. Eight divided by two equals four. And we know this because two times four is eight. Half of eight equals four.

What is one-fifth of five?

In this question, we need to find a fraction of an amount. That amount is five. Let’s model it, shall we? Let’s use pufferfish. Now we can see that there are five fish in the whole amount. But what do we do to find one-fifth of this number? The number one, the numerator in this fraction, tells us that it’s a unit fraction. We’re only looking for one part, not two-fifths or three-fifths or four-fifths, only one-fifth. And the number five, that’s the denominator, tells us how many equal parts to split the whole amount into.

To find a fifth, we divide the whole amount into five equal parts. Each part is worth one-fifth. Now we know that five ones make five. So if we divide five by itself, the answer is one. We found the answer here by dividing five into five. One-fifth of five equals one.

There were 15 birds on a tree, but a third of them flew away. Find the number of birds that flew away.

To begin with in this problem, we’re told about a group of birds. There were 15 of them on a tree. Let’s model our 15 birds using plastic counters. Now, we’re told that some of these birds flew away. And fortunately, we’re not told the number of birds that flew away. This is what we need to find. Instead, we’re told the fraction of the whole amount. This is a third. Now this is a third written in words. But do you remember how to write it using digits? The numerator is one. This shows us that we’re only thinking about one-third and not two-thirds or more. And then the denominator is three. This shows us the number of equal parts that we need to split the whole into.

So to find one-third of 15, we can divide 15 by the denominator, three. If we split 15 into three equal groups, how many will there be in each group? Perhaps you can think of a times tables fact that could help us here. We know that three times five equals 15. 15 divided by three equals five. And we can show this using our counters. We’ve split the whole amount into three equal groups, and each of the three groups, that’s each third, is worth five. So if there were 15 birds on a tree, but a third of them flew away, the number of bird that flew away is five.

Now what have we learned in this video? We have learned how to find unit fractions of amounts or quantities using models to help. We have also explained how we can divide by the denominator.

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