 Lesson Video: Unit Fractions: Halves, Thirds, and Quarters | Nagwa Lesson Video: Unit Fractions: Halves, Thirds, and Quarters | Nagwa

# Lesson Video: Unit Fractions: Halves, Thirds, and Quarters Mathematics

In this video, we will learn how to write unit fractions representing halves, thirds, and quarters of shapes and use models to relate the fraction to the number of shaded parts and the number of parts in the whole.

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### Video Transcript

Unit Fractions: Halves, Thirds, and Quarters

In this video, we will learn how to write unit fractions representing halves, thirds, and quarters of shapes and describe what fraction of a shape is shaded.

Which of these models show halves? How do we know what a half is? Let’s look closely at the models. Here’s a model of a square. The square has been divided into two parts. Does that mean that each part is a half? No, it doesn’t. Halves are equal parts. If we were to divide the square into two equal parts, each part would be a half. So this square has not been divided into halves. Has this triangle been divided into two equal parts? Yes, it has. We can call each part a half. This is how we write a half. This is one part out of two equal parts. Has this circle been divided into two halves? No, it’s been divided into two parts, but they’re not equal parts. So we can’t call the parts of the circle halves.

How about this cube train? Has it been divided into two equal parts? There are six cubes altogether. Three of them are blue, and three of them are orange. Each part of the cube train is equal. Each part has three cubes, so we can call each part a half. So we’ve learned that a half is one of two equal parts. And we write it as a one over two, one out of two equal parts. So we can say that half of the triangle is shaded blue, and half of the cube train is blue. One out of two equal parts are shaded.

This rectangle has been divided into three equal parts. What do we call each of the parts? This is a third, and this is how we write it: one over three, one out of three equal parts. Has a third of this triangle been shaded pink? The triangle has been divided into three parts. But are they equal? No, they’re not. This triangle hasn’t been divided into thirds, just three parts. What fraction of this circle has been shaded pink? The circle has been divided into four equal parts. When we divide a shape into four equal parts, we call each part a quarter or a fourth. And this is how we write it. Has a third of this square been shaded green? Yes, it has. The square has been divided into three equal parts. All of the parts are the same size, and one out of those three parts has been shaded.

Let’s recap what we’ve learned about fractions. If we divide a shape into two equal parts, we call each part a half. And this is how we write a half. A half is one out of two equal parts. When we divide a shape into three equal parts, we call each part a third. This is how we write a third, and a third is one out of three equal parts. And when we divide a shape into four equal parts, we call each part a quarter or a fourth. This is how we write it. A quarter is one out of four equal parts.

Let’s try practicing what we’ve learned with some example questions.

This rectangle is partitioned into equal parts. One out of what equal parts is shaded. Complete the fraction: what quarter of the area is shaded.

This rectangle has been partitioned or divided into equal parts, and one of the parts has been shaded. In the first part of the question, we need to work out how many equal parts the rectangle has been partitioned or divided into. Did you count the number of equal parts? There are four. One out of four equal parts is shaded. And in the second part of the question, we need to write this as a fraction. One out of four equal parts is a quarter. The rectangle has been divided into four equal parts, and one of those parts or one-quarter is shaded.

Consider the shape shown. One out of what equal parts is shaded. Pick the fraction that shows how much of the shape has been shaded.

We’re told to consider, which means think about the shape which is shown. We can see that one of these equal parts has been shaded. In the first part of the question, we need to think about how many equal parts there are altogether. There’s one, two, three equal parts. Each part is the same size, so we can say that one out of three equal parts is shaded. Now we have to pick the fraction that shows how much of the shape is shaded. We know that one out of three equal parts have been shaded. How do we write this as a fraction?

We know that this is not the correct fraction because this says that three out of one equal parts have been shaded. That’s not correct. The other three remaining fractions show that one out of some parts have been shaded. The first fraction is one out of three shaded parts, or one-third. This must be the correct fraction because one out of three parts in our shape have been shaded. If one out of three equal parts is shaded, the fraction of the shape that has been shaded is one-third.

We’re shown a picture of a rectangle. How many equal parts has it been divided into? There are two equal parts. We call each part a half. One of these halves has been shaded. The fraction of the shape which has been shaded is one-half.

What have we learned in this video? We’ve learned that halves, thirds, and quarters are equal parts of a whole shape. We’ve also learned that a half is one out of two equal parts, a third is one out of three equal parts, and a quarter is one out of four equal parts.