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Video: Unit Fractions

Tim Burnham

Here, we explain that unit fractions have 1 as a numerator and that the denominator tells us how many shares the whole is divided into.

05:22

Video Transcript

We’re gonna look at unit fractions in this video. We’ll see what a fraction is and what it means to say a half or a third or a quarter and so on. Fractions help us to see what share of a whole amount we’re talking about. For example, if we’re doing a bit of archery practice and said that we hit the target once, it doesn’t really tell us very much about how good we are. We really need to know how many attempts we had in total to know if hitting the target once was impressive or not. If we only had one go, then hitting the target is probably quite good. But if we had a hundred goes, then it sounds less good. This is where fractions come in handy. They tell us about the proportion of something. So fractions like a half and one hundredth mean one out of two or one out of a hundred, and they tell us what proportion of the whole amount that we’re talking about.

For example, if we did a test and we got one out of seven right. That means we got six out of the seven wrong. It tells us that we’ve got a very small proportion of the questions right.

We could apply similar logic to populations for example. So in China for example, there are about one point four billion people, and the population of the entire world is about seven point six billion. So roughly, a fifth of the world’s population live in China. Not exactly, but roughly a fifth. So if we express that as a fraction one over five, one out of five people, we can even see it visually here. For if we have five people, one of those people lives in China. So that’s the rough proportion of the world’s population who live in China.

Now, a unit fraction then is just a fraction with a one on top. And unit fractions let us compare one part to the whole of something. As a quick aside, the top of a fraction, the number on the top of a fraction is called a numerator; and the number on the bottom of a fraction is called a denominator. And if you find those words hard to remember, remember numerators got a “U” in it and that’s like “upstairs”, and denominators got a “D” in it and that’s like “downstairs”.

So let’s have a look at a few more examples where we’re gonna cut up shapes and create unit fractions from those shapes. So let’s start off with a square. We’ve divided it into two equal parts. And if we shade in one of them, we’ve shaded in a half, one out of two parts of the square.

And this circle, we’ve divided into three equal-sized shares, and we’ve shaded in one of them. So the fraction a third means one part is shaded out of three equal-sized shares or three parts.

Now, what fraction of this shape is shaded? Well, it doesn’t matter which part we’ve shaded in, but there are eight equal-sized shares. So that’s an eight on the denominator and we’ve shaded in one of them. So, that’s one out of eight. One-eighth is shaded.

And one more, we’ve taken this hexagon, six-sided shape. We’ve divided it up into six equal parts. So that’s going to be six on the denominator. And we’ve shaded in one of them. So that’s a one out of six, is the fraction that represents this shaded area.

Now, it’s important to remember that we must divide the shape up into equal-sized shares. So for example, if we take this trapezium shape, we can split it into two equal parts and shade one of them. So, we’ve got one out of two equal-sized shares shaded. So the fraction that represents the shaded area is a half. But if we split it into three parts like this, they’re not all the same size. They may have the same width, these little sections here, but they don’t have the same area. We can see this one in the middle has a much bigger area than this one on the end. So we can’t say that that is one out of three because they’re not equal-sized shares to start off with.

So, let’s just think about what we’ve learnt then. Unit fractions have a one on top, for example a quarter. They compare one part with the whole. So in our previous example, that’s one out of four, and the four had to be equally sized shares. So the number on the bottom of the fraction tells us how many equally sized shares we split the whole thing up into. And can you remember which way around the numerator and denominator go? Well, numerator has got a “U” for “upstairs” in it, and denominator has got a “D” for “downstairs” in it. So that should tell you which way round they go.