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We’re gonna look at unit fractions in this video.
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We’ll see what a fraction is and what it means to say a half or a third or a quarter and so on.
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Fractions help us to see what share of a whole amount we’re talking about.
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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.
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We really need to know how many attempts we had in total to know if hitting the target once was impressive or not.
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If we only had one go, then hitting the target is probably quite good.
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But if we had a hundred goes, then it sounds less good.
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This is where fractions come in handy.
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They tell us about the proportion of something.
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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.
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For example, if we did a test and we got one out of seven right.
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That means we got six out of the seven wrong.
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It tells us that we’ve got a very small proportion of the questions right.
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We could apply similar logic to populations for example.
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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.
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So roughly, a fifth of the world’s population live in China.
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Not exactly, but roughly a fifth.
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So if we express that as a fraction one over five, one out of five people, we can even see it visually here.
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For if we have five people, one of those people lives in China.
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So that’s the rough proportion of the world’s population who live in China.
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Now, a unit fraction then is just a fraction with a one on top.
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And unit fractions let us compare one part to the whole of something.
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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.
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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”.
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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.
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So let’s start off with a square.
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We’ve divided it into two equal parts.
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And if we shade in one of them, we’ve shaded in a half, one out of two parts of the square.
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And this circle, we’ve divided into three equal-sized shares, and we’ve shaded in one of them.
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So the fraction a third means one part is shaded out of three equal-sized shares or three parts.
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Now, what fraction of this shape is shaded?
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Well, it doesn’t matter which part we’ve shaded in, but there are eight equal-sized shares.
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So that’s an eight on the denominator and we’ve shaded in one of them.
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So, that’s one out of eight.
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One-eighth is shaded.
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And one more, we’ve taken this hexagon, six-sided shape.
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We’ve divided it up into six equal parts.
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So that’s going to be six on the denominator.
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And we’ve shaded in one of them.
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So that’s a one out of six, is the fraction that represents this shaded area.
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Now, it’s important to remember that we must divide the shape up into equal-sized shares.
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So for example, if we take this trapezium shape, we can split it into two equal parts and shade one of them.
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So, we’ve got one out of two equal-sized shares shaded.
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So the fraction that represents the shaded area is a half.
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But if we split it into three parts like this, they’re not all the same size.
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They may have the same width, these little sections here, but they don’t have the same area.
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We can see this one in the middle has a much bigger area than this one on the end.
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So we can’t say that that is one out of three because they’re not equal-sized shares to start off with.
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So, let’s just think about what we’ve learnt then.
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Unit fractions have a one on top, for example a quarter.
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They compare one part with the whole.
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So in our previous example, that’s one out of four, and the four had to be equally sized shares.
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So the number on the bottom of the fraction tells us how many equally sized shares we split the whole thing up into.
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And can you remember which way around the numerator and denominator go?
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Well, numerator has got a “U” for “upstairs” in it, and denominator has got a “D” for “downstairs” in it.
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So that should tell you which way round they go.