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A proper fraction is what than one.
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In order to understand what a proper fraction is, we need to start by reminding ourselves what a fraction is.
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Fractions are ways of showing numbers that aren’t whole; they’re parts of numbers.
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If we think of this rectangle that is representing one whole and we split it into five equal parts, and we can say that each part shows a fifth.
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And this gives us the bottom number or the denominator in a fraction.
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Now, the top number or the numerator in a fraction shows the number of parts that we’ve selected or the parts that we’re talking about.
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And so, if three of our five parts have been shaded in, we could say three-fifths have been shaded.
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Our numerator is three and our denominator is five.
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And the whole fraction is less than one; it’s smaller than one.
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Now on some occasions, we might have a fraction where the numerator is larger than the denominator.
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What if the three-fifths was written as eight-fifths?
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We know that five-fifths are the same as one whole, five out of five.
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And so eight-fifths is a fraction that’s greater than one.
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In fact, eight-fifths is worth one whole and three-fifths or one and three-fifths.
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Now what do we call these two types of fractions?
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Well, the fraction on the right, and that’s a fraction where the numerator is larger than the denominator, a fraction that’s larger or greater than one, is called an improper fraction.
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And the fraction on the left — these are the fractions that we learned about when we first start finding out about fractions — is called a proper fraction.
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These are, when the numerator is less than the denominator.
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And these are fractions that are smaller than one.
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So we can complete our sentence with the word smaller.
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Proper fractions are fractions where the numerator, that’s a number of parts that we’re talking about, is less than the denominator.
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That’s the number of parts in total.
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So if we’re only talking about part of the total amount, we’re talking about an amount that’s smaller than one.
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The missing word in our sentence is smaller.
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A proper fraction is smaller than one.