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