The numerator of a proper fraction is what.
This question isn’t asking us about the numerator of any fraction. We need to describe the numerator of a proper fraction. And to do this, we need to understand what a proper fraction is. It’s also worthwhile thinking about what the opposite of a proper fraction is. We call these improper fractions.
Firstly, a proper fraction is a fraction that has a value less than one whole. And just to remind ourselves about the opposite, an improper fraction is a fraction with a value greater than one whole. So, if we think about proper fractions for a moment, some examples might be two-thirds, one-quarter, or maybe seven-eighths. We know that each of these are proper fractions because they all have a value less than one.
But what can we say about the numerators of these proper fractions? The numerators tell us how many parts we’ve selected. So, in the first fraction, we can see two shaded parts. In the second one, we can see one. And in the third, we can see seven. And the denominator, or the bottom number, in each fraction shows us the number of equal parts that the whole has been split into altogether. So, in the first fraction, we can see two out of three have been shaded, then one out of four, and then seven out of eight.
For a fraction to be a proper fraction and less than one, it means not all the parts have been shaded. In other words, less than all of them have been shaded. That’s why the value is less than one. So, if we look at the numbers in our proper fractions, the numerator is always less than the denominator. Two is less than three. One is less than four. And seven is less than eight. A proper fraction always has a value less than one. And so, we can say that the numerator of a proper fraction is less than its denominator.