Which is greater, one-eighth or one-seventh?
Here we have two fractions, one-eighth and one-seventh. And we’re asked, which is the greater? Well we can tell just by looking at them, can’t we? One-eighth has the number eight as its denominator, and eight is greater than seven. So surely, one-eighth is larger fraction than one-seventh.
Well, we need to think a little bit more carefully than this. And in particular, we need to think about what the denominator in a fraction means. The denominator in a fraction shows the number of equal parts that one whole has been split into. So when we talk about eighths, we’re talking about one whole that has been split into eight equal parts. And, the fraction one-eighth is one out of those eight equal parts.
As we’ve said already, sevenths sound like they might be less than eighths. But, what sevenths means is that we’ve divided the same whole into seven equal parts. But because we’re dividing the whole into less equal parts, we can see that each seventh is actually larger than the eighths. One-seventh is greater than one-eighth.
So, we don’t just look at the denominator and think that we know the answer, just because one denominator is larger than the other. We have to think about what the denominator in a fraction means. If one whole is split into eight equal parts, each part will be smaller than if we split the same whole into seven equal parts. So, out of the two fractions, one-eighth and one-seventh, the greater fraction is one-seventh.