 So let's see if we can go past the whole numbers and the integers and introduce a new type of number. And so this begins with the idea that when we're working in base N, we can always bundle N objects to form a single larger unit. And we can do this repeatedly. So for example, in base 3, we could take 3 objects and bundle them together. And then we can take 3 of these objects and bundle them. And then take 3 of these objects and bundle them together and so on. And as we saw when we did things like division or subtraction, it was sometimes convenient to reverse the process. So we can take a large object and break it apart into 3 smaller objects. And we can take each of these smaller objects and break them apart into 3 even smaller objects. And we can take these smaller objects and break it apart into 3 even smaller objects. And then if we do that one more time, we'll get back to our single unit. And at this point, the question that we might ask is, why couldn't we continue this process? And there's no reason why we couldn't. So let's suppose we begin with our smallest whole number unit. Now, rather than worrying about base N and only breaking this into N smaller pieces, let's suppose I just break it into however many pieces I feel like breaking it into. So I can break it into N pieces and each one of these is going to be some smaller unit. And because we've fragmented the unit, we'll call each of these pieces a unit fraction. And the name of that unit is going to correspond to how many pieces we've broken the unit into. Well, again, remember arithmetic is bookkeeping. If you remember this, then there is no difference between the arithmetic of the fractions and the arithmetic of the whole numbers. Here, because I've broken the unit into four parts, each part is going to be a fourth. And we want to be able to specify how many of which units. So let's say I take this set here. And so here I have three. There's our how many of the things we call fourths. And those are our unit. So we would call this amount three fourths. And we're going to write it in this form where we have the fractional form of our amount. And again, the important thing to remember is arithmetic is bookkeeping. And this fractional form tells us how many of which units. And in particular, the numerator numbers. It tells us how many. In this case, the numerator three tells us that we have three somethings. What about those somethings? Well, the denominator denotes it tells us what the units are. And so here our denominator tells us that the units are fourths. And when I write this fraction, three fourths, what it tells me is I have three things, each of which is a fourth. The number of things is three. The unit are fourths.