 Let's take a look at fractions. So one of the important dichotomies when dealing with fractions is the whole and part dichotomy. And so the idea is that I might take an object, so here's a whole object, and I could also divide it, I could break it up into a number of equal parts. And I can view each of these parts in one of two distinct ways. Either I can view it as one part out of a whole bunch, or I can view it as a part in and of itself. So I can either think about this as an object by itself, or as one part out of four. And if I consider the latter case, I can view this as the fraction one-fourth, or one over four. Now, in this case I can say that any one of these parts is a unit, and so we call each of these parts a unit fraction. Well, just as before when we had our units, like ones, tens, hundreds, and thousands, we could talk about collections of units, three ones, four tens, five thousands, and so on. And so this could extend our idea to non-unit fractions, and now I could start to talk about a collection of units. So for example, suppose I wanted to draw a representation of three-fifths. So what that's going to be is I'm going to start off by dividing the whole into five parts. So there's my five equal parts that I'm going to divide the whole into. And then I want to take three of these parts. So each one of these is one-fifth, so I'm going to take three of those parts. And there's my representation of the amount three-fifths. And we can also go backwards. So we have a shaded amount here out of a whole. And so what I'd like to do is I'd like to think about what fraction is represented here. And so the first thing I might do is I might count. There's seven parts, one, two, three, four, five, six, seven. There's seven parts. So each of these parts corresponds to the unit fraction one-seventh. And here, because I've shaded two of them, then the fraction that I have represented here is two-sevenths.