 So let's go back to this idea of division having two distinct interpretations, and both of them are going to be useful. So again, the idea is that a division like a divided by b, I can view this as a partative question. I'm going to take a, and I'm going to divide it, break it into b equal parts, and my goal is to find out how big each part is. Or I could do it as a quantitative division. I'm going to take a, and break it into parts of size b, and I want to find out how many parts there are. And the tape diagram can be used to model both divisions. So for example, let's take 24 divided by 4. We'll show them partatively and quotatively using a tape diagram. So we'll start with our partative division. It's the more natural way to read the division, if not to actually perform it. So with partative division, I'm going to take a tape that represents 24, and I'm going to break it into four equal pieces. So there's my tape representing 24. I'll break it into four equal parts, and my question is how big each part is going to be. Well, if this is 24, I want all of these parts to have the same size, and maybe I don't know how big those parts are, so maybe I'll take a guess. Suppose each part is 5, well, that's all of them are going to be 5, and well, that's not quite enough. That's 10, 20, so I am still not quite at 24 yet, so I've got to increase the size of those parts a little bit. So I'll increase the size by one more, so that's 20, 21, 22, 23, 24. This is everything, and so each of these parts is a 5 and a 1, so each of those parts represents a 6. And so there's my partative division. On the other hand, if I want to form the quotitive division, I'm going to divide 24 into parts of size 4, which is the quota. So I'll have my figure representing 24, and I'll mark off parts of size 4. So there's a part, there's another, there's another, there's another. Let's see what I have to do for it. 4, 8, 12, 16, I have a couple more parts I can make. That's 20, and that last one is going to be 4, and the quotient is going to be the number of parts. So here my parts are of size 4, and there's 1, 2, 3, 4, 5, 6 of them, and there's my quotient.