 Okay, let's look at another way we can do that division using a tape diagram, but this time we'll also draw in the idea of our area model. So remember, division and multiplication are very closely related, and the key here is that if I know the two sides of a rectangle, then the product corresponds to the area, but then if I have the area in one side, the other side is going to correspond to a quotient. And this allows us to produce an area model for division. So let's take an example. So suppose I want to divide 221 by 17. And so what I can do, I can start off with the rectangle, the area is 221, and the one side of the rectangle is 17. So I have a rectangle, one side is 17, the area is 221, and the question that I want to answer is, what is the other side? Well, the nice thing about this is I can take parts, and I don't have to take the whole thing all at once. So maybe I'll take a chunk of the rectangle. How big? Well, let's make it easy on ourselves. What if I take a piece of size 10? Now, I have to know something a little bit in advance here. I have to know that if I do take a piece of size 10, the resulting rectangle is going to have area 17 by 10, 170, which is conveniently smaller than the actual rectangle I'm dealing with. So I take a piece of size 10, the area of that portion, 170, and again, conveniently smaller than what I'm working with 221. Well, that means I have some left over area. So I can take another piece, and how big is that going to be? Well, I know it's not going to be 10, because that's going to be too big. 170 plus 170 is 340, so I'll take a smaller bit. How about 2? So I take a rectangle that's 2 by 17, and the area of that rectangle is 34, and click check here, that's 170 plus 34. That's 204 as my area so far, which means that there's still some area left over here, and I can get the last of that area by taking one more bit of size 1, and that last rectangle has area 17. So now this rectangle 17 by 10 plus 2 plus 1 has area 17 by 10, 170 plus 34 plus 17. So that's going to be 221. This is my entire rectangle, and my quotient is the length of that top side, 10 plus 2 plus 1 is going to be 13. Well, let's do a more complicated problem, 1537 divided by 29. Again, it's worth noting that at this point we have not yet mentioned, we have not actually examined the standard algorithm for a division. We don't have a process for dividing by two digit numbers. No problem, we can still do this. I have an area of 1,537, and one side has length 29, and it will be convenient, not absolutely necessary, but certainly convenient if I split this side here of length 29 into two easy-to-work-with portions, a 20 and a 9, for example, but not necessarily required. Again, many people think in quarters, so maybe this 29 could be better split into a 25 and a 4. It doesn't make a difference. Alright, so I'm going to take bits. So let's see, I'll take a chunk of the rectangle, and I didn't have any, maybe I'll call it 20, and so this rectangle 20 by 20, this rectangle 20 by 9, and I can fill out what those areas are going to be, and the entire rectangle at area 1,537, here's part, here's another part, and I want to find what's left over. So let's go ahead and keep track of that. So this first bit here has area 400, so I'm going to subtract that out of my original area. So I have 1,137 left over, and then this area here, area 180, so I'll subtract that amount. And again, it helps if you think about how you do subtraction. I might do this 180 as subtract 200, then return 20. So that's going to be subtract 200, that leaves me 937. Returning 20 leaves me 957 left. So after I've taken out this portion here, the rest of the rectangle has area 957. Now, let's take another chunk of the rectangle. So again, this time I might notice that this area here, 400, 580, I can definitely take out another piece of size 580, and what do I have left over? Well again, I'm going to subtract off the area here and that area, and after I do that, subtracting the 400, subtracting 180, and now the remaining rectangles must have area 377. Well, I can't take off another piece of size 20, that's going to be too big, but I can certainly take off a piece of size 10 or so. And so after I do that subtraction, 290, there's going to be 87 left over as my area, and again, a piece of size 10 is too big, and I find that the last chunk must be of size 3. So now my area of the figure, a couple of 400 to 260, all of these added together should add up to 1537, and that tells me that the rectangle with area 1537 is a 29 by 2040 53, and so the quotient is going to be 53.