 So let's take a look at an example of a division. So for example, we might take a look at 4, 2, 3, base 5, divided by 3, 2, base 5. And so it's important to remember there are two ways of interpreting a division. Either we can view this division partatively, where we're going to take 4, 2, 3, base 5 objects, and distribute them equally among 3, 2, base 5 recipients. Well, this may be a little bit hard to envision. If we can't visualize how many 3, 2, base 5 is, it's hard to do the division this way. And we'll see that in general, partitive division is difficult to envision. Or we could look at this quotient as a quotitive division. We're going to take 4, 2, 3, base 5 objects, and we're going to form sets of 3, 2, base 5 objects. And this is much easier to do because I can see what a 3, 2, base 5 object looks like. It's three things and two things. So we'll use this approach. So let's take a look at our quotient. This is going to be 4, 2, 3, base 5, divided by 3, 2, base 5. And again, here's why it's important to read this number as 4, 2, 3, base 5, and not as 4, 2, 3, base 5, because what it tells us is that we have four big things, 2, medium, and 3, small. And from this, we want to form sets of 3, 2, base 5. And that's 3, medium, 2, small. And so now we know how much should go in each bag. Let's start bagging. So we'll bring in a bag. And the first thing we notice is that while we need to put 3, medium, and 2, small into this bag, we don't actually have 3, medium to put in. That's OK, because we're working in base 5, we can break this big thing into 5, medium things. And once I do that, I now have 3, medium, and 2, small. So I'll put them into this bag, and I'll set the bag aside. I'll bring in another bag, break up another one of these big things. And while I have plenty of mediums, I don't have enough smalls. But again, that's OK because I'm working in base 5. I can take any object and break it into 5 smaller objects. And in this particular case, I want to take one of these medium things and break it into 5 small things. So I'll do that, and then fill my bag with 3, medium, 2, small, set it aside, bring in another bag, fill it, set it aside, bring in another bag. And again, we don't have enough medium things, so we'll break up a big thing into 5, medium, and fill the next bag, bring in another bag. And again, now we don't have enough small things, so we'll take a medium thing and break it into 5 small things. And then that allows us to fill the next bag, another bag. And we don't have enough medium things, so we'll take the big thing and break it into 5, medium, and then fill this bag. And at this point, notice we only have two medium things and one small thing left. We can't fill any more bags. So in this division, our quotient is the number of bags. And to write down this value, let's go ahead and set down one mark for each bag that we have. So we'll mark this one, this one, this one, this one, this one, and this one. And remember, we're working in base 5, so we can bundle 5 of these objects and trade for 1 of the medium-sized objects. So our quotient then is going to be 1 medium, 1 small. And we have remainder, 2 medium, 1 small. And again, we can write this in base 5 notation by dropping the unit symbols and explicitly indicating the base. And that gives us our quotient for 2, 3, base 5 divided by 3, 2, base 5 is 1, 1, base 5, with remainder, 2, 1, base 5. So let's take a look at the division, 2, 0, 3, base 5 divided by 3. And again, we can view division in two ways. We can view this as a partative division, where we take a set of 2, 0, 3, base 5 objects. That's 2 of something, 0 of something, 3 of something. And we distribute it equally among three recipients. Well, actually, I can visualize what that looks like. So let's go ahead and do this as a partative division. So again, we'll set down our dividend. That's 2 of something, 0 of something, and 3 of something. And we'll set down boxes for our three recipients. Now, the first thing we might notice is that we actually have three of these small boxes. So let's go ahead and give one of those small boxes to everybody. And now we have two of the large squares, but we have three recipients. So we can't give one square to two of the recipients and not give something to the third person. So the only way we can proceed at this point is we have to break up some of these large squares. And since we're working base 5, then every large square can be broken up into five smaller boxes. So here, I'll take this big square, I'll split it, I'll break it apart into five pieces, I'll take the other one, also break it apart into five pieces. And now I can give everybody one of the blocks. And I still have blocks left over, so I'll give everybody another one of the blocks. And there's still enough blocks left over, so I'll give everybody a third block. And now I only have one block left, but I can break this up again. And again, because we're working in base 5, I can break this block up into five smaller pieces, so I'll break it apart. And I'll distribute an additional small cube to everybody. And now I just have two of these little cubes left over. And because these are the smallest unit, I can't break them apart further. Or can I? We'll talk about that a little bit later on. For now, we can't break it apart any further. And so our quotient is, how much did everybody get? Well, everybody got three blocks and two small cubes. So the quotient is 3-2, base 5, with remainder, 2.