 Well, let's take a look at the subtraction problem. So we can remove subtraction as a removal of units, and again, important reminder, arithmetic is bookkeeping. Because we're trying to remove things, we do have to be a little bit more careful about how we keep track of things, and we'll see a couple ways that we might be able to do that. So let's do the subtraction. 234 base 5 minus 103 base 5. Arithmetic is bookkeeping, and so what this is saying is that we have two big things, three medium, four small, and from this we want to remove one big thing and three small objects. And here, the bookkeeping aspect, it's helpful to put a reminder someplace of the things that we want to remove and to check them off as we've removed them. So we want to remove one big thing, so we'll take that away, check off that we've removed it. We also want to remove three small squares, so we'll remove them and check off the fact that we have removed them. And so there's our subtraction. And so arithmetic is bookkeeping. What we have left is one big thing, three medium, and one small. And again, if we want to write our final answer in base 5 notation, we'll drop the unit designations and then we'll write down the fact that we are dealing in base 5. And so here's our final answer, 1, 3, 1, base 5. Now let's take another example, 2, 1, 3, base 6, minus 3, 5, base 6. And so again, arithmetic is bookkeeping. What we have is two large, one medium, three small, and I want to remove three medium, five small, except there's a problem. I only have one medium. How can I remove three of them? And likewise, I only have three smalls. How can I remove five of them? In order to do this subtraction, you might do what's called borrowing. Well, actually, it's not really borrowing. The important observation here is that what we take is never, ever return. This is not borrowing. It is better to think about it as trading. Remember, how you speak influences how you think. So in this type of subtraction, it is very, very, very important not to call this procedure borrowing. You never return what is taken. It is trading. Alternatively, you can think about it as unbundling because remember, every unit is formed from some number of smaller units. And so what can we do? Well, we can trade. Since we're working base 6, we can take one large and trade it for 6 medium. Again, the other way of looking at this is we're going to take one of these large and break it apart into 6 medium. And likewise, we can trade one medium for 6 small. And what that gives us is enough medium and enough small to be able to remove 3 medium and 5 small. So I'll remove 3 medium. I'll remove 5 small. And arithmetic is bookkeeping. What I want to do is I want to write down how many of which units. And what I have left, I have one large, 3 medium, and 4 small. And to get my final answer, I'll drop the unit designations and I'll spell out the base. And so this subtraction to 1, 3, base 6 minus 3, 5, base 6 is going to give me 1, 3, 4, base 6.