 So let's talk about how you might perform a subtraction. If I use tape diagrams or counting down, they very naturally lead to a method known as subtraction by decomposition. And the basic idea is that if I want to find the value of the subtraction a-b, what I'm going to do is I'm going to break b and possibly a down into a number of useful parts. And then at that point, what I'm going to do is I'm going to remove the parts of b from the parts of a. So for example, let's say I want to take the subtraction 87 minus 23. And again, to put this in perspective, we have not yet at this point learned a formal algorithm for performing any sort of subtraction. However, that shouldn't make too much of a difference because we have an idea of what we're doing when we subtract. So I'm going to subtract 23 from 87. And so the idea is I can think about 87 as being composed of the parts 80 and 7. And likewise, I can think of 23 as being composed of the parts 20 and 3. And so what I want to do is I want to subtract 23. Well, I want to subtract 20 and 3 from whatever I can subtract it from. So I can subtract 20 from 80, that leaves me 60. I can subtract 3 from 7, that leaves me with 4. And so when I subtract the parts, I get the parts 60 and 4. And I can retrieve my final answer as the number 64. Now another way of looking at this again once we gain a little bit more facility with basic arithmetic is to think about it as follows. I started with 87, I subtracted 20, and then I subtracted 3, and then I got my remainder 64. Well, let's take a look at a different example, 103 minus 47. So again, I can think about the number that I'm subtracting as 40 and 7. So I can start with 103, and I can subtract 40. This is essentially just a benchmark counting down subtraction. So I'm going to subtract 40, and that takes me back to 63. Now I can subtract 7. Now if I don't know how to cross a 10 with a subtraction, that's okay. Because all I have to do is figure out how I'm going to subtract 7 using what I can subtract. So again, I can think about this as a counting down problem. I want to count back 7. Well, I might start by counting back 3, that takes me down to 60, and then count back 4, subtract 4, and that takes me, let's see, 59, 58, 57 to 56. And so all together I've gone back 43, 47. I've gone back 47 from 103, and I've gotten back to 56.