In a way, it involves thinking like an abacus. 3 from 2 is 9, carry the one. Subtracting 3 from 2 gives you a negative number. You can’t have those on an abacus. So what you do is realize that -1 is the same as -10 + 9. That’s where the 9 comes from, it’s what you have to add back after you subtract the 10. Of course, you have to account for that 10, which is really a 1 in the 10’s column. Hence, carry the one. To reduce the 10’s column by 1, you can either subtract 1 from the top number, or add 1 to the bottom number. Both result in the same thing. It doesn’t matter if you have 3-7 or 4-8. Either way it’s -4. Of course, in abacus-land, you think of -4 as -10 +6. That’s the six, and you have to “carry the one” again, which means you have to change 3-1 to either 2-1 or 3-2. Either way, you get 1.
It seems odd to me, especially the idea of fiddling with the bottom number WHICH MUST NEVER BE CHANGED! (Why do I think it’s ok to fiddle with one, but not the other?)
What I like about it, is that it’s very good to get used to thinking of things like -4 as -10 + 6. Those kind of substitutions are really helpful. Think about something like 897. It’s much easier to do it as 8(100-3) = 8100 - 83 = 800 - 24. Getting kids to realize that most any irritating number can be replaced with an operation involving simple numbers is a good thing.
