Does it matter which order you subtract the columns in?

You may realize that, when it comes to the columns, you don't have to do subtraction in any particular order. This might seem to fly in the face of conventional theory, after all, we know that subtraction does not adhere to the commutative property. That means that it does matter which order you subtract entire numbers in. For example, 59 - 23 is not the same as 23 - 51. (In the second case, we would have to get a negative number. We don't go into negative numbers on this site, yet).

So how can it be that the order of the columns doesn't matter? Look at it this way, 59 -23 is the same as (50 + 9) - (20 + 3). Now, you can't move any of those numbers from one side of the minus sign to the other without changing them. But you can move the numbers on any side of a plus sign (because addition is commutative). What that means, is that you can switch the 50 with the 9, and switch the 20 with the 3. That would make the example look like (9 + 50) - (3 + 20).

That would actually seem like a stupid thing to do, because then you would have the ones come first and write the answer backwards, from right to left. Isn't that the way they taught you to to it in school, though? It does seem stupid, doesn't it? I think it is, too. It makes more sense to me to subtract the higher columns first. Yes, you could do it the other way around, but then you would have to ask: Why would the schools want you to do it this way?" I haven't found an answer that makes good sense yet.

close this window