Hmm... pretty interesting. It's a bit slow, especially with larger numbers, mostly because you have keep repeating the process until you're dealing with double-digit numbers.

I wanted to figure out how to do the procedure with triple digit numbers so I tried 180 x 195.

It turns out that you'll need to reduce the value you're working with down to 100 and then add rather that subtract. So for instance it would be...

180 80
195 95

180 + 95 = 275
195 + 80 = 275
80 x 95 = 7600 (in order to get this without doing normal multiplication, you'd have to do the process over again with the smaller numbers which is why it's time wasting)

I don't know how to explain this very well, I lack the words, but basically, to get the correct answer, you need to increase 275 to 27500 and then add the 7500 to it

27500 + 7500 = 35100

180 x 195 = 35100

Seems slow and overly complicated. It's a different way of doing things, I wouldn't say extraordinary.

What's wrong with long multiplication if you're going to use a system that breaks things down then I don't like the abstract complexity of these types of systems. You're getting the answer but in a way that means people really aren't going to understand what's going on. At least with long multiplication there's far less abstract and it's much easier to understand why you're doing what you're doing. I think 'magical' things like this lead to less understanding and maintain ignorance.

87x98

7x8=56
7x90=630
80x8=640
80x90=7200

56+630+640+7200=8526

Come on, is that really so hard? Four basic multiplication steps and one addition step and it's obvious what's going on.

It's also obvious how it applies to three or four digit numbers, and it's still simple.

For something like 87*98 I'd likely start with 87*100=8700 then subtract 87*2 from that unless I had a calculator, of course.