To multiply 11 by 12 you just "split" the 12 and put a zero between the digits: 1_0_2. Then you add the digits in the 12: 1+2 = 3. Then you add the result of the 2nd operation to the zero in the first split: 1_0+3_2 = 1_3_2 = 132.
This technique works for any 2 digit number multiplied by 11.
What IS especially depressing is that the slowest and least efficient arithmetic techniques keep being passed on for generations. Mainly because it's easier to teach the dumb way and teachers are too lazy to learn how to teach anything new. The result of this is that most students end up hating arithmetic and calculation, and subsequently any further math, because they are never taught the fast and fun way to do things.
If you ever have a job interview at a hedge fund or trading firm, you will not get past the phone screen if you can't do this sort of arithmetic in your head.
Well, to each his own. I always hated the kind of math where you have to remember a basketful of little tricks, like your method of computing products of 11. I have always much preferred "the-method-I-invented-on-the-spot", my approximate method using nearby known numbers being one of them.
The most exciting math tests for me were always the ones where I couldn't remember the 'trick' for half the problems, and would re-invent the solution. It didn't always go well, but the GREAT SCOTT!!! moments were some of the best in all of college.
Approximate estimation is what you need to multiply other two digit numbers quickly. It just happens that there's a trick for multiples of 11. There's actually probably less than 20 other "tricks" that help with rapid calculations.
I don't understand why this trick is necessary. For 11x<number> you can just do 10x<number> + <number> which is easy until you get to 3 digit numbers, but even then continues to work.
Speed. The "trick" breaks down the problem so there's always a simpler summation to perform. In half of the possible products, one only has to add the sum of the digits to zero. For the rest, just slot the 2nd digit of the sum where the zero goes, and add 1 to the first digit. Most people can do either of those two simple additions faster than they can do sums like 210+21 or 390+39. If one is already quick with the latter kind of addition, then the trick is unnecessary.
This technique works for any 2 digit number multiplied by 11.
What IS especially depressing is that the slowest and least efficient arithmetic techniques keep being passed on for generations. Mainly because it's easier to teach the dumb way and teachers are too lazy to learn how to teach anything new. The result of this is that most students end up hating arithmetic and calculation, and subsequently any further math, because they are never taught the fast and fun way to do things.
If you ever have a job interview at a hedge fund or trading firm, you will not get past the phone screen if you can't do this sort of arithmetic in your head.