This **** is stupid. Even if my example is incorrect and I got it wrong, it's still stupid because in most cases you'll end up having to divide and multiply large numbers anyways. Such as 15 x 68. Just do as you were thought in school, it's much easier Assuming you all were thought the same method as I was
I just noticed that if I had added 17 to the 10 in 1020, then I would actually have gotten the answer which was 2720. However, this is not how it was show in the example above. Also, multiplying 85 and 32 is just as time consuming as multiplying 15 and 68.
Just so you know it works for numbers not as close to 100 too, though it tends to be a little more difficult. 82 x 73 = 5986...10082 = 18, 100  73 = 27, 18 x 27= 486, 18+27=45. Now here's the silly part, if the number of the mulitplication is triple digits you have to subtract the first number, in this case 4, from the addition, which is 45 so 454=41. 10041=59, not add on the last two digits of your multiplication and you get 5785. 65 x 89 = 5785. 10065= 35, 10089=11, 35 x 11=385, 35+11=46, 463=43, 10043=57, add on the 85 from the multiplication and you get 5785. Did it twice just to prove (mostly to myself) that it wasn't a fluke.
That is about as correct as saying the spelling of a word in English has something to do with the study of english.

Also thumb all you want, being in the majority doesn't make you right.
Because it's helpful to understand why it works, for one, your mobile phone doesn't do **** if your serious about math. You wouldn't have your precious phone, computer, TV, medications, or any technology whatsoever if people didn't care to understand mathematics.
As a math teacher, I want to make a suggestion. When proving a formula to be equal to another, you can't cross one over the equals sign. You are trying to prove they are equal, and by moving values over the equals, you already assume they are. This could NOT work, but it might seem like it does because of how you solved this. I challenge you to try again though. I'm curious if you can actually do that. Show your work like you have here, and I'll give you some extra points on your next quiz.
Except that there is a much easier method that actually works all of the time, for numbers of any size.
I present: The Lattice Method
9x9=81, 7x9=63, 9x6=54, 7x6=42
2=2, 4+4+3=11(or 1, carry 1), 1+1+6+5=13(or 3, carry 1), 1+8=9
9312
Never even seen this method before, but here goes.
Each big box is split into two  Tens/Ones, from multiplying the two side digits. EG, you get 6/3 from multiplying 9 and 7 (9*7=63), and 4/2 from 6*7
Then you start from the bottom right, which each diagonal row being a separate units column. In this case, 2 is the first digit. Then 3+4+4 = 11, so 1 is the second digit and the 10 carries across into the next. So then you have 1 + 6 + 1 + 5, which equals 13. Again, the 10 carries across and 3 is your 3rd digit. Finally, 1 + 8 = 9, giving 9312
Seems a bit confusing to me, but if you've grown up with it it makes a lot more sense.
So this method makes it look like it's 76,140 but the trick is when it gives you a number above 4 digits is to add the first digit of the 140 we got from multiplying the 14 and 10 to the last digit of the 76 we got from subtracting the answer of 14+10 from 100 and you get 7740