Split the digits, add them, and drop the sum in the middle. It works because multiplying by eleven is the same as multiplying by ten and adding the number again.
Take 43 times 11. Split the digits: 4 and 3. Add them: 7. Put that between the two: 473. Done.
Try 62 times 11. Split to 6 and 2, add to 8, and the answer is 682. The method is not a trick you have to trust; it falls straight out of what eleven is.
Eleven is ten plus one. So 43 times 11 is 43 times 10, which is 430, plus 43, which is 473. Writing that out, the tens digit of the answer is the original tens digit plus the original units digit. That is exactly the sum you dropped in the middle.
Which tells you where it breaks. If the digits sum to more than nine, there is a carry: 78 gives 7, 15, 8, and the 1 has to carry into the hundreds, making 858. The shortcut still works, but only if you remember it is arithmetic and not magic.
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