Why does this math trick work? 35 by 11 is 385 because 3+5 is 8, so it's the digit in the middle.
Same for:
72 by 11 is 792 because 7+2 is 9, so it's the digit in the middle.
I see it works because 35 by 10 is 350, or 72 by 10 is 720. The 0 is replaced with the extra digit. The last digit is 5 by 1 or 2 by 1, so it stays the same.
But why should the middle digit be the sum of the first and last?

When performed in written calculation,
$$ab\times11$$ is
$$\ \ \ \ ab\\ab\\\ \ \overline{acb}$$
so that the digits are $a,a+b,b$. This breaks when there is a carry, e.g. $76\times11=836$.
