Calculate $12345 \pmod{11}$ and $12345\times 98765 \pmod{11}$ by hand.

Question

I know the answers to those questions, but I'd like to know how to do them by hand.

Answer 1

Hint:

$$10 \equiv -1 \pmod{11}$$

You might like to write $12345=10000+2000+300+40+5$.