Could anyone tell me why $3/7\equiv 9 \mod12$? How is this operation defined and why sometimes modulo division is impossible, like in the case of $3/4 \mod 12$? See here for more details, I'm refering to page 95.
I can't grasp why $3/7\equiv 9 \mod12$. I divide $3$ by $7$, what I get is $3 = 0 \times 7 + 3$, the remainder is $3$. Now how is it equal to $9$ mod $12$?