11. When the integer $a$ is divided by the interger $b$ where $b>0$, the division algorithm gives a quotient of $q$ and a remainder of $r$. Show that if $b \ a$, when $-a$ is divided by $b$, the division algorithm gives a quotient of $-(q+1)$ and a remainder of $b-r$, while if $b \mid a$, the quotient is $-q$ and the remainder is zero.