Question 1042516
I will prove only (a).  You do the rest....

{{{abs(x) = x}}} if x > 0; {{{abs(x) = -x}}} if x < 0.  (And of course, {{{abs(0) = 0}}} .)

Given: n < 0.

Case I. m > 0.
===> {{{m/n < 0}}}, and so {{{abs(m/n) = -(m/n) = m/(-n) = abs(m)/abs(n)}}}

Case II. m < 0.
===> {{{m/n > 0}}}, and so {{{abs(m/n) = m/n = (-m)/(-n) = abs(m)/abs(n)}}}.

Case III. m = 0 is trivial after substitution of 0 for m to both sides of the equation.

Hope you get the drift...