Don't tell me the whole answer...I just need a hint, I guess.

I'm supposed to prove thatadivbis non-negative whenaandbhave the same sign, and non-positive when they have different signs.

Am I on the right track with this (this is just the first case I'm supposed to consider)?

Case 1. Assumea ≥0 andb< 0.rb≥ 0, sor≤ 0.

Thenadivb=q= (a-r) /b

Sincer≤ 0 anda≥ 0,adivbcan be rewritten as ( |a|+ |r| ) /b

Sinceb< 0,adivbcan be rewritten as (-1)( |a|+ |r| ) / |b|

Since ( |a|+ |r| ) / |b| is non-negative, the valueadivbis non-positive in this case.