well, you already know how to convert from mixed to improper, so let's simply do the division.
[tex]\bf -2\frac{1}{2}\div 6\implies -\cfrac{5}{2}\div 6\implies \cfrac{-5}{2}\div \cfrac{6}{1}\implies \cfrac{-5}{2}\cdot \cfrac{1}{6}\implies -\cfrac{5}{12}[/tex]
