We need convert the mixed numbers to improper fractions.
[tex]1\dfrac{5}{8}=\dfrac{1\cdot8+5}{8}=\dfrac{8+5}{8}=\dfrac{13}{8}\\\\1\dfrac{3}{5}=\dfrac{1\cdot5+3}{5}=\dfrac{5+3}{5}=\dfrac{8}{5}[/tex]
Divide the number by a fraction, this is the same as multiply this number by the reciprocal of the fraction:
[tex]1\dfrac{5}{8}\div\left(-1\dfrac{3}{5}\right)=-\dfrac{13}{8}\div\dfrac{8}{5}=-\dfrac{13}{8}\cdot\dfrac{5}{8}=-\dfrac{(13)(5)}{(8)(8)}=-\dfrac{65}{64}\\\\\boxed{1\dfrac{5}{8}\div\left(-1\dfrac{3}{5}\right)=-1\dfrac{1}{64}}[/tex]
