a) $\frac{1}{6}\;-\;\frac{1}{2} = \frac{1}{6}\;-\;\frac{3}{6} = \frac{1\;-\;3}{6} = \frac{-2}{6} = \frac{-1}{2}$

b) $\frac{-7}{8}\;-\;(-1) = \frac{-7}{8}\;-\;\frac{-8}{8} = \frac{-7\;-\;(-8)}{8} = \frac{1}{8}$

c) $\frac{2}{5}\;-\;\frac{5}{6} = \frac{12}{30}\;-\;\frac{25}{30} = \frac{12\;-\;25}{30} = \frac{-13}{30}$

d) $\frac{-1}{15}\;-\;\frac{1}{16} = \frac{-16}{240}\;-\;\frac{15}{240} = \frac{-16\;-\;15}{240} = \frac{-31}{240}$

e) $\frac{7}{24}\;-\;\frac{-5}{36} = \frac{21}{72}\;+\;\frac{10}{72} = \frac{21\;+\;10}{72} = \frac{31}{72}$

f) $\frac{-7}{9}\;-\;\frac{-7}{12} = \frac{-28}{36}\;+\;\frac{21}{36} = \frac{-28\;+\;21}{36} = \frac{-7}{36}$