a. $\dfrac{\frac5{35}}{\frac3{14}} =\dfrac{5}{\underset{5}{\cancel{35}}} \times \frac{\overset{2}{\cancel{14}}}{3} =\dfrac{\cancel 5 \times 2}{\cancel 5 \times 3} = \dfrac 23$.

b. $\dfrac{\dfrac17}{\dfrac{-1}3} = \dfrac 1 7 \times \dfrac 3 {-1} = -\dfrac 3 7$.

c. $\dfrac 1 2 : \dfrac 3 4 = \dfrac 1 {\underset{1}{\cancel2}} \times \dfrac{\overset{2}{\cancel4}}3 =\dfrac 2 3$.

d. $\dfrac{\frac{15}2}{\frac{25}8} = \dfrac{\overset{3}{\cancel{15}}}{\underset{1}{\cancel 2}} \times \frac{\overset{4}{\cancel 8}}{\underset{5}{\cancel{25}}} =\frac{12}5$.

e. $\dfrac 9 7 : \dfrac{-4}5 = \dfrac 97 \times \dfrac5{-4} = -\dfrac{45}{28}$.