\[\begin{aligned} A &= \frac 5 6 - \frac 1 6 \times 7 + \frac 4 9&\\ &=\frac 5 6 - \frac 7 6 + \frac 4 9&\\ &=\frac{15-21+8}{28}&\\ &=\frac 2 {18}&\\ &=\frac 1 9.& \end{aligned}\]

\[\begin{aligned} B &= \left(2 - \frac 1 3\right):\frac{20}9&\\ &=\frac{6-1}3 \times \frac 9 {20}&\\ &=\frac{5}{3}\times \frac{9}{20}&\\ &=\frac{\overset{1}{\cancel{5}}\times\overset{3}{\cancel{9}}}{\underset{1}{\cancel{3}}\times\underset{4}{\cancel{20}}}&\\ &=\frac 3 4.& \end{aligned}\]

\[\begin{aligned} C &= \frac 4 3 + \frac 1 2 : \left(\frac{-3} 4 + \frac 1 6\right)&\\ &= \frac 4 3 + \frac 1 2 : \frac{-9+2}{12}&\\ &=\frac 4 3 + \frac 1 2 \times \frac{-7}{12}&\\ &=\frac 4 3 - \frac 1 2 \times \frac{12} 7&\\ &=\frac 4 3 - \frac 6 7&\\ &=\frac{28-18}{21}&\\ &=\frac{10}{21}.& \end{aligned}\]

\[\begin{aligned} D &= \frac 3 8 - \frac 3 {14} \times \frac 7 6&\\ &=\frac 3 8 - \frac{\overset{1}{\cancel{3}}\times\overset{1}{\cancel 7}}{\underset{2}{\cancel{14}}\times\underset{2}{\cancel 6}}&\\ &=\frac 3 8 - \frac 1 4&\\ &= \frac {3-2} 8&\\ &=\frac 1 8.& \end{aligned}\]