\[ \begin{align*} \dfrac{5}{6} \times \dfrac{2}{9} &= \dfrac{5\times 2}{6\times 9} \\ &= \dfrac{10}{54} \\ &= \dfrac{5}{27} \end{align*} \] \[ \begin{align*} \dfrac{7}{8} \times \dfrac{4}{5} &= \dfrac{7\times 4}{8\times 5} \\ &= \dfrac{28}{40} \\ &= \dfrac{7}{10} \end{align*} \] \[ \begin{align*} \dfrac{9}{10} \times \dfrac{3}{7} &= \dfrac{9\times 3}{10\times 7} \\ &= \dfrac{27}{70} \end{align*} \] \[ \begin{align*} 4 \times \dfrac{2}{15} &= \dfrac{4\times 2}{1\times 15} \\ &= \dfrac{8}{15} \end{align*} \]