Find the quotient:

(i) $\dfrac{2}{3} \div \dfrac{3}{10}$

(ii) $\dfrac{7}{11} \div \dfrac{5}{8}$

(iii) $-\dfrac{4}{7} \div \dfrac{5}{14}$

(i) Given, $\dfrac{2}{3} \div \dfrac{3}{10}$

$\Rightarrow \dfrac{2}{3} \div \dfrac{3}{10} \\[1em] \Rightarrow \dfrac{2}{3} \times \dfrac{10}{3} \\[1em] \Rightarrow \dfrac{2 \times 10}{3 \times 3} \\[1em] \Rightarrow \dfrac{20}{9}.$

Hence, $\dfrac{2}{3} \div \dfrac{3}{10} = \dfrac{20}{9}$.

(ii) Given, $\dfrac{7}{11} \div \dfrac{5}{8}$

$\Rightarrow \dfrac{7}{11} \div \dfrac{5}{8} \\[1em] \Rightarrow \dfrac{7}{11} \times \dfrac{8}{5} \\[1em] \Rightarrow \dfrac{7 \times 8}{11 \times 5} \\[1em] \Rightarrow \dfrac{56}{55}.$

Hence, $\dfrac{7}{11} \div \dfrac{5}{8} = \dfrac{56}{55}$.

(iii) Given, $-\dfrac{4}{7} \div \dfrac{5}{14}$

$\Rightarrow -\dfrac{4}{7} \div \dfrac{5}{14} \\[1em] \Rightarrow -\dfrac{4}{7} \times \dfrac{14}{5} \\[1em] \Rightarrow -\dfrac{4 \times 14}{7 \times 5} \\[1em] \Rightarrow -\dfrac{56}{35} \\[1em] \Rightarrow -\dfrac{8}{5}.$

Hence, $-\dfrac{4}{7} \div \dfrac{5}{14} = -\dfrac{8}{5}$.