Evaluate the following:

(i) $\dfrac{8}{21} \div 4$

(ii) $\dfrac{4}{15} \div \dfrac{2}{5}$

(iii) $8 \div \dfrac{5}{6}$

(iv) $5\dfrac{1}{4} \div \dfrac{7}{8}$

(v) $5\dfrac{1}{3} \div 1\dfrac{1}{9}$

(i) $\dfrac{8}{21} \div 4$

$\Rightarrow \dfrac{8}{21} \div \dfrac{4}{1}\\[1em] \Rightarrow \dfrac{8}{21} \times \dfrac{1}{4}\\[1em] \Rightarrow \dfrac{8}{4} \times \dfrac{1}{21}\\[1em] \Rightarrow 2 \times \dfrac{1}{21}\\[1em] \Rightarrow \dfrac{2}{21}$

Hence, $\dfrac{8}{21} \div 4 = \dfrac{2}{21}$.

(ii) $\dfrac{4}{15} \div \dfrac{2}{5}$

$\Rightarrow \dfrac{4}{15} \times \dfrac{5}{2}\\[1em] \Rightarrow \dfrac{4}{2} \times \dfrac{5}{15}\\[1em] \Rightarrow 2 \times \dfrac{1}{3}\\[1em] \Rightarrow \dfrac{2}{3}$

Hence, $\dfrac{4}{15} \div \dfrac{2}{5} = \dfrac{2}{3}$.

(iii) $8 \div \dfrac{5}{6}$

$\Rightarrow \dfrac{8}{1} \div \dfrac{5}{6}\\[1em] \Rightarrow \dfrac{8}{1} \times \dfrac{6}{5}\\[1em] \Rightarrow \dfrac{8 \times 6}{1 \times 5}\\[1em] \Rightarrow \dfrac{48}{5}\\[1em] \Rightarrow 9\dfrac{3}{5}$

Hence, $8 \div \dfrac{5}{6} = 9\dfrac{3}{5}$.

(iv) $5\dfrac{1}{4} \div \dfrac{7}{8}$

$\Rightarrow \dfrac{21}{4} \div \dfrac{7}{8}\\[1em] \Rightarrow \dfrac{21}{4} \times \dfrac{8}{7}\\[1em] \Rightarrow \dfrac{21}{7} \times \dfrac{8}{4}\\[1em] \Rightarrow 3 \times 2\\[1em] \Rightarrow 6$

Hence, $5\dfrac{1}{4} \div \dfrac{7}{8} = 6$.

(v) $5\dfrac{1}{3} \div 1\dfrac{1}{9}$

$\Rightarrow \dfrac{16}{3} \div \dfrac{10}{9}\\[1em] \Rightarrow \dfrac{16}{3} \times \dfrac{9}{10}\\[1em] \Rightarrow \dfrac{16}{10} \times \dfrac{9}{3}\\[1em] \Rightarrow \dfrac{8}{5} \times 3\\[1em] \Rightarrow \dfrac{24}{5}\\[1em] \Rightarrow 4\dfrac{4}{5}$

Hence, $5\dfrac{1}{3} \div 1\dfrac{1}{9} = 4\dfrac{4}{5}$.