Evaluate the following:

(i) $\dfrac{2}{5} \times \dfrac{3}{7}$

(ii) $\dfrac{3}{5} \times \dfrac{8}{9}$

(iii) $7 \times 1\dfrac{2}{3}$

(i) $\dfrac{2}{5} \times \dfrac{3}{7}$

$\Rightarrow \dfrac{2 \times 3}{5 \times 7}\\[1em] \Rightarrow \dfrac{6}{35}$

Hence, $\dfrac{2}{5} \times \dfrac{3}{7} = \dfrac{6}{35}$.

(ii) $\dfrac{3}{5} \times \dfrac{8}{9}$

$\Rightarrow \dfrac{3 \times 8}{5 \times 9}\\[1em] \Rightarrow \dfrac{3}{9} \times \dfrac{8}{5}\\[1em] \Rightarrow \dfrac{1}{3} \times \dfrac{8}{5}\\[1em] \Rightarrow \dfrac{1 \times 8}{3 \times 5}\\[1em] \Rightarrow \dfrac{8}{15}$

Hence, $\dfrac{3}{5} \times \dfrac{8}{9} = \dfrac{8}{15}$.

(iii) $7 \times 1\dfrac{2}{3}$

$\Rightarrow 7 \times \dfrac{5}{3}\\[1em] \Rightarrow \dfrac{7 \times 5}{3}\\[1em] \Rightarrow \dfrac{35}{3}\\[1em] \Rightarrow 11\dfrac{2}{3}$

Hence, $7 \times 1\dfrac{2}{3} = 11\dfrac{2}{3}$.