Evaluate the following:

(i) $\dfrac{3}{5} \times 180$

(ii) $\dfrac{3}{7}$ of $5\dfrac{5}{6}$

(iii) $\dfrac{5}{18} \div \dfrac{2}{3}$

(i) $\dfrac{3}{5} \times 180$

$\Rightarrow \dfrac{3 \times 180}{5}\\[1em] \Rightarrow 3 \times 36\\[1em] \Rightarrow 108$

Hence, $\dfrac{3}{5} \times 180 = 108$.

(ii) $\dfrac{3}{7}$ of $5\dfrac{5}{6}$

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

Hence, $\dfrac{3}{7}$ of $5\dfrac{5}{6} = 2\dfrac{1}{2}$.

(iii) $\dfrac{5}{18} \div \dfrac{2}{3}$

$\Rightarrow \dfrac{5}{18} \times \dfrac{3}{2}\\[1em] \Rightarrow \dfrac{5}{2} \times \dfrac{3}{18}\\[1em] \Rightarrow \dfrac{5}{2} \times \dfrac{1}{6}\\[1em] \Rightarrow \dfrac{5}{12}$

Hence, $\dfrac{5}{18} \div \dfrac{2}{3} = \dfrac{5}{12}$.