Simplify :

$6\dfrac{1}{5} ÷ 3\dfrac{1}{10}$ of $2\dfrac{1}{2} ÷ \dfrac{1}{4}$

$\Rightarrow 6\dfrac{1}{5} ÷ 3\dfrac{1}{10} \text{ of } 2\dfrac{1}{2} ÷ \dfrac{1}{4}\\[1em] \Rightarrow 6\dfrac{1}{5} ÷ \Big(\dfrac{31}{10} \times \dfrac{5}{2}\Big) ÷ \dfrac{1}{4}\\[1em] \Rightarrow 6\dfrac{1}{5} ÷ \dfrac{31 \times 5}{10 \times 2} ÷ \dfrac{1}{4}\\[1em] \Rightarrow 6\dfrac{1}{5} ÷ \dfrac{155}{20} ÷ \dfrac{1}{4}\\[1em] \Rightarrow \Big(6\dfrac{1}{5} ÷ \dfrac{31}{4}\Big) ÷ \dfrac{1}{4}\\[1em] \Rightarrow \Big(\dfrac{31}{5} ÷ \dfrac{31}{4}\Big) ÷ \dfrac{1}{4}\\[1em] \Rightarrow \Big(\dfrac{31}{5} \times \dfrac{4}{31}\Big) ÷ \dfrac{1}{4}\\[1em] \Rightarrow \dfrac{4}{5} ÷ \dfrac{1}{4} \\[1em] \Rightarrow \dfrac{4}{5} \times 4 \\[1em] \Rightarrow \dfrac{16}{5}\\[1em] \Rightarrow 3\dfrac{1}{5}.$

Hence, $6\dfrac{1}{5} ÷ 3\dfrac{1}{10}$ of $2\dfrac{1}{2} ÷ \dfrac{1}{4} = 3\dfrac{1}{5}$.