Divide :

$32\dfrac{1}{2}$ ÷ $8\dfrac{3}{4}$

We have:

$\begin{array}{ll} \phantom{=} 32\dfrac{1}{2} ÷ 8\dfrac{3}{4} \\ = \dfrac{65}{2} ÷ \dfrac{35}{4} & \text{[Converting mixed to improper fraction]} \\ = \dfrac{65}{2} \times \dfrac{4}{35} & [\text{Reciprocal of } \dfrac{35}{4} \text{ is } \dfrac{4}{35}] \\ = \dfrac{13}{2} \times \dfrac{4}{7} & \text{[Simplifying 65 and 35 ⇒ Divide by 5]} \\ =\dfrac{13}{1} \times \dfrac{2}{7} & \text{[Simplifying 4 and 2 ⇒ Divide by 2]} \\ = \dfrac{13 \times 2}{1 \times 7} \\ = \dfrac{26}{7} \\ = 3\dfrac{5}{7} \end{array}$

∴ The answer is $3\dfrac{5}{7}$