Divide:

$4\dfrac{1}{2} ÷ 6\dfrac{1}{2}$

Solving,

$\Rightarrow 4\dfrac{1}{2} ÷ 6\dfrac{1}{2}\\[1em] \Rightarrow \dfrac{9}{2} ÷ \dfrac{13}{2}\\[1em] \Rightarrow \dfrac{9}{2} \times \dfrac{2}{13}\\[1em] \Rightarrow \dfrac{9 \times 2}{2 \times 13}\\[1em] \Rightarrow \dfrac{9}{13}.$

Hence, $4\dfrac{1}{2} ÷ 6\dfrac{1}{2} = \dfrac{9}{13}$.