Divide:

$1 ÷ 2\dfrac{3}{5}$

$\Rightarrow 1 ÷ 2\dfrac{3}{5}\\[1em] \Rightarrow 1 ÷ \dfrac{13}{5}\\[1em] \Rightarrow 1 \times \dfrac{5}{13}\\[1em] \Rightarrow \dfrac{5}{13}.$

Hence, $1 ÷ 2\dfrac{3}{5} = \dfrac{5}{13}$.