Divide :

$3\dfrac{11}{15}$ ÷ $19\dfrac{3}{5}$

We have:

$\begin{array}{ll} \phantom{=} 3\dfrac{11}{15} ÷ 19\dfrac{3}{5} \\ = \dfrac{56}{15} ÷ \dfrac{98}{5} & \text{[Converting mixed to improper fraction]} \\ = \dfrac{56}{15} \times \dfrac{5}{98} & [\text{Reciprocal of } \dfrac{98}{5} \text{ is } \dfrac{5}{98}] \\ = \dfrac{56}{3} \times \dfrac{1}{98} & \text{[Simplifying 5 and 15 ⇒ Divide by 5]} \\ = \dfrac{4}{3} \times \dfrac{1}{7} & \text{[Simplifying 56 and 98 ⇒ Divide by 14]} \\ = \dfrac{4 \times 1}{3 \times 7} \\ = \dfrac{4}{21} \end{array}$

∴ The answer is $\dfrac{4}{21}$