Divide :

$\dfrac{13}{46}$ ÷ $2\dfrac{1}{11}$

We have:

$\begin{array}{ll} \phantom{=} \dfrac{13}{46} ÷ 2\dfrac{1}{11} \\ = \dfrac{13}{46} ÷ \dfrac{23}{11} & \text{[Converting mixed to improper fraction]} \\ = \dfrac{13}{46} \times \dfrac{11}{23} & [\text{Reciprocal of } \dfrac{23}{11} \text{ is } \dfrac{11}{23}] \\ = \dfrac{13 \times 11}{46 \times 23} \\ = \dfrac{143}{1058} \end{array}$

∴ The answer is $\dfrac{143}{1058}$