Divide :

$8\dfrac{1}{21}$ ÷ $1\dfrac{6}{7}$

We have:

$\begin{array}{ll} \phantom{=} 8\dfrac{1}{21} ÷ 1\dfrac{6}{7} \\ = \dfrac{169}{21} ÷ \dfrac{13}{7} & \text{[Converting mixed to improper fraction]} \\ = \dfrac{169}{21} \times \dfrac{7}{13} & [\text{Reciprocal of } \dfrac{13}{7} \text{ is} \dfrac{7}{13}] \\ = \dfrac{13}{21} \times \dfrac{7}{1} & \text{[Simplifying 169 and 13 ⇒ Divide by 13]} \\ = \dfrac{13}{3} \times \dfrac{1}{1} & \text{[Simplifying 7 and 21 ⇒ Divide by 7]} \\ = \dfrac{13 \times 1}{3 \times 1} \\ = \dfrac{13}{3} \\ = 4\dfrac{1}{3} \end{array}$

∴ The answer is $4\dfrac{1}{3}$