Simplify 6 1/3 ÷ 2 1/7

$$6 \frac{1}{3} = \frac{(6 \times 3) + 1}{3} = \frac{18 + 1}{3} = \frac{19}{3}$$ $$2 \frac{5}{6} = \frac{(2 \times 6) + 5}{6} = \frac{12 + 5}{6} = \frac{17}{6}$$

$$\frac{19}{3} \div \frac{17}{6} = \frac{19}{3} \times \frac{6}{17}$$ $$= \frac{19 \times 6}{3 \times 17} = \frac{19 \times (3 \times 2)}{3 \times 17}$$

Cancel out the common factor of 3:

$$= \frac{19 \times 2}{17} = \frac{38}{17}$$

The expression now becomes:

$$\frac{\frac{33}{7}}{\frac{38}{17}} = \frac{33}{7} \div \frac{38}{17}$$

To divide by a fraction, multiply by its reciprocal:

$$= \frac{33}{7} \times \frac{17}{38}$$

$$= \frac{33 \times 17}{7 \times 38} = \frac{561}{266}$$

The fraction $\frac{561}{266}$ cannot be simplified further as there are no common factors between the numerator and the denominator.