To divide two fractions, such as $\frac{3}{5} \div \frac{1}{6}$, you follow these steps:

1. Rewrite the division as multiplication by the reciprocal of the second fraction: $\frac{3}{5} \div \frac{1}{6} = \frac{3}{5} \times \frac{6}{1}$

2. Multiply the numerators and multiply the denominators: $\frac{3 \times 6}{5 \times 1} = \frac{18}{5}$

3. Since $\frac{18}{5}$ is already in its simplest form (no common factors between 18 and 5), we can leave it as an improper fraction, or convert it to a mixed number if preferred: $\frac{18}{5} = 3 \frac{3}{5}$

So, the answer is: $\frac{18}{5} \text{ or } 3 \frac{3}{5}$

Would you like more details, or have any questions?

Here are some related questions you might find helpful:

1. How do you multiply two fractions?
2. How do you convert an improper fraction to a mixed number?
3. Why do we multiply by the reciprocal when dividing fractions?
4. What are some methods for simplifying fractions?
5. How do you convert a mixed number back into an improper fraction?

Tip: When dividing fractions, remember to "flip" (take the reciprocal of) the second fraction and then multiply!