To divide the mixed numbers $3 \frac{1}{5}$ by $5 \frac{2}{3}$, follow these steps:

Step 1: Convert the mixed numbers into improper fractions.

• $3 \frac{1}{5} = \frac{16}{5}$
• $5 \frac{2}{3} = \frac{17}{3}$

Step 2: Use the rule for dividing fractions:

$\frac{16}{5} \div \frac{17}{3} = \frac{16}{5} \times \frac{3}{17}$

Step 3: Multiply the numerators and the denominators:

$\frac{16 \times 3}{5 \times 17} = \frac{48}{85}$

Final Answer:

$\frac{48}{85}$

The result of $3 \frac{1}{5} \div 5 \frac{2}{3}$ is $\frac{48}{85}$.

Would you like more details on these steps or have any other questions?

Here are 5 related questions to explore:

1. How do you convert a mixed number into an improper fraction?
2. How do you multiply and divide fractions?
3. What are some applications of dividing fractions?
4. How would you simplify a fraction like $\frac{48}{85}$ if possible?
5. How do you add or subtract mixed numbers?

Tip: When dividing fractions, remember to multiply by the reciprocal of the second fraction.