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.

Learn how to divide mixed numbers like 3 1/5 by 5 2/3 with a step-by-step solution. This problem covers essential arithmetic concepts, including converting mixed numbers to improper fractions and dividing fractions using the reciprocal rule. Suitable for students in Grades 5-7.

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