To divide fractions, we follow these steps:

1. **Convert mixed numbers to improper fractions**:
   - \( 5 \frac{3}{5} \) becomes \( \frac{28}{5} \) (since \( 5 \times 5 + 3 = 28 \)).
   - \( 3 \frac{1}{2} \) becomes \( \frac{7}{2} \) (since \( 3 \times 2 + 1 = 7 \)).

2. **Apply the division rule for fractions**:  
   \[
   \frac{28}{5} \div \frac{7}{2} = \frac{28}{5} \times \frac{2}{7}
   \]
   (We multiply by the reciprocal of the second fraction).

3. **Multiply the numerators and denominators**:
   \[
   \frac{28 \times 2}{5 \times 7} = \frac{56}{35}
   \]

4. **Simplify the fraction**:
   \[
   \frac{56}{35} = \frac{8}{5}
   \]

The result is **\( \frac{8}{5} \)** or \( 1 \frac{3}{5} \) in mixed number form.

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. How do you multiply mixed numbers directly?
2. What is the process for converting an improper fraction back to a mixed number?
3. How do you simplify complex fractions?
4. What happens when you divide by a whole number instead of a fraction?
5. How do you add and subtract mixed numbers?

**Tip:** Always simplify your fractions at the end for a clean result!

Learn how to divide mixed numbers such as 5 3/5 by 3 1/2 with this easy-to-follow guide. This solution breaks down the conversion of mixed numbers to improper fractions and applies the rule of dividing fractions. Perfect for students in Grades 5-6 learning about fractions and mixed numbers.

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