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To solve the expression \(\frac{7}{13} \div \frac{5}{7}\), we will follow these steps:

1. **Rewrite the division as multiplication**:
   \[
   \frac{7}{13} \div \frac{5}{7} = \frac{7}{13} \times \frac{7}{5}
   \]

2. **Multiply the fractions**:
   \[
   \frac{7}{13} \times \frac{7}{5} = \frac{7 \times 7}{13 \times 5} = \frac{49}{65}
   \]

So, the value of \(\frac{7}{13} \div \frac{5}{7}\) is \(\frac{49}{65}\).

The correct answer is **d. \(\frac{49}{65}\)**.

Would you like more details or have any questions?

Here are some related questions to consider:
1. How do you multiply two fractions?
2. What is the reciprocal of a fraction?
3. How do you simplify a fraction after multiplying?
4. Can you divide fractions directly without converting to multiplication?
5. How do you convert a division problem into a multiplication problem?

**Tip**: When dividing fractions, remember to multiply by the reciprocal of the divisor.

Learn how to solve the division of fractions, specifically 7/13 ÷ 5/7, by converting the division to multiplication and applying the reciprocal rule. This guide is suitable for students in Grades 6-8.

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