Understanding the Problem
To solve the problem, we need to find the sum of two fractions, \( \frac{1}{5} \) and \( \frac{6}{5} \), and then divide this sum by their product.
Step 1: Calculate the Sum
- Sum of the fractions:
- \( \frac{1}{5} + \frac{6}{5} = \frac{1 + 6}{5} = \frac{7}{5} \)
Step 2: Calculate the Product
- Product of the fractions:
- \( \frac{1}{5} \times \frac{6}{5} = \frac{1 \times 6}{5 \times 5} = \frac{6}{25} \)
Step 3: Divide the Sum by the Product
- Division of the sum by the product:
- To divide by a fraction, you multiply by its reciprocal.
- Thus, \( \text{Division} = \frac{7}{5} \div \frac{6}{25} = \frac{7}{5} \times \frac{25}{6} \)
Step 4: Simplify the Expression
- Cancelling common factors:
- Multiply: \( \frac{7 \times 25}{5 \times 6} \)
- Simplifying \( \frac{25}{5} = 5 \):
- This results in \( \frac{7 \times 5}{6} = \frac{35}{6} \)
Final Result
- The final answer is:
- \( \frac{35}{6} \)
This concludes the solution, showing how to find the sum of two fractions and dividing it by their product while simplifying the calculations along the way.