Understanding the Problem
To solve the problem, we need to divide the sum of two fractions, \( \frac{1}{5} \) and \( \frac{6}{5} \), by their product.
Step 1: Calculate the Sum
- First, we find the sum of the two fractions:
\[
\text{Sum} = \frac{1}{5} + \frac{6}{5}
\]
- Since both fractions have the same denominator, we can directly add the numerators:
\[
\text{Sum} = \frac{1 + 6}{5} = \frac{7}{5}
\]
Step 2: Calculate the Product
- Next, we find the product of the two fractions:
\[
\text{Product} = \frac{1}{5} \times \frac{6}{5}
\]
- To multiply fractions, we multiply the numerators and the denominators:
\[
\text{Product} = \frac{1 \times 6}{5 \times 5} = \frac{6}{25}
\]
Step 3: Divide the Sum by the Product
- Now, we divide the sum by the product:
\[
\text{Result} = \frac{\frac{7}{5}}{\frac{6}{25}}
\]
- Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\text{Result} = \frac{7}{5} \times \frac{25}{6}
\]
- Carrying out the multiplication:
\[
\text{Result} = \frac{7 \times 25}{5 \times 6} = \frac{175}{30}
\]
- Simplifying \( \frac{175}{30} \):
- Divide both numerator and denominator by 5:
\[
\text{Result} = \frac{35}{6}
\]
Final Answer
Thus, the result of dividing the sum of \( \frac{1}{5} \) and \( \frac{6}{5} \) by their product is \( \frac{35}{6} \).