The product of two fractions is `(11)/(5)`. If one of the fractions is `(3)/(5)`, then find the sum of the two fractions.

Options

A. `4(4)/(15)`
B. `(16)/(25)`
C. `(6)/(25)`
D. `3(4)/(15)`

Answer

To solve the problem step by step, we will follow these instructions:

1. **Identify the given information**: We know that the product of two fractions is \( \frac{11}{5} \) and one of the fractions is \( \frac{3}{5} \).

2. **Let the unknown fraction be \( x \)**: We can represent the unknown fraction as \( x \).

3. **Set up the equation for the product of the fractions**:
\[ x \cdot \frac{3}{5} = \frac{11}{5} \]

4. **Solve for \( x \)**: To find \( x \), we can multiply both sides of the equation by \( \frac{5}{3} \) to isolate \( x \):
\[ x = \frac{11}{5} \cdot \frac{5}{3} \]
Simplifying this gives:
\[ x = \frac{11 \cdot 5}{5 \cdot 3} = \frac{11}{3} \]

5. **Now we have both fractions**: The two fractions are \( \frac{3}{5} \) and \( \frac{11}{3} \).

6. **Find the sum of the two fractions**: To add \( \frac{3}{5} \) and \( \frac{11}{3} \), we need a common denominator. The least common multiple (LCM) of 5 and 3 is 15.

7. **Convert each fraction to have the common denominator**:
\[ \frac{3}{5} = \frac{3 \cdot 3}{5 \cdot 3} = \frac{9}{15} \]
\[ \frac{11}{3} = \frac{11 \cdot 5}{3 \cdot 5} = \frac{55}{15} \]

8. **Add the two fractions**:
\[ \frac{9}{15} + \frac{55}{15} = \frac{9 + 55}{15} = \frac{64}{15} \]

9. **Final answer**: The sum of the two fractions is \( \frac{64}{15} \).