1. **Stating the problem:** We need to find the sum of the fractions $\frac{3}{25} + \frac{1}{2} + \frac{7}{10} + \frac{3}{5} + \frac{11}{50}$.\n\n2. **Find a common denominator:** The denominators are 25, 2, 10, 5, and 50. The least common denominator (LCD) is 50 because 50 is the smallest number divisible by all these denominators.\n\n3. **Convert each fraction to have denominator 50:**\n$\frac{3}{25} = \frac{3 \times 2}{25 \times 2} = \frac{6}{50}$\n$\frac{1}{2} = \frac{1 \times 25}{2 \times 25} = \frac{25}{50}$\n$\frac{7}{10} = \frac{7 \times 5}{10 \times 5} = \frac{35}{50}$\n$\frac{3}{5} = \frac{3 \times 10}{5 \times 10} = \frac{30}{50}$\n$\frac{11}{50}$ stays the same.\n\n4. **Add the numerators:**\n$$\frac{6}{50} + \frac{25}{50} + \frac{35}{50} + \frac{30}{50} + \frac{11}{50} = \frac{6 + 25 + 35 + 30 + 11}{50} = \frac{107}{50}$$\n\n5. **Simplify the fraction if possible:** 107 and 50 have no common factors other than 1, so the fraction is already in simplest form.\n\n6. **Convert to mixed number:**\n$$\frac{107}{50} = 2 \frac{7}{50}$$\n\n**Final answer:** $2 \frac{7}{50}$ or as an improper fraction $\frac{107}{50}$.