1. **State the problem:** We need to find the sum of the fractions $\frac{3}{5} + \frac{9}{10} + \frac{13}{15}$.\n\n2. **Find a common denominator:** The denominators are 5, 10, and 15. The least common multiple (LCM) of these is 30.\n\n3. **Convert each fraction to have denominator 30:**\n$$\frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30}$$\n$$\frac{9}{10} = \frac{9 \times 3}{10 \times 3} = \frac{27}{30}$$\n$$\frac{13}{15} = \frac{13 \times 2}{15 \times 2} = \frac{26}{30}$$\n\n4. **Add the fractions:**\n$$\frac{18}{30} + \frac{27}{30} + \frac{26}{30} = \frac{18 + 27 + 26}{30} = \frac{71}{30}$$\n\n5. **Simplify if possible:** 71 and 30 have no common factors other than 1, so the fraction is already in simplest form.\n\n6. **Convert to mixed number (optional):**\n$$\frac{71}{30} = 2 \frac{11}{30}$$\n\n**Final answer:** $\frac{71}{30}$ or $2 \frac{11}{30}$.