Perform the following fraction additions and simplify the results where possible.

Решение:

1. \(\frac{1}{2} + \frac{2}{3} = \frac{1 \times 3}{2 \times 3} + \frac{2 \times 2}{3 \times 2} = \frac{3}{6} + \frac{4}{6} = \frac{3+4}{6} = \frac{7}{6}\)
2. \(\frac{7}{8} + \frac{3}{5} = \frac{7 \times 5}{8 \times 5} + \frac{3 \times 8}{5 \times 8} = \frac{35}{40} + \frac{24}{40} = \frac{35+24}{40} = \frac{59}{40}\)
3. \(\frac{6}{7} + \frac{5}{11} = \frac{6 \times 11}{7 \times 11} + \frac{5 \times 7}{11 \times 7} = \frac{66}{77} + \frac{35}{77} = \frac{66+35}{77} = \frac{101}{77}\)
4. \(\frac{14}{15} + \frac{11}{12} = \frac{14 \times 4}{15 \times 4} + \frac{11 \times 5}{12 \times 5} = \frac{56}{60} + \frac{55}{60} = \frac{56+55}{60} = \frac{111}{60}\)

Ответ: 1. \(\frac{7}{6}\); 2. \(\frac{59}{40}\); 3. \(\frac{101}{77}\); 4. \(\frac{111}{60}\).