2 Найдите сумму: а) \(\frac{1}{5} + \frac{2}{4} + \frac{4}{5} + \frac{7}{11}\); б) \(\frac{2}{3} + \frac{3}{18} + \frac{5}{6} + \frac{7}{18}\).

Найдем сумму дробей.

1. \(\frac{1}{5} + \frac{2}{4} + \frac{4}{5} + \frac{7}{11} = (\frac{1}{5} + \frac{4}{5}) + \frac{2}{4} + \frac{7}{11} = \frac{5}{5} + \frac{1}{2} + \frac{7}{11} = 1 + \frac{1}{2} + \frac{7}{11} = \frac{22}{22} + \frac{11}{22} + \frac{14}{22} = \frac{22 + 11 + 14}{22} = \frac{47}{22}\)
2. \(\frac{2}{3} + \frac{3}{18} + \frac{5}{6} + \frac{7}{18} = \frac{2}{3} + \frac{5}{6} + \frac{3}{18} + \frac{7}{18} = \frac{2 \cdot 2}{3 \cdot 2} + \frac{5}{6} + \frac{10}{18} = \frac{4}{6} + \frac{5}{6} + \frac{5}{9} = \frac{9}{6} + \frac{5}{9} = \frac{3}{2} + \frac{5}{9} = \frac{3 \cdot 9}{2 \cdot 9} + \frac{5 \cdot 2}{9 \cdot 2} = \frac{27}{18} + \frac{10}{18} = \frac{37}{18}\)

Ответ:

1. \(\frac{47}{22}\);
2. \(\frac{37}{18}\).