Проверочная работа № 2 2 Найдите сумму: a) \(\frac{1}{5} + \frac{2}{11} + \frac{4}{5} + \frac{7}{11}\); б) \(\frac{2}{3} + \frac{3}{18} + \frac{5}{6} + \frac{7}{18}\).

Решим примеры:

a) \(\frac{1}{5} + \frac{2}{11} + \frac{4}{5} + \frac{7}{11}\) = \((\frac{1}{5} + \frac{4}{5}) + (\frac{2}{11} + \frac{7}{11})\) = \(\frac{1 + 4}{5} + \frac{2 + 7}{11}\) = \(\frac{5}{5} + \frac{9}{11}\) = 1 + \(\frac{9}{11}\) = 1 \(\frac{9}{11}\)

б) \(\frac{2}{3} + \frac{3}{18} + \frac{5}{6} + \frac{7}{18}\) = \((\frac{2}{3} + \frac{5}{6}) + (\frac{3}{18} + \frac{7}{18})\) = \((\frac{2 \cdot 2}{3 \cdot 2} + \frac{5}{6}) + \frac{3 + 7}{18}\) = \((\frac{4}{6} + \frac{5}{6}) + \frac{10}{18}\) = \(\frac{4 + 5}{6} + \frac{5}{9}\) = \(\frac{9}{6} + \frac{5}{9}\) = \(\frac{3}{2} + \frac{5}{9}\) = \(\frac{3 \cdot 9}{2 \cdot 9} + \frac{5 \cdot 2}{9 \cdot 2}\) = \(\frac{27}{18} + \frac{10}{18}\) = \(\frac{27 + 10}{18}\) = \(\frac{37}{18}\) = 2 \(\frac{1}{18}\)

Ответ: a) 1 \(\frac{9}{11}\); б) 2 \(\frac{1}{18}\).