Проверочная работа № 3 2 Найдите значение выражения: a) \(\frac{3}{14} + (\frac{2}{7} + \frac{1}{2});\) б) \(\frac{11}{56} + (\frac{6}{7} - \frac{3}{8});\) в) \((\frac{5}{8} + \frac{1}{6}) - \frac{7}{24};\) г) \(\frac{15}{36} - (\frac{1}{3} - \frac{1}{12}).\)

Решим примеры:

a) \(\frac{3}{14} + (\frac{2}{7} + \frac{1}{2})\) = \(\frac{3}{14} + (\frac{2 \cdot 2}{7 \cdot 2} + \frac{1 \cdot 7}{2 \cdot 7})\) = \(\frac{3}{14} + (\frac{4}{14} + \frac{7}{14})\) = \(\frac{3}{14} + \frac{4 + 7}{14}\) = \(\frac{3}{14} + \frac{11}{14}\) = \(\frac{3 + 11}{14}\) = \(\frac{14}{14}\) = 1

б) \(\frac{11}{56} + (\frac{6}{7} - \frac{3}{8})\) = \(\frac{11}{56} + (\frac{6 \cdot 8}{7 \cdot 8} - \frac{3 \cdot 7}{8 \cdot 7})\) = \(\frac{11}{56} + (\frac{48}{56} - \frac{21}{56})\) = \(\frac{11}{56} + \frac{48 - 21}{56}\) = \(\frac{11}{56} + \frac{27}{56}\) = \(\frac{11 + 27}{56}\) = \(\frac{38}{56}\) = \(\frac{19}{28}\)

в) \((\frac{5}{8} + \frac{1}{6}) - \frac{7}{24}\) = \((\frac{5 \cdot 3}{8 \cdot 3} + \frac{1 \cdot 4}{6 \cdot 4}) - \frac{7}{24}\) = \((\frac{15}{24} + \frac{4}{24}) - \frac{7}{24}\) = \(\frac{15 + 4}{24} - \frac{7}{24}\) = \(\frac{19}{24} - \frac{7}{24}\) = \(\frac{19 - 7}{24}\) = \(\frac{12}{24}\) = \(\frac{1}{2}\)

г) \(\frac{15}{36} - (\frac{1}{3} - \frac{1}{12})\) = \(\frac{15}{36} - (\frac{1 \cdot 4}{3 \cdot 4} - \frac{1}{12})\) = \(\frac{15}{36} - (\frac{4}{12} - \frac{1}{12})\) = \(\frac{15}{36} - \frac{4 - 1}{12}\) = \(\frac{15}{36} - \frac{3}{12}\) = \(\frac{15}{36} - \frac{3 \cdot 3}{12 \cdot 3}\) = \(\frac{15}{36} - \frac{9}{36}\) = \(\frac{15 - 9}{36}\) = \(\frac{6}{36}\) = \(\frac{1}{6}\)

Ответ: a) 1; б) \(\frac{19}{28}\); в) \(\frac{1}{2}\); г) \(\frac{1}{6}\).