1 Выполните действия: a) 1\(\frac{2}{3}\) + 1\(\frac{1}{3}\) - 2\(\frac{1}{3}\); б) 2\(\frac{1}{6}\) + 3\(\frac{2}{3}\) + 4\(\frac{5}{6}\); в) 7\(\frac{5}{12}\) - 1\(\frac{5}{6}\) + \(\frac{3}{24}\); г) 9\(\frac{7}{18}\) - 6\(\frac{2}{36}\) + 11\(\frac{2}{9}\).

Решение:

1. 
   

   а)

   
   \(1\frac{2}{3} + 1\frac{1}{3} - 2\frac{1}{3} = \frac{5}{3} + \frac{4}{3} - \frac{7}{3} = \frac{5+4-7}{3} = \frac{2}{3}\)
   

   б)

   
   \(2\frac{1}{6} + 3\frac{2}{3} + 4\frac{5}{6} = 2\frac{1}{6} + 3\frac{4}{6} + 4\frac{5}{6} = (2+3+4) + (\frac{1}{6} + \frac{4}{6} + \frac{5}{6}) = 9 + \frac{1+4+5}{6} = 9 + \frac{10}{6} = 9 + 1\frac{4}{6} = 9 + 1\frac{2}{3} = 10\frac{2}{3}\)
   

   в)

   
   \(7\frac{5}{12} - 1\frac{5}{6} + \frac{3}{24} = 7\frac{10}{24} - 1\frac{20}{24} + \frac{3}{24} = \frac{178}{24} - \frac{44}{24} + \frac{3}{24} = \frac{178-44+3}{24} = \frac{137}{24} = 5\frac{17}{24}\)
   

   г)

   
   \(9\frac{7}{18} - 6\frac{2}{36} + 11\frac{2}{9} = 9\frac{14}{36} - 6\frac{2}{36} + 11\frac{8}{36} = (9-6+11) + (\frac{14}{36} - \frac{2}{36} + \frac{8}{36}) = 14 + \frac{14-2+8}{36} = 14 + \frac{20}{36} = 14 + \frac{5}{9} = 14\frac{5}{9}\)
   

Ответ: а) \(\frac{2}{3}\); б) \(10\frac{2}{3}\); в) \(5\frac{17}{24}\); г) \(14\frac{5}{9}\).