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

Решение:

a)
\( 1\frac{2}{3} + 3\frac{1}{3} - 2\frac{1}{3} = \frac{5}{3} + \frac{10}{3} - \frac{7}{3} = \frac{5+10-7}{3} = \frac{8}{3} = 2\frac{2}{3} \)

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

в)
\( 7\frac{5}{12} - 1\frac{5}{6} + 3\frac{1}{24} = 7\frac{10}{24} - 1\frac{20}{24} + 3\frac{1}{24} = (7-1+3) + \frac{10-20+1}{24} = 9 + \frac{-9}{24} = 9 - \frac{9}{24} = 9 - \frac{3}{8} = 8\frac{5}{8} \)

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

Ответ: а) \(2\frac{2}{3}\); б) \(10\frac{2}{3}\); в) \(8\frac{5}{8}\); г) \(14\frac{5}{9}\).