86. Выполните действие: a) \(4\frac{5}{6} + 2\frac{3}{8}\); \(\text{ б)}\) 7\(\frac{5}{18}\) - 1\(\frac{7}{12}\)\); \(\text{ в)}\) 3\(\frac{4}{9}\) + 2\(\frac{2}{7}\)\); \(\text{ г)}\) 5\(\frac{3}{14}\) - 1\(\frac{1}{21}\).

Решение:

1. а) \( 4\frac{5}{6} + 2\frac{3}{8} = \frac{29}{6} + \frac{19}{8} = \frac{29 \cdot 4}{24} + \frac{19 \cdot 3}{24} = \frac{116 + 57}{24} = \frac{173}{24} = 7\frac{5}{24} \)
2. б) \( 7\frac{5}{18} - 1\frac{7}{12} = \frac{131}{18} - \frac{19}{12} = \frac{131 \cdot 2}{36} - \frac{19 \cdot 3}{36} = \frac{262 - 57}{36} = \frac{205}{36} = 5\frac{25}{36} \)
3. в) \( 3\frac{4}{9} + 2\frac{2}{7} = \frac{31}{9} + \frac{16}{7} = \frac{31 \cdot 7}{63} + \frac{16 \cdot 9}{63} = \frac{217 + 144}{63} = \frac{361}{63} = 5\frac{46}{63} \)
4. г) \( 5\frac{3}{14} - 1\frac{1}{21} = \frac{73}{14} - \frac{22}{21} = \frac{73 \cdot 3}{42} - \frac{22 \cdot 2}{42} = \frac{219 - 44}{42} = \frac{175}{42} = \frac{25}{6} = 4\frac{1}{6} \)

Ответ: а) \(7\frac{5}{24}\); б) \(5\frac{25}{36}\); в) \(5\frac{46}{63}\); г) \(4\frac{1}{6}\).