83. Выполните действие: a) 4+3; 6) 8-70; B)2+6; г) 213-120.

Решение:

а) \(4 \frac{1}{6} + 3 \frac{2}{5} = \frac{25}{6} + \frac{17}{5} = \frac{25 \cdot 5 + 17 \cdot 6}{30} = \frac{125 + 102}{30} = \frac{227}{30} = 7 \frac{17}{30}\) б) \(8 \frac{3}{4} - 7 \frac{5}{6} = \frac{35}{4} - \frac{47}{6} = \frac{35 \cdot 3 - 47 \cdot 2}{12} = \frac{105 - 94}{12} = \frac{11}{12}\) в) \(2 \frac{11}{12} + 6 \frac{5}{8} = \frac{35}{12} + \frac{53}{8} = \frac{35 \cdot 2 + 53 \cdot 3}{24} = \frac{70 + 159}{24} = \frac{229}{24} = 9 \frac{13}{24}\) г) \(2 \frac{13}{14} - 1 \frac{20}{21} = \frac{41}{14} - \frac{41}{21} = 41 \cdot (\frac{1}{14} - \frac{1}{21}) = 41 \cdot \frac{3-2}{42} = 41 \cdot \frac{1}{42} = \frac{41}{42}\)

Ответ: а) \(7 \frac{17}{30}\); б) \(\frac{11}{12}\); в) \(9 \frac{13}{24}\); г) \(\frac{41}{42}\)

Ответ: а) \(7 \frac{17}{30}\); б) \(\frac{11}{12}\); в) \(9 \frac{13}{24}\); г) \(\frac{41}{42}\)