3. Выполните действия: a) \(7\frac{5}{12} + 4\frac{3}{8}\) б) \(3\frac{3}{20} + 2\frac{19}{30}\) в) \(9\frac{5}{6} - 2\frac{3}{4}\) г) \(3\frac{3}{10} - 1\frac{7}{15}\)

Решение:

1. а) \( 7\frac{5}{12} + 4\frac{3}{8} = (7+4) + (\frac{5}{12} + \frac{3}{8}) = 11 + \frac{5 \cdot 2 + 3 \cdot 3}{24} = 11 + \frac{10+9}{24} = 11\frac{19}{24} \)
2. б) \( 3\frac{3}{20} + 2\frac{19}{30} = (3+2) + (\frac{3}{20} + \frac{19}{30}) = 5 + \frac{3 \cdot 3 + 19 \cdot 2}{60} = 5 + \frac{9+38}{60} = 5\frac{47}{60} \)
3. в) \( 9\frac{5}{6} - 2\frac{3}{4} = (9-2) + (\frac{5}{6} - \frac{3}{4}) = 7 + \frac{5 \cdot 2 - 3 \cdot 3}{12} = 7 + \frac{10-9}{12} = 7\frac{1}{12} \)
4. г) \( 3\frac{3}{10} - 1\frac{7}{15} = (3-1) + (\frac{3}{10} - \frac{7}{15}) = 2 + \frac{3 \cdot 3 - 7 \cdot 2}{30} = 2 + \frac{9-14}{30} = 2 - \frac{5}{30} = 2 - \frac{1}{6} = 1\frac{5}{6} \)

Ответ: а) \(11\frac{19}{24}\); б) \(5\frac{47}{60}\); в) \(7\frac{1}{12}\); г) \(1\frac{5}{6}\).