2. Найдите значение выражения: а) \(7\frac{15}{16} + 2\frac{11}{24}\); б) \(7\frac{11}{12} : 3\frac{1}{6}\); в) \(1\frac{5}{19} \cdot (6 - 3\frac{5}{18})\);

2. Найдите значение выражения:

1. а) \(7\frac{15}{16} + 2\frac{11}{24} = 7\frac{15 \cdot 3}{16 \cdot 3} + 2\frac{11 \cdot 2}{24 \cdot 2} = 7\frac{45}{48} + 2\frac{22}{48} = 9\frac{67}{48} = 9 + \frac{48}{48} + \frac{19}{48} = 10\frac{19}{48}\)
2. б) \(7\frac{11}{12} : 3\frac{1}{6} = \frac{7 \cdot 12 + 11}{12} : \frac{3 \cdot 6 + 1}{6} = \frac{84 + 11}{12} : \frac{18 + 1}{6} = \frac{95}{12} : \frac{19}{6} = \frac{95}{12} \cdot \frac{6}{19} = \frac{5 \cdot 19 \cdot 6}{6 \cdot 2 \cdot 19} = \frac{5}{2} = 2\frac{1}{2}\)
3. в) \(1\frac{5}{19} \cdot (6 - 3\frac{5}{18}) = \frac{1 \cdot 19 + 5}{19} \cdot (6 - \frac{3 \cdot 18 + 5}{18}) = \frac{24}{19} \cdot (6 - \frac{54 + 5}{18}) = \frac{24}{19} \cdot (6 - \frac{59}{18}) = \frac{24}{19} \cdot (\frac{6 \cdot 18}{18} - \frac{59}{18}) = \frac{24}{19} \cdot (\frac{108}{18} - \frac{59}{18}) = \frac{24}{19} \cdot \frac{49}{18} = \frac{12 \cdot 2 \cdot 49}{19 \cdot 9 \cdot 2} = \frac{12 \cdot 49}{19 \cdot 9} = \frac{4 \cdot 3 \cdot 49}{19 \cdot 3 \cdot 3} = \frac{4 \cdot 49}{19 \cdot 3} = \frac{196}{57} = 3\frac{25}{57}\)

Ответ: а) \(10\frac{19}{48}\); б) \(2\frac{1}{2}\); в) \(3\frac{25}{57}\)