1. Найдите значение выражения. a) 4 1/12 - 6,5; б) (-9 3/7) * (-1 10/11); 2. -2 2/9 + 0,9 * (-2 1/3); 3. -1,25 - (-5/12) : (1 1/3 * 2,5 - 7/8).

Решение:

1. а) \( 4\frac{1}{12} - 6,5 \)
   \( 4\frac{1}{12} - 6\frac{1}{2} = \frac{49}{12} - \frac{13}{2} = \frac{49 - 78}{12} = -\frac{29}{12} = -2\frac{5}{12} \)
2. б) \( \left( -9\frac{3}{7} \right) \cdot \left( -1\frac{10}{11} \right) \)
   \( -\frac{66}{7} \cdot \left( -\frac{21}{11} \right) = \frac{66}{7} \cdot \frac{21}{11} = \frac{(6 \cdot 11) \cdot (3 \cdot 7)}{7 \cdot 11} = 6 \cdot 3 = 18 \)
3. 2. \( -2\frac{2}{9} + 0,9 \cdot \left( -2\frac{1}{3} \right) \)
   \( -2\frac{2}{9} + \frac{9}{10} \cdot \left( -\frac{7}{3} \right) = -2\frac{2}{9} - \frac{9 \cdot 7}{10 \cdot 3} = -2\frac{2}{9} - \frac{(3 \cdot 3) \cdot 7}{10 \cdot 3} = -2\frac{2}{9} - \frac{21}{10} \)
   \( -\frac{20}{9} - \frac{21}{10} = \frac{-200 - 189}{90} = -\frac{389}{90} = -4\frac{29}{90} \)
4. 3. \( -1,25 - \left( -\frac{5}{12} \right) : \left( 1\frac{1}{3} \cdot 2,5 - \frac{7}{8} \right) \)
   \( -1,25 = -1\frac{1}{4} = -\frac{5}{4} \)
   \( 1\frac{1}{3} \cdot 2,5 = \frac{4}{3} \cdot \frac{5}{2} = \frac{20}{6} = \frac{10}{3} \)
   \( \frac{10}{3} - \frac{7}{8} = \frac{80 - 21}{24} = \frac{59}{24} \)
   \( -\frac{5}{4} - \left( -\frac{5}{12} \right) : \frac{59}{24} = -\frac{5}{4} + \frac{5}{12} \cdot \frac{24}{59} = -\frac{5}{4} + \frac{5 \cdot 24}{12 \cdot 59} = -\frac{5}{4} + \frac{5 \cdot 2}{59} = -\frac{5}{4} + \frac{10}{59} \)
   \( \frac{-5 \cdot 59 + 10 \cdot 4}{4 \cdot 59} = \frac{-295 + 40}{236} = -\frac{255}{236} = -1\frac{19}{236} \)

Ответ: а) -2 5/12; б) 18; 2) -4 29/90; 3) -1 19/236.