51. Найдите разность: 1) \(7\frac{5}{6} - 3\frac{2}{3};\) 2) \(8\frac{5}{12} - 6\frac{7}{20};\) 3) \(11\frac{11}{12} - 5\frac{7}{9};\) 4) \(9\frac{17}{24} - 8\frac{11}{36}.\)

Выполним вычисления:

1. \(7\frac{5}{6} - 3\frac{2}{3} = 7 - 3 + \frac{5}{6} - \frac{2}{3} = 4 + \frac{5}{6} - \frac{2 \cdot 2}{3 \cdot 2} = 4 + \frac{5}{6} - \frac{4}{6} = 4 + \frac{5 - 4}{6} = 4 + \frac{1}{6} = 4\frac{1}{6}\)
2. \(8\frac{5}{12} - 6\frac{7}{20} = 8 - 6 + \frac{5}{12} - \frac{7}{20} = 2 + \frac{5 \cdot 5}{12 \cdot 5} - \frac{7 \cdot 3}{20 \cdot 3} = 2 + \frac{25}{60} - \frac{21}{60} = 2 + \frac{25 - 21}{60} = 2 + \frac{4}{60} = 2 + \frac{1}{15} = 2\frac{1}{15}\)
3. \(11\frac{11}{12} - 5\frac{7}{9} = 11 - 5 + \frac{11}{12} - \frac{7}{9} = 6 + \frac{11 \cdot 3}{12 \cdot 3} - \frac{7 \cdot 4}{9 \cdot 4} = 6 + \frac{33}{36} - \frac{28}{36} = 6 + \frac{33 - 28}{36} = 6 + \frac{5}{36} = 6\frac{5}{36}\)
4. \(9\frac{17}{24} - 8\frac{11}{36} = 9 - 8 + \frac{17}{24} - \frac{11}{36} = 1 + \frac{17 \cdot 3}{24 \cdot 3} - \frac{11 \cdot 2}{36 \cdot 2} = 1 + \frac{51}{72} - \frac{22}{72} = 1 + \frac{51 - 22}{72} = 1 + \frac{29}{72} = 1\frac{29}{72}\)

Ответ: 1) \(4\frac{1}{6}\); 2) \(2\frac{1}{15}\); 3) \(6\frac{5}{36}\); 4) \(1\frac{29}{72}\)