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) \(9\frac{17}{24} - 8\frac{11}{36}\)

Решение:

1. \( 7\frac{5}{6} - 3\frac{2}{3} = (7-3) + (\frac{5}{6} - \frac{2}{3}) = 4 + \frac{5 - 2 \times 2}{6} = 4 + \frac{5-4}{6} = 4\frac{1}{6} \)


2. \( 8\frac{5}{12} - 6\frac{7}{20} = (8-6) + (\frac{5}{12} - \frac{7}{20}) = 2 + \frac{5 \times 5 - 7 \times 3}{60} = 2 + \frac{25-21}{60} = 2\frac{4}{60} = 2\frac{1}{15} \)


3. \( 11\frac{11}{12} - 5\frac{7}{9} = (11-5) + (\frac{11}{12} - \frac{7}{9}) = 6 + \frac{11 \times 3 - 7 \times 4}{36} = 6 + \frac{33-28}{36} = 6\frac{5}{36} \)


4. \( 9\frac{17}{24} - 8\frac{11}{36} = (9-8) + (\frac{17}{24} - \frac{11}{36}) = 1 + \frac{17 \times 3 - 11 \times 2}{72} = 1 + \frac{51-22}{72} = 1\frac{29}{72} \)