51. Найдите разность:

Решение:

1. \( 7\frac{5}{6} - 3\frac{2}{3} = \frac{7 \cdot 6 + 5}{6} - \frac{3 \cdot 3 + 2}{3} = \frac{47}{6} - \frac{11}{3} = \frac{47}{6} - \frac{11 \cdot 2}{6} = \frac{47 - 22}{6} = \frac{25}{6} = 4\frac{1}{6} \)
2. \( 8\frac{5}{12} - 6\frac{7}{20} = \frac{8 \cdot 12 + 5}{12} - \frac{6 \cdot 20 + 7}{20} = \frac{101}{12} - \frac{127}{20} = \frac{101 \cdot 5}{60} - \frac{127 \cdot 3}{60} = \frac{505 - 381}{60} = \frac{124}{60} = \frac{31}{15} = 2\frac{1}{15} \)
3. \( 11\frac{11}{12} - 5\frac{7}{9} = \frac{11 \cdot 12 + 11}{12} - \frac{5 \cdot 9 + 7}{9} = \frac{132 + 11}{12} - \frac{45 + 7}{9} = \frac{143}{12} - \frac{52}{9} = \frac{143 \cdot 3}{36} - \frac{52 \cdot 4}{36} = \frac{429 - 208}{36} = \frac{221}{36} = 6\frac{5}{36} \)
4. \( 9\frac{17}{24} - 8\frac{11}{36} = \frac{9 \cdot 24 + 17}{24} - \frac{8 \cdot 36 + 11}{36} = \frac{216 + 17}{24} - \frac{288 + 11}{36} = \frac{233}{24} - \frac{299}{36} = \frac{233 \cdot 3}{72} - \frac{299 \cdot 2}{72} = \frac{699 - 598}{72} = \frac{101}{72} = 1\frac{29}{72} \)

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