277. Вычислите значение выражения:

Решение:

1. \( 8\frac{9}{14} - 3\frac{3}{7} = \frac{8 · 14 + 9}{14} - \frac{3 · 7 + 3}{7} = \frac{112+9}{14} - \frac{21+3}{7} = \frac{121}{14} - \frac{24}{7} = \frac{121}{14} - \frac{24 · 2}{7 · 2} = \frac{121}{14} - \frac{48}{14} = \frac{73}{14} = 5\frac{3}{14} \)
2. \( 7\frac{5}{12} - 3\frac{7}{24} = \frac{7 · 12 + 5}{12} - \frac{3 · 24 + 7}{24} = \frac{84+5}{12} - \frac{72+7}{24} = \frac{89}{12} - \frac{79}{24} = \frac{89 · 2}{12 · 2} - \frac{79}{24} = \frac{178}{24} - \frac{79}{24} = \frac{99}{24} = \frac{33}{8} = 4\frac{1}{8} \)
3. \( 12\frac{11}{12} - 5\frac{13}{18} = \frac{12 · 12 + 11}{12} - \frac{5 · 18 + 13}{18} = \frac{144+11}{12} - \frac{90+13}{18} = \frac{155}{12} - \frac{103}{18} = \frac{155 · 3}{12 · 3} - \frac{103 · 2}{18 · 2} = \frac{465}{36} - \frac{206}{36} = \frac{259}{36} = 7\frac{7}{36} \)

Ответ: 1) \( 5\frac{3}{14} \); 2) \( 4\frac{1}{8} \); 3) \( 7\frac{7}{36} \).