47. Вычислите: 1) \(\frac{5}{6} + \frac{2}{7}\); 2) \(\frac{11}{25} - \frac{3}{10}\); 3) \(\frac{15}{16} - \frac{3}{4}\); 4) \(\frac{3}{20} + \frac{7}{15}\); 5) \(\frac{13}{16} - \frac{7}{12}\); 6) \(\frac{9}{14} + \frac{5}{21}\); 7) \(\frac{16}{35} - \frac{5}{14}\); 8) \(\frac{2}{5} - \frac{1}{3} - \frac{7}{30}\); 9) \(\frac{3}{4} - \frac{2}{9} + \frac{5}{36}\)

Решение:

1. \( \frac{5}{6} + \frac{2}{7} = \frac{5 \cdot 7 + 2 \cdot 6}{42} = \frac{35 + 12}{42} = \frac{47}{42} = 1\frac{5}{42} \)
2. \( \frac{11}{25} - \frac{3}{10} = \frac{11 \cdot 2 - 3 \cdot 5}{50} = \frac{22 - 15}{50} = \frac{7}{50} \)
3. \( \frac{15}{16} - \frac{3}{4} = \frac{15 - 3 \cdot 4}{16} = \frac{15 - 12}{16} = \frac{3}{16} \)
4. \( \frac{3}{20} + \frac{7}{15} = \frac{3 \cdot 3 + 7 \cdot 4}{60} = \frac{9 + 28}{60} = \frac{37}{60} \)
5. \( \frac{13}{16} - \frac{7}{12} = \frac{13 \cdot 3 - 7 \cdot 4}{48} = \frac{39 - 28}{48} = \frac{11}{48} \)
6. \( \frac{9}{14} + \frac{5}{21} = \frac{9 \cdot 3 + 5 \cdot 2}{42} = \frac{27 + 10}{42} = \frac{37}{42} \)
7. \( \frac{16}{35} - \frac{5}{14} = \frac{16 \cdot 2 - 5 \cdot 5}{70} = \frac{32 - 25}{70} = \frac{7}{70} = \frac{1}{10} \)
8. \( \frac{2}{5} - \frac{1}{3} - \frac{7}{30} = \frac{2 \cdot 6 - 1 \cdot 10 - 7}{30} = \frac{12 - 10 - 7}{30} = \frac{-5}{30} = -\frac{1}{6} \)
9. \( \frac{3}{4} - \frac{2}{9} + \frac{5}{36} = \frac{3 \cdot 9 - 2 \cdot 4 + 5}{36} = \frac{27 - 8 + 5}{36} = \frac{24}{36} = \frac{2}{3} \)

Ответ: 1) \(1\frac{5}{42}\); 2) \(\frac{7}{50}\); 3) \(\frac{3}{16}\); 4) \(\frac{37}{60}\); 5) \(\frac{11}{48}\); 6) \(\frac{37}{42}\); 7) \(\frac{1}{10}\); 8) \(-\frac{1}{6}\); 9) \(\frac{2}{3}\).