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} - \(\frac{2}{9}\) + \(\frac{5}{36}\).

1. \(\frac{5}{6} + \frac{2}{7}\)

   • НОК(6, 7) = 42
   • \(\frac{5}{6} + \frac{2}{7} = \frac{5 \cdot 7}{6 \cdot 7} + \frac{2 \cdot 6}{7 \cdot 6} = \frac{35}{42} + \frac{12}{42} = \frac{35+12}{42} = \frac{47}{42}\)

2. \(\frac{11}{25} - \frac{3}{10}\)

   • НОК(25, 10) = 50
   • \(\frac{11}{25} - \frac{3}{10} = \frac{11 \cdot 2}{25 \cdot 2} - \frac{3 \cdot 5}{10 \cdot 5} = \frac{22}{50} - \frac{15}{50} = \frac{22-15}{50} = \frac{7}{50}\)

3. \(\frac{15}{16} - \frac{3}{4}\)

   • НОК(16, 4) = 16
   • \(\frac{15}{16} - \frac{3}{4} = \frac{15}{16} - \frac{3 \cdot 4}{4 \cdot 4} = \frac{15}{16} - \frac{12}{16} = \frac{15-12}{16} = \frac{3}{16}\)

4. \(\frac{3}{20} + \frac{7}{15}\)

   • НОК(20, 15) = 60
   • \(\frac{3}{20} + \frac{7}{15} = \frac{3 \cdot 3}{20 \cdot 3} + \frac{7 \cdot 4}{15 \cdot 4} = \frac{9}{60} + \frac{28}{60} = \frac{9+28}{60} = \frac{37}{60}\)

5. \(\frac{13}{16} - \frac{7}{12}\)

   • НОК(16, 12) = 48
   • \(\frac{13}{16} - \frac{7}{12} = \frac{13 \cdot 3}{16 \cdot 3} - \frac{7 \cdot 4}{12 \cdot 4} = \frac{39}{48} - \frac{28}{48} = \frac{39-28}{48} = \frac{11}{48}\)

6. \(\frac{9}{14} + \frac{5}{21}\)

   • НОК(14, 21) = 42
   • \(\frac{9}{14} + \frac{5}{21} = \frac{9 \cdot 3}{14 \cdot 3} + \frac{5 \cdot 2}{21 \cdot 2} = \frac{27}{42} + \frac{10}{42} = \frac{27+10}{42} = \frac{37}{42}\)

7. \(\frac{16}{35} - \frac{5}{14}\)

   • НОК(35, 14) = 70
   • \(\frac{16}{35} - \frac{5}{14} = \frac{16 \cdot 2}{35 \cdot 2} - \frac{5 \cdot 5}{14 \cdot 5} = \frac{32}{70} - \frac{25}{70} = \frac{32-25}{70} = \frac{7}{70} = \frac{1}{10}\)

8. \(\frac{2}{5} + \frac{1}{3} - \frac{7}{30}\)

   • НОК(5, 3, 30) = 30
   • \(\frac{2}{5} + \frac{1}{3} - \frac{7}{30} = \frac{2 \cdot 6}{5 \cdot 6} + \frac{1 \cdot 10}{3 \cdot 10} - \frac{7}{30} = \frac{12}{30} + \frac{10}{30} - \frac{7}{30} = \frac{12+10-7}{30} = \frac{15}{30} = \frac{1}{2}\)

9. \(\frac{3}{4} - \frac{2}{9} + \frac{5}{36}\)

   • НОК(4, 9, 36) = 36
   • \(\frac{3}{4} - \frac{2}{9} + \frac{5}{36} = \frac{3 \cdot 9}{4 \cdot 9} - \frac{2 \cdot 4}{9 \cdot 4} + \frac{5}{36} = \frac{27}{36} - \frac{8}{36} + \frac{5}{36} = \frac{27-8+5}{36} = \frac{24}{36} = \frac{2}{3}\)

Ответ: 1) \(\frac{47}{42}\); 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) \(\frac{1}{2}\); 9) \(\frac{2}{3}\).