47. Calculate:

Решение:

1. \( \frac{2}{3} + \frac{5}{8} = \frac{2 \times 8}{3 \times 8} + \frac{5 \times 3}{8 \times 3} = \frac{16}{24} + \frac{15}{24} = \frac{16 + 15}{24} = \frac{31}{24} \)
2. \( \frac{7}{12} - \frac{3}{8} = \frac{7 \times 2}{12 \times 2} - \frac{3 \times 3}{8 \times 3} = \frac{14}{24} - \frac{9}{24} = \frac{14 - 9}{24} = \frac{5}{24} \)
3. \( \frac{11}{16} - \frac{5}{8} = \frac{11}{16} - \frac{5 \times 2}{8 \times 2} = \frac{11}{16} - \frac{10}{16} = \frac{11 - 10}{16} = \frac{1}{16} \)
4. \( \frac{6}{35} + \frac{3}{10} = \frac{6 \times 2}{35 \times 2} + \frac{3 \times 7}{10 \times 7} = \frac{12}{70} + \frac{21}{70} = \frac{12 + 21}{70} = \frac{33}{70} \)
5. \( \frac{8}{15} - \frac{4}{9} = \frac{8 \times 3}{15 \times 3} - \frac{4 \times 5}{9 \times 5} = \frac{24}{45} - \frac{20}{45} = \frac{24 - 20}{45} = \frac{4}{45} \)
6. \( \frac{4}{15} + \frac{7}{12} = \frac{4 \times 4}{15 \times 4} + \frac{7 \times 5}{12 \times 5} = \frac{16}{60} + \frac{35}{60} = \frac{16 + 35}{60} = \frac{51}{60} = \frac{17}{20} \)
7. \( \frac{11}{48} - \frac{5}{36} = \frac{11 \times 3}{48 \times 3} - \frac{5 \times 4}{36 \times 4} = \frac{33}{144} - \frac{20}{144} = \frac{33 - 20}{144} = \frac{13}{144} \)
8. \( \frac{4}{5} - \frac{2}{3} + \frac{4}{15} = \frac{4 \times 3}{5 \times 3} - \frac{2 \times 5}{3 \times 5} + \frac{4}{15} = \frac{12}{15} - \frac{10}{15} + \frac{4}{15} = \frac{12 - 10 + 4}{15} = \frac{6}{15} = \frac{2}{5} \)
9. \( \frac{7}{8} + \frac{11}{12} - \frac{5}{6} = \frac{7 \times 3}{8 \times 3} + \frac{11 \times 2}{12 \times 2} - \frac{5 \times 4}{6 \times 4} = \frac{21}{24} + \frac{22}{24} - \frac{20}{24} = \frac{21 + 22 - 20}{24} = \frac{23}{24} \)

Ответ: 1) \( \frac{31}{24} \); 2) \( \frac{5}{24} \); 3) \( \frac{1}{16} \); 4) \( \frac{33}{70} \); 5) \( \frac{4}{45} \); 6) \( \frac{17}{20} \); 7) \( \frac{13}{144} \); 8) \( \frac{2}{5} \); 9) \( \frac{23}{24} \).