47. Вычислите: 1) 2/3 + 5/8; 2) 7/12 - 3/8; 3) 11/16 - 5/8; 4) 6/35 + 3/10; 5) 8/15 - 4/9; 6) 4/15 + 7/12; 7) 11/48 - 5/36; 8) 4/5 - 2/3 + 4/15; 9) 7/8 + 11/12 - 5/6

Решение:

1. 
   

   1)
   \[ \frac{2}{3} + \frac{5}{8} = \frac{2 \times 8}{3 \times 8} + \frac{5 \times 3}{8 \times 3} = \frac{16}{24} + \frac{15}{24} = \frac{16 + 15}{24} = \frac{31}{24} = 1\frac{7}{24} \]

   
   
2. 
   

   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. 
   

   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. 
   

   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. 
   

   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. 
   

   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. 
   

   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. 
   

   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. 
   

   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) $$1\frac{7}{24}$$, 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) $$\frac{23}{24}$$.