276. Найдите сумму:

Решение:

1. \( 5\frac{7}{8} + 6\frac{3}{10} = \frac{5 · 8 + 7}{8} + \frac{6 · 10 + 3}{10} = \frac{40+7}{8} + \frac{60+3}{10} = \frac{47}{8} + \frac{63}{10} = \frac{47 · 5}{8 · 5} + \frac{63 · 4}{10 · 4} = \frac{235}{40} + \frac{252}{40} = \frac{487}{40} = 12\frac{7}{40} \)
2. \( 6\frac{3}{8} + 2\frac{5}{9} = \frac{6 · 8 + 3}{8} + \frac{2 · 9 + 5}{9} = \frac{48+3}{8} + \frac{18+5}{9} = \frac{51}{8} + \frac{23}{9} = \frac{51 · 9}{8 · 9} + \frac{23 · 8}{9 · 8} = \frac{459}{72} + \frac{184}{72} = \frac{643}{72} = 8\frac{67}{72} \)
3. \( 1\frac{8}{21} + 4\frac{3}{14} + 2\frac{2}{7} = \frac{1 · 21 + 8}{21} + \frac{4 · 14 + 3}{14} + \frac{2 · 7 + 2}{7} = \frac{21+8}{21} + \frac{56+3}{14} + \frac{14+2}{7} = \frac{29}{21} + \frac{59}{14} + \frac{16}{7} = \frac{29 · 2}{21 · 2} + \frac{59 · 3}{14 · 3} + \frac{16 · 6}{7 · 6} = \frac{58}{42} + \frac{177}{42} + \frac{96}{42} = \frac{331}{42} = 7\frac{37}{42} \)

Ответ: 1) \( 12\frac{7}{40} \); 2) \( 8\frac{67}{72} \); 3) \( 7\frac{37}{42} \).