6. Выполнить сложение:

Решение:

1. \( 6 + 3 \frac{4}{5} = (6+3) + \frac{4}{5} = 9 \frac{4}{5} \)
2. \( 10 \frac{13}{14} + 5 = (10+5) + \frac{13}{14} = 15 \frac{13}{14} \)
3. \( 8 \frac{3}{4} + 2 \frac{11}{12} = 8 \frac{3 \cdot 3}{4 \cdot 3} + 2 \frac{11}{12} = 8 \frac{9}{12} + 2 \frac{11}{12} = (8+2) + (\frac{9}{12} + \frac{11}{12}) = 10 + \frac{20}{12} = 10 + 1 \frac{8}{12} = 11 \frac{8}{12} = 11 \frac{2}{3} \)
4. \( 12 \frac{15}{16} + 2 \frac{2}{32} = 12 \frac{15 \cdot 2}{16 \cdot 2} + 2 \frac{2}{32} = 12 \frac{30}{32} + 2 \frac{2}{32} = (12+2) + (\frac{30}{32} + \frac{2}{32}) = 14 \frac{32}{32} = 14 + 1 = 15 \)
5. \( 4 \frac{9}{14} + 5 \frac{11}{12} = 4 \frac{9 \cdot 6}{14 \cdot 6} + 5 \frac{11 \cdot 7}{12 \cdot 7} = 4 \frac{54}{84} + 5 \frac{77}{84} = (4+5) + (\frac{54}{84} + \frac{77}{84}) = 9 + \frac{131}{84} = 9 + 1 \frac{47}{84} = 10 \frac{47}{84} \)
6. \( 3 \frac{1}{3} + \frac{14}{21} = 3 \frac{1 \cdot 7}{3 \cdot 7} + \frac{14}{21} = 3 \frac{7}{21} + \frac{14}{21} = 3 + (\frac{7}{21} + \frac{14}{21}) = 3 \frac{21}{21} = 3 + 1 = 4 \)

Ответ: 6-а) \( 9 \frac{4}{5} \), 6-б) \( 15 \frac{13}{14} \), 6-в) \( 11 \frac{2}{3} \), 6-г) \( 15 \), 6-д) \( 10 \frac{47}{84} \), 6-е) \( 4 \).