219. Выполните сложение: а) \frac{3}{13}+5\frac{7}{13}; в) 2\frac{5}{9}+9; д) 4\frac{5}{11}+1\frac{6}{11}; б) 6\frac{2}{17}+3\frac{11}{17}; г) 8+7\frac{5}{6}; е) 9\frac{11}{15}+5\frac{8}{15}.

219. Выполните сложение:

а) \(\frac{3}{13}+5\frac{7}{13}\) \(\frac{3}{13}+5\frac{7}{13} = \frac{3}{13} + \frac{5 \cdot 13 + 7}{13} = \frac{3}{13} + \frac{65 + 7}{13} = \frac{3}{13} + \frac{72}{13} = \frac{3 + 72}{13} = \frac{75}{13} = 5\frac{10}{13}\) б) \(6\frac{2}{17}+3\frac{11}{17}\) \(6\frac{2}{17}+3\frac{11}{17} = \frac{6 \cdot 17 + 2}{17} + \frac{3 \cdot 17 + 11}{17} = \frac{102 + 2}{17} + \frac{51 + 11}{17} = \frac{104}{17} + \frac{62}{17} = \frac{104 + 62}{17} = \frac{166}{17} = 9\frac{13}{17}\) в) \(2\frac{5}{9}+9\) \(2\frac{5}{9}+9 = \frac{2 \cdot 9 + 5}{9} + 9 = \frac{18 + 5}{9} + 9 = \frac{23}{9} + 9 = \frac{23}{9} + \frac{9 \cdot 9}{9} = \frac{23}{9} + \frac{81}{9} = \frac{23 + 81}{9} = \frac{104}{9} = 11\frac{5}{9}\) г) \(8+7\frac{5}{6}\) \(8+7\frac{5}{6} = 8 + \frac{7 \cdot 6 + 5}{6} = 8 + \frac{42 + 5}{6} = 8 + \frac{47}{6} = \frac{8 \cdot 6}{6} + \frac{47}{6} = \frac{48}{6} + \frac{47}{6} = \frac{48 + 47}{6} = \frac{95}{6} = 15\frac{5}{6}\) д) \(4\frac{5}{11}+1\frac{6}{11}\) \(4\frac{5}{11}+1\frac{6}{11} = \frac{4 \cdot 11 + 5}{11} + \frac{1 \cdot 11 + 6}{11} = \frac{44 + 5}{11} + \frac{11 + 6}{11} = \frac{49}{11} + \frac{17}{11} = \frac{49 + 17}{11} = \frac{66}{11} = 6\) е) \(9\frac{11}{15}+5\frac{8}{15}\) \(9\frac{11}{15}+5\frac{8}{15} = \frac{9 \cdot 15 + 11}{15} + \frac{5 \cdot 15 + 8}{15} = \frac{135 + 11}{15} + \frac{75 + 8}{15} = \frac{146}{15} + \frac{83}{15} = \frac{146 + 83}{15} = \frac{229}{15} = 15\frac{4}{15}\)

Ответ: а) \(5\frac{10}{13}\); б) \(9\frac{13}{17}\); в) \(11\frac{5}{9}\); г) \(15\frac{5}{6}\); д) 6; е) \(15\frac{4}{15}\)

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