219. Выполните сложение: а) \(4\frac{5}{17} + \frac{8}{17}\) ; б) \(3\frac{5}{21} + 4\frac{8}{21}\) ; в) \(13 + 12\frac{11}{12}\) ; г) \(9\frac{5}{6} + 7\) ; д) \(3\frac{12}{23} + 4\frac{11}{23}\) ; е) \(7\frac{15}{19} + 4\frac{14}{19}\)

Решение:

а)

\( 4\frac{5}{17} + \frac{8}{17} = 4 + \frac{5+8}{17} = 4 + \frac{13}{17} = 4\frac{13}{17} \)

б)

\( 3\frac{5}{21} + 4\frac{8}{21} = (3+4) + (\frac{5}{21} + \frac{8}{21}) = 7 + \frac{5+8}{21} = 7 + \frac{13}{21} = 7\frac{13}{21} \)

в)

\( 13 + 12\frac{11}{12} = (13+12) + \frac{11}{12} = 25 + \frac{11}{12} = 25\frac{11}{12} \)

г)

\( 9\frac{5}{6} + 7 = (9+7) + \frac{5}{6} = 16 + \frac{5}{6} = 16\frac{5}{6} \)

д)

\( 3\frac{12}{23} + 4\frac{11}{23} = (3+4) + (\frac{12}{23} + \frac{11}{23}) = 7 + \frac{12+11}{23} = 7 + \frac{23}{23} = 7+1 = 8 \)

е)

\( 7\frac{15}{19} + 4\frac{14}{19} = (7+4) + (\frac{15}{19} + \frac{14}{19}) = 11 + \frac{15+14}{19} = 11 + \frac{29}{19} = 11 + 1 \frac{10}{19} = 12\frac{10}{19} \)

Ответ: а) \( 4\frac{13}{17} \); б) \( 7\frac{13}{21} \); в) \( 25\frac{11}{12} \); г) \( 16\frac{5}{6} \); д) \( 8 \); е) \( 12\frac{10}{19} \).