№4. Выполните действия: a) \(\frac{18}{19} - \frac{7}{19} + \frac{3}{19}\); б) \(\frac{9}{11} - \frac{3}{11} - \frac{2}{11}\); в) \((\frac{11}{15} - \frac{3}{15}) + \frac{7}{15}\); г) \((\frac{13}{16} - \frac{13}{16}) - \frac{3}{16}\); д) \((\frac{17}{47} + \frac{12}{47}) - \frac{41}{47} - \frac{37}{47}\); е) \((\frac{19}{24} + \frac{23}{24}) - (\frac{9}{24} + \frac{13}{24})\).

Выполним действия с дробями:

a) \(\frac{18}{19} - \frac{7}{19} + \frac{3}{19}\)

\[\frac{18}{19} - \frac{7}{19} + \frac{3}{19} = \frac{18 - 7 + 3}{19} = \frac{11 + 3}{19} = \frac{14}{19}\]

б) \(\frac{9}{11} - \frac{3}{11} - \frac{2}{11}\)

\[\frac{9}{11} - \frac{3}{11} - \frac{2}{11} = \frac{9 - 3 - 2}{11} = \frac{6 - 2}{11} = \frac{4}{11}\]

в) \((\frac{11}{15} - \frac{3}{15}) + \frac{7}{15}\)

\[(\frac{11}{15} - \frac{3}{15}) + \frac{7}{15} = \frac{11 - 3}{15} + \frac{7}{15} = \frac{8}{15} + \frac{7}{15} = \frac{8 + 7}{15} = \frac{15}{15} = 1\]

г) \((\frac{13}{16} - \frac{13}{16}) - \frac{3}{16}\)

\[(\frac{13}{16} - \frac{13}{16}) - \frac{3}{16} = 0 - \frac{3}{16} = -\frac{3}{16}\]

д) \((\frac{17}{47} + \frac{12}{47}) - \frac{41}{47} - \frac{37}{47}\)

\[(\frac{17}{47} + \frac{12}{47}) - \frac{41}{47} - \frac{37}{47} = \frac{17 + 12}{47} - \frac{41}{47} - \frac{37}{47} = \frac{29}{47} - \frac{41}{47} - \frac{37}{47} = \frac{29 - 41 - 37}{47} = \frac{-12 - 37}{47} = \frac{-49}{47} = -\frac{49}{47}\]

е) \((\frac{19}{24} + \frac{23}{24}) - (\frac{9}{24} + \frac{13}{24})\)

\[(\frac{19}{24} + \frac{23}{24}) - (\frac{9}{24} + \frac{13}{24}) = \frac{19 + 23}{24} - \frac{9 + 13}{24} = \frac{42}{24} - \frac{22}{24} = \frac{42 - 22}{24} = \frac{20}{24} = \frac{5}{6}\]

Ответ: a) \(\frac{14}{19}\); б) \(\frac{4}{11}\); в) 1; г) \(-\frac{3}{16}\); д) \(-\frac{49}{47}\); е) \(\frac{5}{6}\)

Отлично! У тебя всё получится!