8) $5+4\frac{13}{19}-\left(8\frac{2}{11}-7\frac{6}{19}\right)+\left(4\frac{2}{5}-12\frac{9}{11}\right)$

Question

Вопрос: $Фото задания: 8) $5+4\frac{13}{19}-\left(8\frac{2}{11}-7\frac{6}{19}\right)+\left(4\frac{2}{5}-12\frac{9}{11}\right)$$ Фото задания

Accepted Answer

\[8\frac{2}{11}-7\frac{6}{19}=1+\frac{2}{11}-\frac{6}{19}=1-\frac{28}{209}=\frac{181}{209}\]

\[4\frac{2}{5}-12\frac{9}{11}=-8+\frac{2}{5}-\frac{9}{11}=-8-\frac{23}{55}=-\frac{463}{55}\]

\[5+4\frac{13}{19}-\frac{181}{209}-\frac{463}{55}=9+\frac{13}{19}-\frac{181}{209}-\frac{463}{55}\]

Так как $\frac{13}{19}=\frac{143}{209}$, получаем:

\[9+\frac{143-181}{209}-\frac{463}{55}=9-\frac{38}{209}-\frac{463}{55}=9-\frac{190}{1045}-\frac{8797}{1045}=\frac{418}{1045}=\frac{2}{5}\]

Ответ: $\frac{2}{5}$

8) \(5+4\frac{13}{19}-\left(8\frac{2}{11}-7\frac{6}{19}\right)+\left(4\frac{2}{5}-12\frac{9}{11}\right)\)