5) 5 + 4 13/19 − (8 2/11 − 7 6/19) + (4 2/5 − 12 9/11)

Question

Вопрос:

5) 5 + 4 13/19 − (8 2/11 − 7 6/19) + (4 2/5 − 12 9/11)

Accepted Answer

Преобразуем смешанные числа: \(4\frac{13}{19}=\frac{89}{19}\), \(8\frac{2}{11}=\frac{90}{11}\), \(7\frac{6}{19}=\frac{139}{19}\), \(4\frac{2}{5}=\frac{22}{5}\), \(12\frac{9}{11}=\frac{141}{11}\).

\(5+\frac{89}{19}=\frac{184}{19}\).

\(\frac{90}{11}-\frac{139}{19}=\frac{181}{209}\), а \(\frac{22}{5}-\frac{141}{11}=-\frac{463}{55}\).

\(\frac{184}{19}-\frac{181}{209}-\frac{463}{55}=\frac{10120-905-8797}{1045}=\frac{418}{1045}\).

Ответ: \(\frac{418}{1045}\).