57. Тип 13 № 11433: Вычислите \(\frac{7}{5} + \frac{18}{35} + 1\frac{22}{27} + 4 : 6\frac{2}{13}\)

Решение:

1. \(1\frac{22}{27} = \frac{1 \cdot 27 + 22}{27} = \frac{49}{27}\)
2. \(6\frac{2}{13} = \frac{6 \cdot 13 + 2}{13} = \frac{80}{13}\)
3. \(\frac{7}{5} + \frac{18}{35} = \frac{7 \cdot 7 + 18}{35} = \frac{49 + 18}{35} = \frac{67}{35}\)
4. \(\frac{67}{35} + \frac{49}{27} = \frac{67 \cdot 27 + 49 \cdot 35}{35 \cdot 27} = \frac{1809 + 1715}{945} = \frac{3524}{945}\)
5. \(4 : \frac{80}{13} = 4 \cdot \frac{13}{80} = \frac{4 \cdot 13}{80} = \frac{52}{80} = \frac{13}{20}\)
6. \(\frac{3524}{945} + \frac{13}{20} = \frac{3524 \cdot 4 + 13 \cdot 189}{945 \cdot 4} = \frac{14096 + 2457}{3780} = \frac{16553}{3780}\)

Ответ: \(\frac{16553}{3780}\)