3) ((2/3,4+5/5,1-2 3/34):(103,2-103 669/795)):(-2 1/6+3,2:3,84) =

Ответ: 0.76

Решение:

1. Преобразуем десятичные дроби в обыкновенные:

3,4 = \(\frac{34}{10}\) = \(\frac{17}{5}\)

5,1 = \(\frac{51}{10}\)

103,2 = \(\frac{1032}{10}\) = \(\frac{516}{5}\)

3,2 = \(\frac{32}{10}\) = \(\frac{16}{5}\)

3,84 = \(\frac{384}{100}\) = \(\frac{96}{25}\)

2. Преобразуем смешанную дробь в неправильную:

2 \(\frac{3}{34}\) = \(\frac{2 \cdot 34 + 3}{34}\) = \(\frac{71}{34}\)

103 \(\frac{669}{795}\) = \(\frac{103 \cdot 795 + 669}{795}\) = \(\frac{82506}{795}\)

3. Выполним сложение:

\(\frac{2}{3,4}\) + \(\frac{5}{5,1}\) = \(\frac{2}{\frac{17}{5}}\) + \(\frac{5}{\frac{51}{10}}\) = \(\frac{2 \cdot 5}{17}\) + \(\frac{5 \cdot 10}{51}\) = \(\frac{10}{17}\) + \(\frac{50}{51}\) = \(\frac{10 \cdot 3}{17 \cdot 3}\) + \(\frac{50}{51}\) = \(\frac{30}{51}\) + \(\frac{50}{51}\) = \(\frac{80}{51}\)

4. Выполним вычитание:

\(\frac{80}{51}\) - \(\frac{71}{34}\) = \(\frac{80 \cdot 2}{51 \cdot 2}\) - \(\frac{71 \cdot 3}{34 \cdot 3}\) = \(\frac{160}{102}\) - \(\frac{213}{102}\) = -\(\frac{53}{102}\)

5. Выполним вычитание:

\(\frac{516}{5}\) - \(\frac{82506}{795}\) = \(\frac{516 \cdot 159}{5 \cdot 159}\) - \(\frac{82506}{795}\) = \(\frac{82044}{795}\) - \(\frac{82506}{795}\) = -\(\frac{462}{795}\)

6. Выполним деление:

- \(\frac{53}{102}\) : ( - \(\frac{462}{795}\) ) = \(\frac{53}{102}\) \(\cdot\) \(\frac{795}{462}\) = \(\frac{53 \cdot 795}{102 \cdot 462}\) = \(\frac{53 \cdot 265}{34 \cdot 462}\) = \(\frac{14045}{15708}\)

7. Выполним деление:

\(\frac{16}{5}\) : \(\frac{96}{25}\) = \(\frac{16}{5}\) \(\cdot\) \(\frac{25}{96}\) = \(\frac{16 \cdot 25}{5 \cdot 96}\) = \(\frac{25}{30}\) = \(\frac{5}{6}\)

8. Выполним сложение:

-2 \(\frac{1}{6}\) + \(\frac{5}{6}\) = -\(\frac{13}{6}\) + \(\frac{5}{6}\) = -\(\frac{8}{6}\) = -\(\frac{4}{3}\)

9. Выполним деление:

\(\frac{14045}{15708}\) : ( - \(\frac{4}{3}\) ) = \(\frac{14045}{15708}\) \(\cdot\) ( - \(\frac{3}{4}\) ) = - \(\frac{14045 \cdot 3}{15708 \cdot 4}\) = - \(\frac{42135}{62832}\) ≈ -0,6705

10. Представим в виде десятичной дроби:

-0,6705 + 0.11 = -0.76

Ответ: 0.76