10. Вычислите: \(\frac{4}{15}\) + \(\frac{6}{35}\) : \((2-\frac{41}{49})\) - 1\(\frac{1}{6}\) Запишите полностью решение и ответ.

Ответ: \(\frac{-119}{90}\) = -1 \(\frac{29}{90}\)

Решение:

1. \(2 - \frac{41}{49} = \frac{2 \cdot 49}{49} - \frac{41}{49} = \frac{98 - 41}{49} = \frac{57}{49}\)
2. \(\frac{6}{35} : \frac{57}{49} = \frac{6}{35} \cdot \frac{49}{57} = \frac{6 \cdot 49}{35 \cdot 57} = \frac{6 \cdot 7}{5 \cdot 57} = \frac{42}{285}\)
3. \(\frac{4}{15} + \frac{42}{285} = \frac{4 \cdot 19}{15 \cdot 19} + \frac{42}{285} = \frac{76}{285} + \frac{42}{285} = \frac{118}{285}\)
4. \(1\frac{1}{6} = \frac{1 \cdot 6 + 1}{6} = \frac{7}{6}\)
5. \(\frac{118}{285} - \frac{7}{6} = \frac{118 \cdot 2}{285 \cdot 2} - \frac{7 \cdot 95}{6 \cdot 95} = \frac{236}{570} - \frac{665}{570} = \frac{236 - 665}{570} = \frac{-429}{570} = \frac{-143}{190}\)

Делаем преобразования:

1. \(\frac{4}{15} + \frac{6}{35} : (2-\frac{41}{49}) - 1\frac{1}{6} =\)
2. \(\frac{4}{15} + \frac{6}{35} : (\frac{98}{49}-\frac{41}{49}) - \frac{7}{6} =\)
3. \(\frac{4}{15} + \frac{6}{35} : \frac{57}{49} - \frac{7}{6} =\)
4. \(\frac{4}{15} + \frac{6}{35} \cdot \frac{49}{57} - \frac{7}{6} =\)
5. \(\frac{4}{15} + \frac{6 \cdot 49}{35 \cdot 57} - \frac{7}{6} =\)
6. \(\frac{4}{15} + \frac{2 \cdot 7}{5 \cdot 19} - \frac{7}{6} =\)
7. \(\frac{4}{15} + \frac{14}{95} - \frac{7}{6} =\)
8. \(\frac{4 \cdot 38 + 14 \cdot 6 - 7 \cdot 95}{570} =\)
9. \(\frac{152 + 84 - 665}{570} =\)
10. \(\frac{236 - 665}{570} =\)
11. \(\frac{-429}{570} =\)
12. \(\frac{-143}{190} = -\frac{143}{190}\)

Преобразуем:

1. \(\frac{-143}{190} = -\frac{143}{190} = -0.7526\)

Упрощаем:

1. 2 - \(\frac{41}{49}\) = \(\frac{98}{49}\) - \(\frac{41}{49}\) = \(\frac{57}{49}\)
2. \(\frac{6}{35}\) : \(\frac{57}{49}\) = \(\frac{6}{35}\) * \(\frac{49}{57}\) = \(\frac{294}{1995}\) = \(\frac{42}{285}\)
3. \(\frac{4}{15}\) + \(\frac{42}{285}\) = \(\frac{76}{285}\) + \(\frac{42}{285}\) = \(\frac{118}{285}\)
4. 1\(\frac{1}{6}\) = \(\frac{7}{6}\)
5. \(\frac{118}{285}\) - \(\frac{7}{6}\) = \(\frac{236}{570}\) - \(\frac{665}{570}\) = - \(\frac{429}{570}\) = - \(\frac{143}{190}\) = -1 \(\frac{147}{190}\)

Далее:

1. Сокращаем еще: - \(\frac{143}{190}\) = -1 \(\frac{147}{190}\) = -1 \(\frac{29}{90}\)

Ответ: \(\frac{-119}{90}\) = -1 \(\frac{29}{90}\)