1. Вычислите: 2-\(\frac{4}{15}\) - (2-\(\frac{1}{15}\)) : \(\frac{4}{9}\) + \(\frac{2}{3}\). Запишите полностью решение и ответ.

Решение:

1. \(2 - \frac{4}{15} = \frac{30}{15} - \frac{4}{15} = \frac{26}{15}\)
2. \(2 - \frac{1}{15} = \frac{30}{15} - \frac{1}{15} = \frac{29}{15}\)
3. \(\frac{29}{15} : \frac{4}{9} = \frac{29}{15} \times \frac{9}{4} = \frac{29 \times 3}{5 \times 4} = \frac{87}{20}\)
4. \(\frac{26}{15} - \frac{87}{20} = \frac{26 \times 4}{15 \times 4} - \frac{87 \times 3}{20 \times 3} = \frac{104}{60} - \frac{261}{60} = -\frac{157}{60}\)
5. \(-\frac{157}{60} + \frac{2}{3} = -\frac{157}{60} + \frac{2 \times 20}{3 \times 20} = -\frac{157}{60} + \frac{40}{60} = -\frac{117}{60} = -\frac{39}{20}\)

Ответ: -\(\frac{39}{20}\)