3. Вычислите: (1\frac{1}{3}-0,2)\cdot 30-(2\frac{1}{3}+1\frac{2}{7}):\frac{5}{9}

3. Вычислите:

$$\left(1\frac{1}{3}-0,2\right)\cdot 30-\left(2\frac{1}{3}+1\frac{2}{7}\right):\frac{5}{9}$$

1. \(1\frac{1}{3} - 0,2 = \frac{4}{3} - \frac{1}{5} = \frac{20 - 3}{15} = \frac{17}{15}\)
2. \(\frac{17}{15} \cdot 30 = \frac{17 \cdot 30}{15} = 17 \cdot 2 = 34\)
3. \(2\frac{1}{3} + 1\frac{2}{7} = \frac{7}{3} + \frac{9}{7} = \frac{7 \cdot 7 + 9 \cdot 3}{21} = \frac{49 + 27}{21} = \frac{76}{21}\)
4. \(\frac{76}{21} : \frac{5}{9} = \frac{76}{21} \cdot \frac{9}{5} = \frac{76 \cdot 9}{21 \cdot 5} = \frac{76 \cdot 3}{7 \cdot 5} = \frac{228}{35}\)
5. \(34 - \frac{228}{35} = \frac{34 \cdot 35 - 228}{35} = \frac{1190 - 228}{35} = \frac{962}{35} = 27\frac{17}{35}\)

Ответ: 27\(\frac{17}{35}\)