4.169 Вычислите: $$\frac{(8,62-8,37 + 1(\frac{23}{60}+\frac{1}{5}))\cdot \frac{3}{11}}{(3,5-2\frac{3}{4}):\frac{1}{5} - 2,5}$$

Решение:

$$\frac{(8,62-8,37 + 1(\frac{23}{60}+\frac{1}{5}))\cdot \frac{3}{11}}{(3,5-2\frac{3}{4}):\frac{1}{5} - 2,5} = $$

1. $$\frac{23}{60}+\frac{1}{5} = \frac{23}{60}+\frac{12}{60} = \frac{35}{60}=\frac{7}{12}$$
2. $$8,62-8,37 = 0,25$$
3. $$0,25 + \frac{7}{12} = \frac{1}{4} + \frac{7}{12} = \frac{3}{12} + \frac{7}{12} = \frac{10}{12} = \frac{5}{6}$$
4. $$\frac{5}{6} \cdot \frac{3}{11} = \frac{5 \cdot 3}{6 \cdot 11} = \frac{5 \cdot 1}{2 \cdot 11} = \frac{5}{22}$$
5. $$3,5-2\frac{3}{4} = 3,5 - 2,75 = 0,75$$
6. $$0,75:\frac{1}{5} = \frac{3}{4} \cdot 5 = \frac{15}{4} = 3,75$$
7. $$3,75 - 2,5 = 1,25$$
8. $$\frac{\frac{5}{22}}{1,25} = \frac{\frac{5}{22}}{\frac{5}{4}} = \frac{5}{22} \cdot \frac{4}{5} = \frac{1}{11} \cdot \frac{2}{1} = \frac{2}{11}$$

Ответ: $$\frac{2}{11}$$