85. Найдите 60 % значения выражения (\frac{2}{3}+3\frac{7}{24}):(4\frac{2}{3}-1\frac{1}{8}).

85. Найдите 60 % значения выражения

$$(\frac{2}{3}+3\frac{7}{24}):(4\frac{2}{3}-1\frac{1}{8})$$

1) $$(\frac{2}{3}+3\frac{7}{24})=(\frac{2}{3}+\frac{3 \cdot 24+7}{24})=(\frac{2}{3}+\frac{72+7}{24})=(\frac{2}{3}+\frac{79}{24})=(\frac{2 \cdot 8}{3 \cdot 8}+\frac{79}{24})=(\frac{16}{24}+\frac{79}{24})=\frac{95}{24}$$

2) $$(4\frac{2}{3}-1\frac{1}{8})=(\frac{4 \cdot 3+2}{3}-\frac{1 \cdot 8+1}{8})=(\frac{12+2}{3}-\frac{8+1}{8})=(\frac{14}{3}-\frac{9}{8})=(\frac{14 \cdot 8}{3 \cdot 8}-\frac{9 \cdot 3}{8 \cdot 3})=(\frac{112}{24}-\frac{27}{24})=\frac{85}{24}$$

3) $$(\frac{95}{24}:\frac{85}{24})=\frac{95}{24} \cdot \frac{24}{85}=\frac{95}{85}=\frac{5 \cdot 19}{5 \cdot 17}=\frac{19}{17}$$

4) Найдём 60% от \frac{19}{17}:

$$\frac{19}{17} \cdot \frac{60}{100}=\frac{19}{17} \cdot \frac{3 \cdot 20}{5 \cdot 20}=\frac{19}{17} \cdot \frac{3}{5}=\frac{57}{85}$$

Ответ: $$\frac{57}{85}$$