5. Вычислите: \(\frac{5}{9}:(\frac{7}{18}+\frac{11}{20}):\frac{11}{25}:\frac{12}{16}\)

5. Вычислите: \(\frac{5}{9}:(\frac{7}{18}+\frac{11}{20}):\frac{11}{25}:\frac{12}{16}\)

1) \(\frac{7}{18} + \frac{11}{20} = \frac{7 \cdot 10}{18 \cdot 10} + \frac{11 \cdot 9}{20 \cdot 9} = \frac{70}{180} + \frac{99}{180} = \frac{169}{180}\)

2) \(\frac{5}{9} : \frac{169}{180} = \frac{5}{9} \cdot \frac{180}{169} = \frac{5 \cdot 180}{9 \cdot 169} = \frac{900}{1521} = \frac{100}{169}\)

3) \(\frac{100}{169} : \frac{11}{25} = \frac{100}{169} \cdot \frac{25}{11} = \frac{100 \cdot 25}{169 \cdot 11} = \frac{2500}{1859}\)

4) \(\frac{2500}{1859} : \frac{12}{16} = \frac{2500}{1859} \cdot \frac{16}{12} = \frac{2500 \cdot 16}{1859 \cdot 12} = \frac{40000}{22308} = \frac{10000}{5577}\)

Ответ: \(\frac{10000}{5577}\)