1. Вычислите: \(\frac{7}{11}\cdot(\frac{8}{11}+\frac{4}{33}):6\frac{1}{16}-\frac{11}{10}:24\)

1. Вычислите: \(\frac{7}{11}\cdot(\frac{8}{11}+\frac{4}{33}):6\frac{1}{16}-\frac{11}{10}:24\)

Решение:

1) \(\frac{8}{11} + \frac{4}{33} = \frac{8 \cdot 3}{11 \cdot 3} + \frac{4}{33} = \frac{24}{33} + \frac{4}{33} = \frac{28}{33}\)

2) \(\frac{7}{11} \cdot \frac{28}{33} = \frac{7 \cdot 28}{11 \cdot 33} = \frac{196}{363}\)

3) \(6\frac{1}{16} = \frac{6 \cdot 16 + 1}{16} = \frac{97}{16}\)

4) \(\frac{196}{363} : \frac{97}{16} = \frac{196}{363} \cdot \frac{16}{97} = \frac{196 \cdot 16}{363 \cdot 97} = \frac{3136}{35211}\)

5) \(\frac{11}{10} : 24 = \frac{11}{10} : \frac{24}{1} = \frac{11}{10} \cdot \frac{1}{24} = \frac{11 \cdot 1}{10 \cdot 24} = \frac{11}{240}\)

6) \(\frac{3136}{35211} - \frac{11}{240} = \frac{3136 \cdot 240}{35211 \cdot 240} - \frac{11 \cdot 35211}{240 \cdot 35211} = \frac{752640}{8450640} - \frac{387321}{8450640} = \frac{365319}{8450640}\)

Сократим дробь на 3:

\(\frac{365319:3}{8450640:3} = \frac{121773}{2816880}\)

Ответ: \(\frac{121773}{2816880}\)