Вычислить:
$$5. \frac{(85\frac{7}{30} - 83\frac{5}{18}) : 2\frac{2}{3}}{0,04}.$$
Решение.
\(5. \frac{(85\frac{7}{30} - 83\frac{5}{18}) : 2\frac{2}{3}}{0,04} = 18\frac{1}{3}\)
\(
1) 85\frac{7}{30} - 83\frac{5}{18} = 85\frac{21}{90} - 83\frac{25}{90} = 84 + 1 + \frac{21}{90} - 83\frac{25}{90} = 84 + \frac{90}{90} + \frac{21}{90} - 83\frac{25}{90} = 84 - 83 + (\frac{90}{90} + \frac{21}{90} - \frac{25}{90}) = 1 + \frac{90 + 21 - 25}{90} = 1 + \frac{86}{90} = 1\frac{43}{45};
\)
\(
2) 1\frac{43}{45} : 2\frac{2}{3} = \frac{88}{45} : \frac{8}{3} = \frac{88}{45} \cdot \frac{3}{8} = \frac{88 \cdot 3}{45 \cdot 8} = \frac{11 \cdot 1}{15 \cdot 1} = \frac{11}{15};
\)
\(
3) \frac{11}{15} : 0,04 = \frac{11}{15} : \frac{4}{100} = \frac{11}{15} \cdot \frac{100}{4} = \frac{11}{15} \cdot 25 = \frac{11}{3} \cdot 5 = \frac{55}{3} = 18\frac{1}{3}.
\)
Ответ: \(18\frac{1}{3}.\)
\(5. \frac{(85\frac{7}{30} - 83\frac{5}{18}) : 2\frac{2}{3}}{0,04} = 18\frac{1}{3}\)
\(
1) 85\frac{7}{30} - 83\frac{5}{18} = 85\frac{21}{90} - 83\frac{25}{90} = 84 + 1 + \frac{21}{90} - 83\frac{25}{90} = 84 + \frac{90}{90} + \frac{21}{90} - 83\frac{25}{90} = 84 - 83 + (\frac{90}{90} + \frac{21}{90} - \frac{25}{90}) = 1 + \frac{90 + 21 - 25}{90} = 1 + \frac{86}{90} = 1\frac{43}{45};
\)
\(
2) 1\frac{43}{45} : 2\frac{2}{3} = \frac{88}{45} : \frac{8}{3} = \frac{88}{45} \cdot \frac{3}{8} = \frac{88 \cdot 3}{45 \cdot 8} = \frac{11 \cdot 1}{15 \cdot 1} = \frac{11}{15};
\)
\(
3) \frac{11}{15} : 0,04 = \frac{11}{15} : \frac{4}{100} = \frac{11}{15} \cdot \frac{100}{4} = \frac{11}{15} \cdot 25 = \frac{11}{3} \cdot 5 = \frac{55}{3} = 18\frac{1}{3}.
\)
Ответ: \(18\frac{1}{3}.\)
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