Вычислить:
$$ \frac{0,134 + 0,05}{18\frac{1}{6} - 1\frac{11}{14} - \frac{2}{15} \cdot 2\frac{6}{7}}.$$
Решение:
\(\frac{0,134 + 0,05}{18\frac{1}{6} - 1\frac{11}{14} - \frac{2}{15} \cdot 2\frac{6}{7}} = 0,0115\)
\(
1) 0,134 + 0,05 = 0,184;
\)
\(
2) \frac{2}{15} \cdot 2\frac{6}{7} = \frac{2}{15} \cdot \frac{20}{7} = \frac{2 \cdot 20}{15 \cdot 7} = \frac{2 \cdot 4}{3 \cdot 7} = \frac{8}{21};
\)
\(
3) 18\frac{1}{6} - 1\frac{11}{14} = 18\frac{7}{42} - 1\frac{33}{42} = 17 + 1 + \frac{7}{42} - 1\frac{33}{42} = 17 + \frac{42}{42} + \frac{7}{42} - 1\frac{33}{42} = 17 - 1 +
\)
\(\frac{0,134 + 0,05}{18\frac{1}{6} - 1\frac{11}{14} - \frac{2}{15} \cdot 2\frac{6}{7}} = 0,0115\)
\(
1) 0,134 + 0,05 = 0,184;
\)
\(
2) \frac{2}{15} \cdot 2\frac{6}{7} = \frac{2}{15} \cdot \frac{20}{7} = \frac{2 \cdot 20}{15 \cdot 7} = \frac{2 \cdot 4}{3 \cdot 7} = \frac{8}{21};
\)
\(
3) 18\frac{1}{6} - 1\frac{11}{14} = 18\frac{7}{42} - 1\frac{33}{42} = 17 + 1 + \frac{7}{42} - 1\frac{33}{42} = 17 + \frac{42}{42} + \frac{7}{42} - 1\frac{33}{42} = 17 - 1 +
\)
\(
+ (\frac{42}{42} + \frac{7}{42} - \frac{33}{42}) = 16 + \frac{42 + 7 - 33}{42} = 16\frac{16}{42} = 16\frac{8}{21};
\)
\(
4) 16\frac{8}{21} - \frac{8}{21} = 16;
\)
\(
5) 0,184 : 16 = 0,0115.
\)
Ответ: 0,0115.
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