Вычислить:
$$6. \frac{(140\frac{7}{30} - 138\frac{5}{12}) : 18\frac{1}{6}}{0,002}.$$
Решение.
\(6. \frac{(140\frac{7}{30} - 138\frac{5}{12}) : 18\frac{1}{6}}{0,002} = 50.\)
\(
1) 140\frac{7}{30} - 138\frac{5}{12} = 140\frac{14}{60} - 138\frac{25}{60} = 139 + 1 + \frac{14}{60} - 138\frac{25}{60} = 139 + \frac{60}{60} + \frac{14}{60} - 138\frac{25}{60} = 139 - 138 + (\frac{60}{60} + \frac{14}{60} - \frac{25}{60}) = 1 + \frac{60 + 14 - 25}{60} = 1\frac{49}{60};
\)
\(
2) 1\frac{49}{60} : 18\frac{1}{6} = \frac{109}{60} : \frac{109}{6} = \frac{109}{60} \cdot \frac{6}{109} = \frac{109 \cdot 6}{60 \cdot 109} = \frac{1 \cdot 1}{10 \cdot 1} = \frac{1}{10} = 0,1;
\)
\(
3) 0,1 : 0,002 = 100 : 2 = 50.
\)
Ответ: 50.
\(6. \frac{(140\frac{7}{30} - 138\frac{5}{12}) : 18\frac{1}{6}}{0,002} = 50.\)
\(
1) 140\frac{7}{30} - 138\frac{5}{12} = 140\frac{14}{60} - 138\frac{25}{60} = 139 + 1 + \frac{14}{60} - 138\frac{25}{60} = 139 + \frac{60}{60} + \frac{14}{60} - 138\frac{25}{60} = 139 - 138 + (\frac{60}{60} + \frac{14}{60} - \frac{25}{60}) = 1 + \frac{60 + 14 - 25}{60} = 1\frac{49}{60};
\)
\(
2) 1\frac{49}{60} : 18\frac{1}{6} = \frac{109}{60} : \frac{109}{6} = \frac{109}{60} \cdot \frac{6}{109} = \frac{109 \cdot 6}{60 \cdot 109} = \frac{1 \cdot 1}{10 \cdot 1} = \frac{1}{10} = 0,1;
\)
\(
3) 0,1 : 0,002 = 100 : 2 = 50.
\)
Ответ: 50.
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