Вычислить:
$$ \frac{215\frac{9}{16} - 208\frac{3}{4} + \frac{1}{2}}{0,0001 : 0,005}.$$
Решение.
\( \frac{215\frac{9}{16} - 208\frac{3}{4} + \frac{1}{2}}{0,0001 : 0,005} = 365\frac{5}{8}.\)
\(
1) 215\frac{9}{16} - 208\frac{3}{4} = 215\frac{9}{16} - 208\frac{12}{16} = 214 + 1 + \frac{9}{16} - 208\frac{12}{16} = 214 + \frac{16}{16} + \frac{9}{16} - 208\frac{12}{16} = 214\frac{25}{16} - 208\frac{12}{16} = 214 - 208 + (\frac{25}{16} - \frac{12}{16}) = 6\frac{13}{16};
\)
\(
2) 6\frac{13}{16} + \frac{1}{2} = 6\frac{13}{16} + \frac{8}{16} = 6 + \frac{13 + 8}{16} = 6\frac{21}{16} = 6 + 1\frac{5}{16} = 7\frac{5}{16};
\)
\(
3) 0,0001 : 0,005 = \frac{0,0001}{0,005} = \frac{1}{50};
\)
\(
4) 7\frac{5}{16} : \frac{1}{50} = \frac{117}{16} \cdot \frac{50}{1} = \frac{117 \cdot 50}{16 \cdot 1} = \frac{117 \cdot 25}{8 \cdot 1} = \frac{2925}{8} = 365\frac{5}{8}.
\)
Ответ: \(365\frac{5}{8}.\)
\( \frac{215\frac{9}{16} - 208\frac{3}{4} + \frac{1}{2}}{0,0001 : 0,005} = 365\frac{5}{8}.\)
\(
1) 215\frac{9}{16} - 208\frac{3}{4} = 215\frac{9}{16} - 208\frac{12}{16} = 214 + 1 + \frac{9}{16} - 208\frac{12}{16} = 214 + \frac{16}{16} + \frac{9}{16} - 208\frac{12}{16} = 214\frac{25}{16} - 208\frac{12}{16} = 214 - 208 + (\frac{25}{16} - \frac{12}{16}) = 6\frac{13}{16};
\)
\(
2) 6\frac{13}{16} + \frac{1}{2} = 6\frac{13}{16} + \frac{8}{16} = 6 + \frac{13 + 8}{16} = 6\frac{21}{16} = 6 + 1\frac{5}{16} = 7\frac{5}{16};
\)
\(
3) 0,0001 : 0,005 = \frac{0,0001}{0,005} = \frac{1}{50};
\)
\(
4) 7\frac{5}{16} : \frac{1}{50} = \frac{117}{16} \cdot \frac{50}{1} = \frac{117 \cdot 50}{16 \cdot 1} = \frac{117 \cdot 25}{8 \cdot 1} = \frac{2925}{8} = 365\frac{5}{8}.
\)
Ответ: \(365\frac{5}{8}.\)
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