Вычислить:
$$ \frac{(95\frac{7}{30} - 93\frac{5}{18}) \cdot 2\frac{1}{4} + 0,373}{0,2}.$$
Решение:
\( \frac{(95\frac{7}{30} - 93\frac{5}{18}) \cdot 2\frac{1}{4} + 0,373}{0,2} = 23,865\)
\(
1) 95\frac{7}{30} - 93\frac{5}{18} = 95\frac{21}{90} - 93\frac{25}{90} = 94 + 1 + \frac{21}{90} - 93\frac{25}{90} = 94 + \frac{90}{90} + \frac{21}{90} - 93\frac{25}{90} = 94 - 93 +
\)
\( \frac{(95\frac{7}{30} - 93\frac{5}{18}) \cdot 2\frac{1}{4} + 0,373}{0,2} = 23,865\)
\(
1) 95\frac{7}{30} - 93\frac{5}{18} = 95\frac{21}{90} - 93\frac{25}{90} = 94 + 1 + \frac{21}{90} - 93\frac{25}{90} = 94 + \frac{90}{90} + \frac{21}{90} - 93\frac{25}{90} = 94 - 93 +
\)
\(
+ (\frac{90}{90} + \frac{21}{90} - \frac{25}{90}) = 1 + \frac{90 + 21 - 25}{90} = 1 + \frac{86}{90} = 1\frac{43}{45};\)
\(
2) 1\frac{43}{45} \cdot 2\frac{1}{4} = \frac{88}{45} \cdot \frac{9}{4} = \frac{88 \cdot 9}{45 \cdot 4} = \frac{22 \cdot 1}{5 \cdot 1} = \frac{22}{5} = 4\frac{2}{5} = 4,4;
\)
\(
3) 4,4 + 0,373 = 4,773;
\)
\(
4) 4,773 : 0,2 = 23,865.
\)
Ответ: 23,865.
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