849. Вычислить: 4) \((\frac{3}{5} + 1\frac{7}{10}) \cdot 1\frac{3}{17} - (2\frac{7}{23} - 1\frac{45}{46} - \frac{69}{80}) \cdot 1\frac{1}{3}\)

Решение:

1. \( \frac{3}{5} + 1\frac{7}{10} = \frac{3}{5} + \frac{17}{10} = \frac{6+17}{10} = \frac{23}{10} \)
2. \( \frac{23}{10} \cdot 1\frac{3}{17} = \frac{23}{10} \cdot \frac{20}{17} = \frac{23 \cdot 20}{10 \cdot 17} = \frac{23 \cdot 2}{17} = \frac{46}{17} \)
3. \( 2\frac{7}{23} = \frac{53}{23} \)
4. \( 1\frac{45}{46} = \frac{91}{46} \)
5. \( \frac{53}{23} - \frac{91}{46} = \frac{106 - 91}{46} = \frac{15}{46} \)
6. \( \frac{15}{46} - \frac{69}{80} = \frac{15 \cdot 40 - 69 \cdot 23}{1840} = \frac{600 - 1587}{1840} = -\frac{987}{1840} \)
7. \( -\frac{987}{1840} \cdot 1\frac{1}{3} = -\frac{987}{1840} \cdot \frac{4}{3} = -\frac{987 \cdot 4}{1840 \cdot 3} = -\frac{329 \cdot 4}{1840} = -\frac{329}{460} \)
8. \( \frac{46}{17} - ( -\frac{329}{460} ) = \frac{46}{17} + \frac{329}{460} = \frac{46 \cdot 460 + 329 \cdot 17}{17 \cdot 460} = \frac{21160 + 5593}{7820} = \frac{26753}{7820} \)

Ответ: \(\frac{26753}{7820}\).