Вычислить:
$$ \frac{45\frac{10}{63} - 44\frac{25}{84}}{(2\frac{1}{3} - 1\frac{1}{9}) : 4 - \frac{3}{4}} : 31.$$
\( \frac{45\frac{10}{63} - 44\frac{25}{84}}{(2\frac{1}{3} - 1\frac{1}{9}) : 4 - \frac{3}{4}} : 31 = -\frac{1}{16}.\)
\(
1) 45\frac{10}{63} - 44\frac{25}{84} = 45\frac{40}{252} - 44\frac{75}{252} = 44 + 1 + \frac{40}{252} - 44 - \frac{75}{252} = 44 + \frac{252}{252} + \frac{40}{252} - 44 - \frac{75}{252} =
\)
\(
= 44 - 44 + \frac{252 + 40 - 75}{252} = \frac{217}{252} = \frac{31}{36};
\)
\(
2) 2\frac{1}{3} - 1\frac{1}{9} = 2\frac{3}{9} - 1\frac{1}{9} = 2 - 1 + \frac{3 - 1}{9} = 1 + \frac{2}{9} = 1\frac{2}{9};
\)
\(
3) 1\frac{2}{9} : 4 = \frac{11}{9} \cdot \frac{1}{4} = \frac{11 \cdot 1}{9 \cdot 4} = \frac{11}{36};
\)
\(
4) \frac{11}{36} - \frac{3}{4} = \frac{11}{36} - \frac{27}{36} = \frac{11 - 27}{36} = \frac{-16}{36} = -\frac{4}{9};
\)
\(
5) \frac{31}{36} : (-\frac{4}{9}) = -(\frac{31}{36} \cdot \frac{9}{4}) = -(\frac{31 \cdot 9}{36 \cdot 4}) = -(\frac{31 \cdot 1}{4 \cdot 4}) = -\frac{31}{16} = -1\frac{15}{16};
\)
\(
6) -1\frac{15}{16} : 31 = -(\frac{31}{16} \cdot \frac{1}{31}) = -(\frac{31 \cdot 1}{16 \cdot 31}) = -(\frac{1 \cdot 1}{16 \cdot 1}) = -\frac{1}{16}.
\)
Ответ: \(-\frac{1}{16}\).