Упростить выражение: (8 2/3+5*1 1/8-10:2 2/3)/(8 1/2-5 3/4).

Ответ:

\[\frac{8\frac{2}{3} + 5 \cdot 1\frac{1}{8} - 10\ :2\frac{2}{3}}{8\frac{1}{2} - 5\frac{3}{4}} =\]

\[= \frac{8\frac{2}{3} + 5 \cdot \frac{9}{8} - 10\ :\frac{8}{3}}{\frac{17}{2} - \frac{23}{4}} =\]

\[= \frac{8\frac{2}{3} + \frac{45}{8} - 10 \cdot \frac{3}{8}}{\frac{34}{4} - \frac{23}{4}} =\]

\[= \frac{\frac{26}{3} + \frac{45}{8} - \frac{30}{8}}{\frac{11}{4}} =\]

\[= \frac{\frac{26^{\backslash 8}\ }{3} + \frac{15^{\backslash 3}}{8}}{\frac{11}{4}} =\]

\[= \frac{208 + 45}{24}\ :\frac{11}{4} = \frac{253}{24} \cdot \frac{4}{11} =\]

\[= \frac{23}{2} = 11,5.\]