8. а) \(\left(13\frac{1}{4}-2\frac{5}{27}-10\frac{5}{6}\right)\cdot230\frac{1}{25}-41\frac{1}{4}+20013\); б) \(3\frac{1}{8}:\left[\left(7\frac{5}{12}-6\frac{13}{24}\right)\times\frac{4}{7}+\left(9\frac{1}{18}-8\frac{7}{12}\right):2\frac{3}{7}\right]+2\frac{3}{7}\times4\); в) \(\left[2\frac{1}{28}\times5-\left(2\frac{11}{12}\times\frac{1}{2}+7\frac{11}{12}\right)\right]:\frac{5}{16}+\left(28-31\frac{1}{2}\times\frac{2}{3}\right)\).

а) \(13\frac{1}{4}-2\frac{5}{27}-10\frac{5}{6}=\frac{53}{4}-\frac{59}{27}-\frac{65}{6}=-\frac{1223}{108}\).

\(230\frac{1}{25}=\frac{5751}{25}\), поэтому \(-\frac{1223}{108}\cdot\frac{5751}{25}-\frac{165}{4}+20013=\frac{744805}{108}\).

Ответ: \(\frac{744805}{108}=6896\frac{37}{108}\).

б) \(7\frac{5}{12}-6\frac{13}{24}=\frac{13}{24}\), \(\frac{13}{24}\cdot\frac47=\frac{13}{42}\).

\(9\frac{1}{18}-8\frac{7}{12}=\frac{11}{36}\), а \(\frac{11}{36}:2\frac37=\frac{11}{36}:\frac{17}{7}=\frac{77}{612}\).

В скобках: \(\frac{13}{42}+\frac{77}{612}=\frac{131}{204}\). Тогда \(3\frac18:\frac{131}{204}=\frac{25}{8}\cdot\frac{204}{131}=\frac{1275}{262}\).

\(2\frac37\cdot4=\frac{17}{7}\cdot4=\frac{68}{7}\), следовательно, значение выражения равно \(\frac{1275}{262}+\frac{68}{7}=\frac{17873}{1834}\).

Ответ: \(\frac{17873}{1834}\).

в) \(2\frac{1}{28}\cdot5=\frac{57}{28}\cdot5=\frac{285}{28}\).

\(2\frac{11}{12}\cdot\frac12+7\frac{11}{12}=\frac{35}{12}\cdot\frac12+\frac{95}{12}=\frac{65}{8}\).

В квадратных скобках: \(\frac{285}{28}-\frac{65}{8}=\frac{55}{56}\). Делим на \(\frac5{16}\): \(\frac{55}{56}:\frac5{16}=\frac{22}{7}\).

\(28-31\frac12\cdot\frac23=28-\frac{63}{2}\cdot\frac23=28-21=7\).

Ответ: \(\frac{22}{7}+7=\frac{71}{7}=10\frac17\).