1. Найдите значение выражения: 1) \(9\frac{1}{4}\cdot8-3\frac{2}{3}\cdot4\frac{1}{2}-10\frac{4}{5}\cdot4\frac{7}{12}\); 2) \(1\frac{1}{22}\cdot3\frac{2}{3}-\left(2\frac{5}{6}+3\frac{5}{6}\cdot\frac{7}{23}\right)\cdot\frac{3}{5}\); 3) \(\left(3\frac{1}{4}+2\frac{1}{6}\right)\cdot2\frac{3}{5}:\frac{2}{3}:\frac{4}{9}\); 4) \(\left(5.07:\frac{1}{20}-23.4\cdot\frac{13}{50}\right)\cdot\frac{1}{4}+0.07\).

1) \(9\frac{1}{4}\cdot8-3\frac{2}{3}\cdot4\frac{1}{2}-10\frac{4}{5}\cdot4\frac{7}{12}\)

Преобразуем смешанные числа: \(\frac{37}{4}\cdot8-\frac{11}{3}\cdot\frac{9}{2}-\frac{54}{5}\cdot\frac{55}{12}\).

\(=74-\frac{33}{2}-\frac{99}{4}=\frac{296-66-99}{4}=\frac{131}{4}=32\frac{3}{4}\).

2) \(1\frac{1}{22}\cdot3\frac{2}{3}-\left(2\frac{5}{6}+3\frac{5}{6}\cdot\frac{7}{23}\right)\cdot\frac{3}{5}\)

\(=\frac{23}{22}\cdot\frac{11}{3}-\left(\frac{17}{6}+\frac{23}{6}\cdot\frac{7}{23}\right)\cdot\frac{3}{5}\)

\(=\frac{23}{6}-\left(\frac{17}{6}+\frac{7}{6}\right)\cdot\frac{3}{5}=\frac{23}{6}-4\cdot\frac{3}{5}=\frac{23}{6}-\frac{12}{5}=\frac{43}{30}=1\frac{13}{30}\).

3) \(\left(3\frac{1}{4}+2\frac{1}{6}\right)\cdot2\frac{3}{5}:\frac{2}{3}:\frac{4}{9}\)

\(=\left(\frac{13}{4}+\frac{13}{6}\right)\cdot\frac{13}{5}\cdot\frac{3}{2}\cdot\frac{9}{4}\)

\(=\frac{65}{12}\cdot\frac{13}{5}\cdot\frac{3}{2}\cdot\frac{9}{4}=\frac{1521}{32}=47\frac{17}{32}\).

4) \(\left(5.07:\frac{1}{20}-23.4\cdot\frac{13}{50}\right)\cdot\frac{1}{4}+0.07\)

\(=(5.07\cdot20-23.4\cdot0.26)\cdot0.25+0.07\)

\(=(101.4-6.084)\cdot0.25+0.07=95.316\cdot0.25+0.07=23.829+0.07=23.899\).

Ответ: 1) \(32\frac{3}{4}\); 2) \(1\frac{13}{30}\); 3) \(47\frac{17}{32}\); 4) \(23.899\).