1. Найдите значение выражения: 1) 9 1/4 · 8 − 3 2/3 · 4 1/2 − 10 4/5 · 4 7/12; 2) 1 1/22 · 3 2/3 − (2 5/6 + 3 5/6 · 7/28) · 3/5; 3) (3 1/4 + 2 1/6) : 2 3/5 − 2/3 : 4/9.

1) Преобразуем смешанные числа в неправильные дроби:

\(9\frac{1}{4}=\frac{37}{4},\quad 3\frac{2}{3}=\frac{11}{3},\quad 4\frac{1}{2}=\frac{9}{2},\quad 10\frac{4}{5}=\frac{54}{5},\quad 4\frac{7}{12}=\frac{55}{12}.\)

\(\frac{37}{4}\cdot8-\frac{11}{3}\cdot\frac{9}{2}-\frac{54}{5}\cdot\frac{55}{12}=74-\frac{33}{2}-\frac{99}{2}=74-66=8.\)

2) \(1\frac{1}{22}=\frac{23}{22},\quad 3\frac{2}{3}=\frac{11}{3},\quad 2\frac{5}{6}=\frac{17}{6},\quad 3\frac{5}{6}=\frac{23}{6}.\)

\(\frac{23}{22}\cdot\frac{11}{3}-\left(\frac{17}{6}+\frac{23}{6}\cdot\frac{7}{28}\right)\cdot\frac{3}{5}=\frac{23}{6}-\left(\frac{17}{6}+\frac{23}{24}\right)\cdot\frac{3}{5}.\)

\(\frac{17}{6}+\frac{23}{24}=\frac{91}{24},\quad \frac{91}{24}\cdot\frac{3}{5}=\frac{91}{40}.\)

\(\frac{23}{6}-\frac{91}{40}=\frac{460-273}{120}=\frac{187}{120}=1\frac{67}{120}.\)

3) \(3\frac{1}{4}+2\frac{1}{6}=\frac{13}{4}+\frac{13}{6}=\frac{65}{12}.\)

\(\frac{65}{12}:2\frac{3}{5}=\frac{65}{12}:\frac{13}{5}=\frac{25}{12}.\)

\(\frac{2}{3}:\frac{4}{9}=\frac{2}{3}\cdot\frac{9}{4}=\frac{3}{2}.\)

\(\frac{25}{12}-\frac{3}{2}=\frac{25}{12}-\frac{18}{12}=\frac{7}{12}.\)

Ответ: 1) 8; 2) \(1\frac{67}{120}\); 3) \(\frac{7}{12}\).