351. Найдите значение выражения: 1) 5 3/4 · 8 − 2 1/3 · 1 3/14 − 1 37/48 · 2 2/15; 2) 1 3/22 · 2 14/15 − (1 5/8 + 2 1/8 · 11/17) · 3/7; 3) 6 2/5 · 1 9/16 − (2 1/4)²; 4) (2 7/10 − 1 8/15)² · 9/14.

1)

Преобразуем смешанные числа в неправильные дроби:

\(5\frac{3}{4}=\frac{23}{4}\), \(2\frac{1}{3}=\frac{7}{3}\), \(1\frac{3}{14}=\frac{17}{14}\), \(1\frac{37}{48}=\frac{85}{48}\), \(2\frac{2}{15}=\frac{32}{15}\).

\[\frac{23}{4}\cdot 8-\frac{7}{3}\cdot\frac{17}{14}-\frac{85}{48}\cdot\frac{32}{15}=46-\frac{17}{6}-\frac{34}{9}.\]

\[46-\frac{17}{6}-\frac{34}{9}=\frac{828-51-68}{18}=\frac{709}{18}=39\frac{7}{18}.\]

2)

\[1\frac{3}{22}\cdot2\frac{14}{15}=\frac{25}{22}\cdot\frac{44}{15}=\frac{10}{3}.\]

В скобках:

\[1\frac{5}{8}+2\frac{1}{8}\cdot\frac{11}{17}=\frac{13}{8}+\frac{17}{8}\cdot\frac{11}{17}=\frac{13}{8}+\frac{11}{8}=3.\]

Тогда:

\[\frac{10}{3}-3\cdot\frac{3}{7}=\frac{10}{3}-\frac{9}{7}=\frac{70-27}{21}=\frac{43}{21}=2\frac{1}{21}.\]

3)

\[6\frac{2}{5}\cdot1\frac{9}{16}-\left(2\frac{1}{4}\right)^2=\frac{32}{5}\cdot\frac{25}{16}-\left(\frac{9}{4}\right)^2.\]

\[\frac{32}{5}\cdot\frac{25}{16}=10,\qquad \left(\frac{9}{4}\right)^2=\frac{81}{16}.\]

\[10-\frac{81}{16}=\frac{160-81}{16}=\frac{79}{16}=4\frac{15}{16}.\]

4)

\[2\frac{7}{10}-1\frac{8}{15}=\frac{27}{10}-\frac{23}{15}=\frac{81-46}{30}=\frac{7}{6}.\]

\[\left(\frac{7}{6}\right)^2\cdot\frac{9}{14}=\frac{49}{36}\cdot\frac{9}{14}=\frac{7}{8}.\]

Ответ: 1) \(39\frac{7}{18}\); 2) \(2\frac{1}{21}\); 3) \(4\frac{15}{16}\); 4) \(\frac{7}{8}\).