Найдите значение выражений: 1) \(15\frac{4}{9}-4\frac{4}{9}\cdot3\frac{2}{8}\); 2) \(\frac{81}{88}\cdot\left(6-1\frac{13}{15}\cdot1\frac{19}{21}\right)\); 3) \(\left(5\frac{1}{16}-1\frac{1}{8}\right)\cdot\left(\frac{5}{6}+\frac{3}{14}\right)\); 4) \(5\frac{1}{16}-1\frac{1}{8}\cdot\left(\frac{5}{6}+\frac{3}{14}\right)\).

Преобразуем смешанные числа в неправильные дроби:

\(15\frac{4}{9}=\frac{139}{9}\), \(4\frac{4}{9}=\frac{40}{9}\), \(3\frac{2}{8}=\frac{13}{4}\).

\[\frac{139}{9}-\frac{40}{9}\cdot\frac{13}{4}=\frac{139}{9}-\frac{130}{9}=\frac{9}{9}=1.\]

Ответ: 1.

\(1\frac{13}{15}=\frac{28}{15}\), \(1\frac{19}{21}=\frac{40}{21}\).

\[\frac{81}{88}\cdot\left(6-\frac{28}{15}\cdot\frac{40}{21}\right)=\frac{81}{88}\cdot\left(6-\frac{224}{63}\right).\]

\[6-\frac{224}{63}=\frac{378-224}{63}=\frac{154}{63}=\frac{22}{9}.\]

\[\frac{81}{88}\cdot\frac{22}{9}=\frac{9\cdot22}{88}=\frac{9}{4}=2\frac{1}{4}.\]

Ответ: \(2\frac{1}{4}\).

\[5\frac{1}{16}-1\frac{1}{8}=\frac{81}{16}-\frac{9}{8}=\frac{81}{16}-\frac{18}{16}=\frac{63}{16}.\]

\[\frac{5}{6}+\frac{3}{14}=\frac{35}{42}+\frac{9}{42}=\frac{44}{42}=\frac{22}{21}.\]

\[\frac{63}{16}\cdot\frac{22}{21}=\frac{3\cdot22}{16}=\frac{66}{16}=\frac{33}{8}=4\frac{1}{8}.\]

Ответ: \(4\frac{1}{8}\).

Сначала вычислим значение в скобках:

\[\frac{5}{6}+\frac{3}{14}=\frac{22}{21}.\]

\[1\frac{1}{8}\cdot\frac{22}{21}=\frac{9}{8}\cdot\frac{22}{21}=\frac{33}{28}.\]

\[5\frac{1}{16}-\frac{33}{28}=\frac{81}{16}-\frac{33}{28}=\frac{567-132}{112}=\frac{435}{112}=3\frac{99}{112}.\]

Ответ: \(3\frac{99}{112}\).