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

Решение:

1. $$15\frac{4}{9}-4\frac{4}{9}\cdot3\frac{3}{8}=15\frac{4}{9}-\frac{40}{9}\cdot\frac{27}{8}=15\frac{4}{9}-\frac{5\cdot3}{1\cdot1}=15\frac{4}{9}-15=\frac{4}{9}$$

   Ответ: $$\frac{4}{9}$$

2. $$\frac{81}{88}\cdot(6-1\frac{13}{15}\cdot1\frac{19}{21})=\frac{81}{88}\cdot(6-\frac{28}{15}\cdot\frac{40}{21})=\frac{81}{88}\cdot(6-\frac{4\cdot8}{3\cdot3})=\frac{81}{88}\cdot(6-\frac{32}{9})=\frac{81}{88}\cdot(\frac{54-32}{9})=\frac{81}{88}\cdot\frac{22}{9}=\frac{9\cdot1}{4\cdot1}=\frac{9}{4}=2\frac{1}{4}$$

   Ответ: $$2\frac{1}{4}$$

3. $$ (5\frac{1}{16}-1\frac{1}{8})\cdot(\frac{5}{6}+\frac{3}{14})= (5\frac{1}{16}-1\frac{2}{16})\cdot(\frac{5}{6}+\frac{3}{14}) = 3\frac{15}{16} \cdot (\frac{35}{42} + \frac{9}{42}) = \frac{63}{16} \cdot \frac{44}{42} = \frac{9}{8} \cdot \frac{11}{6} = \frac{3}{8} \cdot \frac{11}{2} = \frac{33}{16} = 2\frac{1}{16} $$

   Ответ: $$2\frac{1}{16}$$

4. $$5\frac{1}{16}-1\frac{1}{8}\cdot(\frac{5}{6}+\frac{3}{14}) = 5\frac{1}{16} - 1\frac{1}{8} \cdot (\frac{35}{42} + \frac{9}{42}) = 5\frac{1}{16} - \frac{9}{8} \cdot \frac{44}{42} = 5\frac{1}{16} - \frac{9}{8} \cdot \frac{22}{21} = 5\frac{1}{16} - \frac{3}{4} \cdot \frac{11}{7} = 5\frac{1}{16} - \frac{33}{28} = 5\frac{1}{16} - 1\frac{5}{28} = 5\frac{7}{112} - 1\frac{20}{112} = 3\frac{99}{112} $$

   Ответ: $$3\frac{99}{112}$$