1) \(15 \frac{4}{9} - 4 \frac{4}{9} \cdot 3 \frac{3}{8} = \frac{139}{9} - \frac{40}{9} \cdot \frac{27}{8} = \frac{139}{9} - \frac{5 \cdot 3}{1 \cdot 1} = \frac{139}{9} - 15 = \frac{139}{9} - \frac{135}{9} = \frac{4}{9}\)
2) \(\frac{81}{88} \cdot (6 - 1 \frac{13}{15} \cdot \frac{19}{21}) = \frac{81}{88} \cdot (6 - \frac{28}{15} \cdot \frac{19}{21}) = \frac{81}{88} \cdot (6 - \frac{4 \cdot 19}{15 \cdot 3}) = \frac{81}{88} \cdot (6 - \frac{76}{45}) = \frac{81}{88} \cdot (\frac{270}{45} - \frac{76}{45}) = \frac{81}{88} \cdot \frac{194}{45} = \frac{9 \cdot 97}{44 \cdot 5} = \frac{873}{220} = 3 \frac{213}{220}\)
3) \((5 \frac{1}{16} - 1 \frac{1}{8}) \cdot (\frac{5}{6} + \frac{3}{14}) = (\frac{81}{16} - \frac{9}{8}) \cdot (\frac{35}{42} + \frac{9}{42}) = (\frac{81}{16} - \frac{18}{16}) \cdot \frac{44}{42} = \frac{63}{16} \cdot \frac{22}{21} = \frac{3 \cdot 11}{8 \cdot 1} = \frac{33}{8} = 4 \frac{1}{8}\)
4) \(5 \frac{1}{16} - 1 \frac{1}{8} \cdot (\frac{5}{6} + \frac{3}{14}) = \frac{81}{16} - \frac{9}{8} \cdot (\frac{35}{42} + \frac{9}{42}) = \frac{81}{16} - \frac{9}{8} \cdot \frac{44}{42} = \frac{81}{16} - \frac{9}{8} \cdot \frac{22}{21} = \frac{81}{16} - \frac{3 \cdot 11}{4 \cdot 7} = \frac{81}{16} - \frac{33}{28} = \frac{567}{112} - \frac{132}{112} = \frac{435}{112} = 3 \frac{105}{112} = 3 \frac{15}{16}\)
Ответ:
1) 4/9
2) 3 213/220
3) 4 1/8
4) 3 15/16
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