Решение карточки №10 с дробями

Карточка №10. Найдите значение выражения: 1. \(\frac{1}{10} - \frac{23}{20} = \frac{2}{20} - \frac{23}{20} = -\frac{21}{20} = -1,05\) 2. \(\frac{5}{2} + \frac{1}{5} = 2,5 + 0,2 = 2,7\) 3. \(\frac{8}{5 \cdot 4} = \frac{8}{20} = \frac{4}{10} = 0,4\) 4. \(\frac{1}{1 + \frac{1}{4}} = \frac{1}{\frac{5}{4}} = \frac{4}{5} = 0,8\) 5. \(\frac{1}{\frac{1}{36} + \frac{1}{45}} = \frac{1}{\frac{5}{180} + \frac{4}{180}} = \frac{1}{\frac{9}{180}} = \frac{180}{9} = 20\) 6. \((\frac{8}{33} + \frac{13}{22}) : \frac{5}{18} = (\frac{16}{66} + \frac{39}{66}) \cdot \frac{18}{5} = \frac{55}{66} \cdot \frac{18}{5} = \frac{5}{6} \cdot \frac{18}{5} = \frac{18}{6} = 3\) 7. \((2\frac{1}{16} - 1\frac{1}{14}) \cdot 28 = (\frac{33}{16} - \frac{15}{14}) \cdot 28 = \frac{33 \cdot 28}{16} - \frac{15 \cdot 28}{14} = \frac{33 \cdot 7}{4} - 15 \cdot 2 = \frac{231}{4} - 30 = 57,75 - 30 = 27,75\) 8. \(4\frac{3}{4} : (1\frac{1}{15} + \frac{3}{5}) = \frac{19}{4} : (\frac{16}{15} + \frac{9}{15}) = \frac{19}{4} : \frac{25}{15} = \frac{19}{4} : \frac{5}{3} = \frac{19}{4} \cdot \frac{3}{5} = \frac{57}{20} = 2,85\) 9. \(9 \cdot (\frac{1}{9})^2 - 19 \cdot \frac{1}{9} = 9 \cdot \frac{1}{81} - \frac{19}{9} = \frac{1}{9} - \frac{19}{9} = -\frac{18}{9} = -2\) 10. \((\frac{19}{25} - \frac{7}{13}) \cdot \frac{13}{12} = \frac{19 \cdot 13 - 7 \cdot 25}{25 \cdot 13} \cdot \frac{13}{12} = \frac{247 - 175}{25 \cdot 13} \cdot \frac{13}{12} = \frac{72}{25 \cdot 13} \cdot \frac{13}{12} = \frac{72}{25 \cdot 12} = \frac{6}{25} = 0,24\)