Реши примеры с дробями: сложение, вычитание, умножение и деление дробей

Конечно, давай решим эти примеры! 1. $$\frac{4}{15} + \frac{3}{5} - \frac{5}{6} = \frac{8}{30} + \frac{18}{30} - \frac{25}{30} = \frac{8 + 18 - 25}{30} = \frac{1}{30}$$ 2. $$\frac{19}{36} + \frac{1}{9} - \frac{5}{8} = \frac{38}{72} + \frac{8}{72} - \frac{45}{72} = \frac{38 + 8 - 45}{72} = \frac{1}{72}$$ 3. $$\frac{12}{19} \cdot \frac{38}{72} \cdot \frac{1}{3} = \frac{12 \cdot 38 \cdot 1}{19 \cdot 72 \cdot 3} = \frac{12 \cdot 2 \cdot 1}{1 \cdot 6 \cdot 3} = \frac{24}{18} = \frac{4}{3}$$ 4. $$\frac{35}{78} \cdot \frac{26}{70} \cdot \frac{4}{7} = \frac{35 \cdot 26 \cdot 4}{78 \cdot 70 \cdot 7} = \frac{5 \cdot 2 \cdot 4}{6 \cdot 10 \cdot 7} = \frac{40}{420} = \frac{2}{21}$$ 5. $$\frac{18}{63} : \frac{90}{252} = \frac{18}{63} \cdot \frac{252}{90} = \frac{18 \cdot 252}{63 \cdot 90} = \frac{18 \cdot 4}{1 \cdot 90} = \frac{72}{90} = \frac{4}{5}$$ 6. $$\frac{54}{77} : \frac{81}{22} = \frac{54}{77} \cdot \frac{22}{81} = \frac{54 \cdot 22}{77 \cdot 81} = \frac{6 \cdot 2}{7 \cdot 9} = \frac{12}{63} = \frac{4}{21}$$ 7. $$(\frac{3}{5})^2 + \frac{14}{55} \cdot \frac{11}{42} - \frac{8}{75} = \frac{9}{25} + \frac{14 \cdot 11}{55 \cdot 42} - \frac{8}{75} = \frac{9}{25} + \frac{2 \cdot 1}{5 \cdot 6} - \frac{8}{75} = \frac{9}{25} + \frac{2}{30} - \frac{8}{75} = \frac{9}{25} + \frac{1}{15} - \frac{8}{75} = \frac{27}{75} + \frac{5}{75} - \frac{8}{75} = \frac{27 + 5 - 8}{75} = \frac{24}{75} = \frac{8}{25}$$ 8. $$(\frac{3}{4})^2 + \frac{7}{8} : \frac{21}{56} - \frac{11}{42} = \frac{9}{16} + \frac{7}{8} \cdot \frac{56}{21} - \frac{11}{42} = \frac{9}{16} + \frac{7 \cdot 56}{8 \cdot 21} - \frac{11}{42} = \frac{9}{16} + \frac{1 \cdot 7}{1 \cdot 3} - \frac{11}{42} = \frac{9}{16} + \frac{7}{3} - \frac{11}{42} = \frac{189}{336} + \frac{784}{336} - \frac{88}{336} = \frac{189 + 784 - 88}{336} = \frac{885}{336} = \frac{295}{112}$$ 9. $$\frac{1}{2} - \frac{21}{54} \cdot \frac{9}{42} + \frac{5}{64} : \frac{25}{32} = \frac{1}{2} - \frac{21 \cdot 9}{54 \cdot 42} + \frac{5}{64} \cdot \frac{32}{25} = \frac{1}{2} - \frac{1 \cdot 1}{6 \cdot 2} + \frac{1}{2 \cdot 5} = \frac{1}{2} - \frac{1}{12} + \frac{1}{10} = \frac{30}{60} - \frac{5}{60} + \frac{6}{60} = \frac{30 - 5 + 6}{60} = \frac{31}{60}$$ Надеюсь, теперь тебе всё понятно!