Тренажер по теме «Действия с обыкновенными дробями». Вычислите: (6/5 - 3/4) * 2/3

1. $(\frac{6}{5} - \frac{3}{4}) \cdot \frac{2}{3} = (\frac{24 - 15}{20}) \cdot \frac{2}{3} = \frac{9}{20} \cdot \frac{2}{3} = \frac{3 \cdot 1}{10 \cdot 1} = \frac{3}{10} = 0,3$ 2. $(\frac{6}{5} - \frac{2}{3}) \cdot \frac{1}{2} = (\frac{18 - 10}{15}) \cdot \frac{1}{2} = \frac{8}{15} \cdot \frac{1}{2} = \frac{4}{15}$ 3. $\frac{11}{18} - \frac{4}{9} \cdot \frac{3}{16} = \frac{11}{18} - \frac{1 \cdot 1}{3 \cdot 4} = \frac{11}{18} - \frac{1}{12} = \frac{22 - 3}{36} = \frac{19}{36}$ 4. $\frac{29}{30} - \frac{5}{6} \cdot \frac{18}{25} = \frac{29}{30} - \frac{1 \cdot 3}{1 \cdot 5} = \frac{29}{30} - \frac{3}{5} = \frac{29 - 18}{30} = \frac{11}{30}$ 5. $\frac{8}{5} \cdot (\frac{3}{4} + \frac{11}{8}) = \frac{8}{5} \cdot (\frac{6 + 11}{8}) = \frac{8}{5} \cdot \frac{17}{8} = \frac{17}{5}$ Ответ: $\frac{17}{5}$ 6. $\frac{18}{7} \cdot (\frac{4}{9} + \frac{15}{18}) = \frac{18}{7} \cdot (\frac{8 + 15}{18}) = \frac{18}{7} \cdot \frac{23}{18} = \frac{23}{7}$ 7. $\frac{8}{5} \cdot \frac{3}{4} + \frac{11}{8} = \frac{2 \cdot 3}{5 \cdot 1} + \frac{11}{8} = \frac{6}{5} + \frac{11}{8} = \frac{48 + 55}{40} = \frac{103}{40}$ 8. $\frac{18}{7} \cdot \frac{4}{9} + \frac{15}{14} = \frac{2 \cdot 4}{7 \cdot 1} + \frac{15}{14} = \frac{8}{7} + \frac{15}{14} = \frac{16 + 15}{14} = \frac{31}{14}$ 9. $15 \cdot (1 + \frac{1}{3} - \frac{1}{5}) = 15 + 15 \cdot \frac{1}{3} - 15 \cdot \frac{1}{5} = 15 + 5 - 3 = 17$ 10. $72 \cdot (\frac{19}{24} - \frac{7}{12} + \frac{3}{8}) = 72 \cdot \frac{19}{24} - 72 \cdot \frac{7}{12} + 72 \cdot \frac{3}{8} = 3 \cdot 19 - 6 \cdot 7 + 9 \cdot 3 = 57 - 42 + 27 = 42$ 11. $\frac{72}{73} \cdot \frac{34}{65} + \frac{72}{73} \cdot \frac{39}{65} = \frac{72}{73} \cdot (\frac{34}{65} + \frac{39}{65}) = \frac{72}{73} \cdot \frac{73}{65} = \frac{72}{65}$ 12. $\frac{107}{89} \cdot \frac{64}{70} + \frac{107}{89} \cdot \frac{25}{70} = \frac{107}{89} \cdot (\frac{64 + 25}{70}) = \frac{107}{89} \cdot \frac{89}{70} = \frac{107}{70}$ 13. $\frac{45}{46} \cdot \frac{49}{51} - \frac{45}{34} \cdot \frac{3}{51} = \frac{45}{46} \cdot \frac{49}{51} - \frac{45}{1} \cdot \frac{1}{17 \cdot 2} \cdot \frac{3}{51} = \text{Для упрощения вынесем } \frac{45}{51}: \frac{45}{51} \cdot (\frac{49}{46} - \frac{3}{34}) = \frac{15}{17} \cdot (\frac{49 \cdot 17 - 3 \cdot 23}{782}) = \frac{15}{17} \cdot (\frac{833 - 69}{782}) = \frac{15}{17} \cdot \frac{764}{782} = \frac{15}{17} \cdot \frac{382}{391} = \frac{5730}{6647}$ 14. $\frac{45}{74} \cdot \frac{3}{55} - \frac{46}{34} \cdot \frac{3}{48} = \text{Вычисления громоздки, проверим опечатки в условии. При прямом расчете: } \frac{27}{814} - \frac{23}{17} \cdot \frac{1}{16} = \frac{27}{814} - \frac{23}{272} = \frac{27 \cdot 136 - 23 \cdot 407}{110704} = \frac{3672 - 9361}{110704} = -\frac{5689}{110704}$