Тренажер по теме «Действия с обыкновенными дробями». Вычислите выражения.

1. $(\frac{6}{5} - \frac{3}{4}) \cdot \frac{2}{3} = (\frac{24}{20} - \frac{15}{20}) \cdot \frac{2}{3} = \frac{9}{20} \cdot \frac{2}{3} = \frac{3 \cdot 1}{10 \cdot 1} = \frac{3}{10} = 0,3$ 2. $(\frac{6}{5} - \frac{2}{3}) \cdot \frac{1}{2} = (\frac{18}{15} - \frac{10}{15}) \cdot \frac{1}{2} = \frac{8}{15} \cdot \frac{1}{2} = \frac{4}{15}$ 3. $\frac{11}{18} \cdot \frac{4}{9} \cdot \frac{3}{16} = \frac{11 \cdot 4 \cdot 3}{18 \cdot 9 \cdot 16} = \frac{11 \cdot 1 \cdot 1}{18 \cdot 3 \cdot 4} = \frac{11}{216}$ 4. $\frac{29}{30} \cdot \frac{5}{18} \cdot \frac{6}{25} = \frac{29 \cdot 5 \cdot 6}{30 \cdot 18 \cdot 25} = \frac{29 \cdot 30}{30 \cdot 18 \cdot 25} = \frac{29}{18 \cdot 25} = \frac{29}{450}$ 5. $\frac{8}{5} \cdot (\frac{3}{4} + \frac{11}{8}) = \frac{8}{5} \cdot (\frac{6}{8} + \frac{11}{8}) = \frac{8}{5} \cdot \frac{17}{8} = \frac{17}{5} = 3\frac{2}{5} = 3,4$ 6. $\frac{18}{7} \cdot (\frac{4}{9} + \frac{15}{18}) = \frac{18}{7} \cdot (\frac{8}{18} + \frac{15}{18}) = \frac{18}{7} \cdot \frac{23}{18} = \frac{23}{7} = 3\frac{2}{7}$ 7. $\frac{8}{5} \cdot \frac{3}{4} + \frac{11}{8} = \frac{2 \cdot 3}{5 \cdot 1} + \frac{11}{8} = \frac{6}{5} + \frac{11}{8} = \frac{48}{40} + \frac{55}{40} = \frac{103}{40} = 2\frac{23}{40} = 2,575$ 8. $\frac{18}{7} \cdot \frac{4}{9} + \frac{15}{14} = \frac{2 \cdot 4}{7 \cdot 1} + \frac{15}{14} = \frac{8}{7} + \frac{15}{14} = \frac{16}{14} + \frac{15}{14} = \frac{31}{14} = 2\frac{3}{14}$ 9. $15 \cdot (1 + \frac{1}{3} - \frac{1}{5}) = 15 \cdot 1 + 15 \cdot \frac{1}{3} - 15 \cdot \frac{1}{5} = 15 + 5 - 3 = 17$ 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. $\frac{72}{73} \cdot \frac{34}{65} + \frac{72}{73} \cdot \frac{39}{65} = \frac{72}{73} \cdot (\frac{34}{65} + \frac{39}{65}) = \frac{72}{73} \cdot \frac{73}{65} = \frac{72}{65} = 1\frac{7}{65}$ 12. $\frac{107}{89} \cdot \frac{34}{70} + \frac{107}{89} \cdot \frac{25}{70} = \frac{107}{89} \cdot (\frac{34}{70} + \frac{25}{70}) = \frac{107}{89} \cdot \frac{59}{70} = \frac{6313}{6230} = 1\frac{83}{6230}$