Вопрос:

1. Вычислите: (6/5 - 3/4) * 2/3.

Фотография

Ответ ассистента

1. $(\frac{6}{5} - \frac{3}{4}) \cdot \frac{2}{3} = (\frac{24}{20} - \frac{15}{20}) \cdot \frac{2}{3} = \frac{9}{20} \cdot \frac{2}{3} = \frac{3}{10} = 0.3$ 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. $\frac{11}{18} - \frac{4}{9} \cdot \frac{3}{16} = \frac{11}{18} - \frac{1 \cdot 1}{3 \cdot 4} = \frac{11}{18} - \frac{1}{12} = \frac{22}{36} - \frac{3}{36} = \frac{19}{36}$ 4. $\frac{29}{30} - \frac{5}{18} \cdot \frac{6}{25} = \frac{29}{30} - \frac{1 \cdot 1}{3 \cdot 5} = \frac{29}{30} - \frac{1}{15} = \frac{29}{30} - \frac{2}{30} = \frac{27}{30} = \frac{9}{10} = 0.9$ 5. $\frac{8}{5} \cdot (\frac{3}{4} + \frac{11}{8}) = \frac{8}{5} \cdot (\frac{6}{8} + \frac{11}{8}) = \frac{8}{5} \cdot \frac{17}{8} = \frac{17}{5} = 3.4$ 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. $\frac{8}{5} \cdot \frac{3}{4} + \frac{11}{8} = \frac{2 \cdot 3}{5 \cdot 1} + \frac{11}{8} = \frac{6}{5} + \frac{11}{8} = \frac{48}{40} + \frac{55}{40} = \frac{103}{40} = 2.575$ 8. $2\frac{4}{9} : (\frac{2}{3} - \frac{2}{7}) = \frac{22}{9} : (\frac{14}{21} - \frac{6}{21}) = \frac{22}{9} : \frac{8}{21} = \frac{22}{9} \cdot \frac{21}{8} = \frac{11 \cdot 7}{3 \cdot 4} = \frac{77}{12} = 6\frac{5}{12}$ 9. $1\frac{5}{6} : (\frac{2}{3} - \frac{2}{7}) = \frac{11}{6} : \frac{8}{21} = \frac{11}{6} \cdot \frac{21}{8} = \frac{11 \cdot 7}{2 \cdot 8} = \frac{77}{16} = 4\frac{13}{16}$ 10. $\frac{2}{7} + \frac{3}{8} : \frac{7}{32} = \frac{2}{7} + \frac{3}{8} \cdot \frac{32}{7} = \frac{2}{7} + \frac{3 \cdot 4}{1 \cdot 7} = \frac{2}{7} + \frac{12}{7} = \frac{14}{7} = 2$ 11. $\frac{35}{24} : \frac{15}{32} - 3 = \frac{35}{24} \cdot \frac{32}{15} - 3 = \frac{7 \cdot 4}{3 \cdot 3} - 3 = \frac{28}{9} - \frac{27}{9} = \frac{1}{9}$ 12. $2 - \frac{15}{28} : \frac{10}{21} = 2 - \frac{15}{28} \cdot \frac{21}{10} = 2 - \frac{3 \cdot 3}{4 \cdot 2} = 2 - \frac{9}{8} = \frac{16}{8} - \frac{9}{8} = \frac{7}{8}$ 13. $24 \cdot \frac{3}{64} - \frac{3}{4} = \frac{3 \cdot 3}{8} - \frac{3}{4} = \frac{9}{8} - \frac{6}{8} = \frac{3}{8}$ 14. $\frac{18}{35} : 12 + \frac{1}{10} = \frac{18}{35} \cdot \frac{1}{12} + \frac{1}{10} = \frac{3}{35 \cdot 2} + \frac{1}{10} = \frac{3}{70} + \frac{7}{70} = \frac{10}{70} = \frac{1}{7}$ 15. $\frac{3}{16} \cdot (\frac{4}{5} + \frac{8}{15}) = \frac{3}{16} \cdot (\frac{12}{15} + \frac{8}{15}) = \frac{3}{16} \cdot \frac{20}{15} = \frac{3}{16} \cdot \frac{4}{3} = \frac{1}{4} = 0.25$ 16. $\frac{27}{40} : 18 + \frac{9}{16} = \frac{27}{40} \cdot \frac{1}{18} + \frac{9}{16} = \frac{3}{40 \cdot 2} + \frac{9}{16} = \frac{3}{80} + \frac{45}{80} = \frac{48}{80} = \frac{3}{5} = 0.6$ 17. $1 - \frac{4}{7} : \frac{16}{21} = 1 - \frac{4}{7} \cdot \frac{21}{16} = 1 - \frac{3}{4} = \frac{1}{4} = 0.25$ 18. $\frac{11}{8} - \frac{15}{16} : \frac{25}{28} = \frac{11}{8} - \frac{15}{16} \cdot \frac{28}{25} = \frac{11}{8} - \frac{3 \cdot 7}{4 \cdot 5} = \frac{11}{8} - \frac{21}{20} = \frac{55}{40} - \frac{42}{40} = \frac{13}{40} = 0.325$ 19. $\frac{35}{39} \cdot \frac{13}{42} - \frac{1}{6} = \frac{5 \cdot 1}{3 \cdot 6} - \frac{1}{6} = \frac{5}{18} - \frac{3}{18} = \frac{2}{18} = \frac{1}{9}$ 20. $\frac{21}{26} : \frac{14}{39} - 2 = \frac{21}{26} \cdot \frac{39}{14} - 2 = \frac{3 \cdot 3}{2 \cdot 2} - 2 = \frac{9}{4} - \frac{8}{4} = \frac{1}{4} = 0.25$

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