Выполни действия: 0.5 - 6/17

1. $0.5 - \frac{6}{17} = \frac{1}{2} - \frac{6}{17} = \frac{17}{34} - \frac{12}{34} = \frac{5}{34}$ 2. $7\frac{25}{32} + 1\frac{2}{21} + 8\frac{15}{32} + 8\frac{5}{21} = (7\frac{25}{32} + 8\frac{15}{32}) + (1\frac{2}{21} + 8\frac{5}{21}) = (7+8+\frac{25}{32} + \frac{15}{32}) + (1+8+\frac{2}{21} + \frac{5}{21}) = (15 + \frac{40}{32}) + (9 + \frac{7}{21}) = 15 + 1\frac{8}{32} + 9 + \frac{1}{3} = 16 + \frac{1}{4} + 9 + \frac{1}{3} = 25 + \frac{3}{12} + \frac{4}{12} = 25\frac{7}{12}$ 3. $8\frac{1}{5} + (k + 1\frac{3}{10}) = 9\frac{18}{23}$ $k + 1\frac{3}{10} = 9\frac{18}{23} - 8\frac{1}{5}$ $k + 1\frac{3}{10} = 9\frac{90}{115} - 8\frac{23}{115}$ $k + 1\frac{3}{10} = 1\frac{67}{115}$ $k = 1\frac{67}{115} - 1\frac{3}{10}$ $k = 1\frac{134}{230} - 1\frac{69}{230}$ $k = \frac{65}{230} = \frac{13}{46}$ 4. $54 \cdot \frac{5}{99} = \frac{54}{1} \cdot \frac{5}{99} = \frac{54 \cdot 5}{1 \cdot 99} = \frac{270}{99} = \frac{30}{11} = 2\frac{8}{11}$ 5. $\frac{2}{243} \cdot \frac{171}{4} = \frac{2 \cdot 171}{243 \cdot 4} = \frac{342}{972} = \frac{19}{54}$ 6. $1\frac{8}{11} \cdot 3\frac{9}{19} \cdot 3\frac{1}{3} = \frac{19}{11} \cdot \frac{66}{19} \cdot \frac{10}{3} = \frac{19 \cdot 66 \cdot 10}{11 \cdot 19 \cdot 3} = \frac{19 \cdot 6 \cdot 10}{19 \cdot 3} = 2 \cdot 10 = 20$ 7. $9\frac{5}{6} + 2\frac{3}{14} \cdot 2\frac{1}{3} = 9\frac{5}{6} + \frac{31}{14} \cdot \frac{7}{3} = 9\frac{5}{6} + \frac{31 \cdot 7}{14 \cdot 3} = 9\frac{5}{6} + \frac{31}{6} = 9\frac{5}{6} + 5\frac{1}{6} = 14\frac{6}{6} = 15$ 8. a) $(\frac{1}{2} + \frac{1}{3})(6\frac{7}{10} + 6\frac{1}{2}) = (\frac{3}{6} + \frac{2}{6})(6\frac{7}{10} + 6\frac{5}{10}) = \frac{5}{6} \cdot (12\frac{12}{10}) = \frac{5}{6} \cdot (13\frac{2}{10}) = \frac{5}{6} \cdot \frac{132}{10} = \frac{5 \cdot 132}{6 \cdot 10} = \frac{660}{60} = 11$ б) $\frac{1}{2} + \frac{1}{3}(6\frac{7}{10} + 6\frac{1}{2}) = \frac{1}{2} + \frac{1}{3}(6\frac{7}{10} + 6\frac{5}{10}) = \frac{1}{2} + \frac{1}{3} \cdot (12\frac{12}{10}) = \frac{1}{2} + \frac{1}{3} \cdot (13\frac{2}{10}) = \frac{1}{2} + \frac{1}{3} \cdot \frac{132}{10} = \frac{1}{2} + \frac{132}{30} = \frac{1}{2} + \frac{22}{5} = \frac{5}{10} + \frac{44}{10} = \frac{49}{10} = 4\frac{9}{10}$ 9. $\frac{1}{2} \cdot \frac{11}{24} \cdot \frac{32}{33} \cdot \frac{3}{4} = \frac{1 \cdot 11 \cdot 32 \cdot 3}{2 \cdot 24 \cdot 33 \cdot 4} = \frac{11 \cdot 32 \cdot 3}{2 \cdot 24 \cdot 33 \cdot 4} = \frac{11 \cdot 4 \cdot 3}{24 \cdot 33} = \frac{11 \cdot 1}{2 \cdot 11} = \frac{1}{2}$ 10. a) $(\frac{2}{3})^2 = \frac{2}{3} \cdot \frac{2}{3} = \frac{4}{9}$ б) $(2\frac{1}{2})^2 = (\frac{5}{2})^2 = \frac{5}{2} \cdot \frac{5}{2} = \frac{25}{4} = 6\frac{1}{4}$ 11. $(\frac{5}{6} + \frac{11}{12})^2 \cdot 9\frac{1}{7} = (\frac{10}{12} + \frac{11}{12})^2 \cdot 9\frac{1}{7} = (\frac{21}{12})^2 \cdot 9\frac{1}{7} = (\frac{7}{4})^2 \cdot 9\frac{1}{7} = \frac{49}{16} \cdot \frac{64}{7} = \frac{49 \cdot 64}{16 \cdot 7} = \frac{7 \cdot 4}{1} = 28$ 12. $\frac{14}{3} \cdot (\frac{11}{14} - \frac{1}{7}) = \frac{14}{3} \cdot (\frac{11}{14} - \frac{2}{14}) = \frac{14}{3} \cdot \frac{9}{14} = \frac{14 \cdot 9}{3 \cdot 14} = \frac{9}{3} = 3$ 13. $15 : \frac{3}{16} = \frac{15}{1} : \frac{3}{16} = \frac{15}{1} \cdot \frac{16}{3} = \frac{15 \cdot 16}{1 \cdot 3} = \frac{5 \cdot 16}{1} = 80$ 14. $\frac{1}{13} : \frac{3}{5} = \frac{1}{13} \cdot \frac{5}{3} = \frac{1 \cdot 5}{13 \cdot 3} = \frac{5}{39}$ 15. $3\frac{6}{7} : 7\frac{1}{2} = \frac{27}{7} : \frac{15}{2} = \frac{27}{7} \cdot \frac{2}{15} = \frac{27 \cdot 2}{7 \cdot 15} = \frac{9 \cdot 2}{7 \cdot 5} = \frac{18}{35}$