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August 2022 1 17 Report

выполните действия и запишите результат в виде k/n (k-целое число, n - натуральное число): 1) -5/7+8/21; 2) -1/2 - 1/3 - 1/6; 3) 3/9*(-3/4); 4) 2 9/13 + (-3 4/13); 5) 2/3 - 1/5 + 4/15; 6) -2 2/3 * (-1 1/8); 7) -1/2 - 1/3 - 1/6; 8) -2/9 - (-1/3); 9) 2/3 : (-5/9)

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Ответ:

$\displaystyle -\frac{5}{7}+\frac{8}{21} =-\frac{5*3}{7*3}+\frac{8}{21} =-\frac{15}{21}+\frac{8}{21} =\frac{-15+8}{21}=-\frac{7}{21}=\frac{-1}{3}$

$\displaystyle -\frac{1}{2}-\frac{1}{3}-\frac{1}{6} =-\frac{1*3}{2*3}-\frac{1*2}{3*2}-\frac{1}{6} =-\frac{3}{6}-\frac{2}{6}-\frac{1}{6} =\frac{-3-2-1}{6}=-\frac{6}{6}=\frac{-1}{1}$

$\displaystyle \frac{3}{9}*(-\frac{3}{4})=-\frac{3*3}{9*4}=-\frac{9}{9*4}=\frac{-1}{4}$

$\displaystyle 2\frac{9}{13}+(-3\frac{4}{13})=\frac{9}{13}-1\frac{4}{13}=\frac{9}{13}-\frac{17}{13}=\frac{9-17}{13}=\frac{-8}{13}$

$\displaystyle \frac{2}{3}-\frac{1}{5}+\frac{4}{15}=\frac{2*5}{3*5}-\frac{1*3}{5*3}+\frac{4}{15}=\frac{10}{15}-\frac{3}{15}+\frac{4}{15}=\frac{10-3+4}{15}=\frac{11}{13}$

$\displaystyle -2\frac{2}{3}*(-1\frac{1}{8})=-\frac{8}{3}*(-\frac{9}{8})=\frac{8*9}{3*8}=\frac{9}{3}=\frac{3}{1}$

$\displaystyle -\frac{1}{2}-\frac{1}{3}-\frac{1}{6} =-\frac{1*3}{2*3}-\frac{1*2}{3*2}-\frac{1}{6} =-\frac{3}{6}-\frac{2}{6}-\frac{1}{6} =\frac{-3-2-1}{6}=-\frac{6}{6}=\frac{-1}{1}$

$\displaystyle -\frac{2}{9}-(-\frac{1}{3})=-\frac{2}{9}+\frac{1}{3}=-\frac{2}{9}+\frac{1*3}{3*3}=-\frac{2}{9}+\frac{3}{9}=\frac{-2+3}{9}=\frac{1}{9}$

$\displaystyle \frac{2}{3}:\frac{-5}{9}=-\frac{2}{3}*\frac{9}{5}=-\frac{2*9}{3*5}=-\frac{2*3}{5}=\frac{-6}{5}$

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