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25/07/2023
25/07/2023
$ \begin{array}{l}
a/\ \left( -\dfrac{4}{15}\right) .\left( -\dfrac{3}{8}\right) .\dfrac{15}{-4} .8=-\dfrac{4.3.15.8}{15.8.4} =-3\\
b/\ ( -50)\left(\dfrac{1}{2} -\dfrac{1}{5} +\dfrac{1}{25}\right) +120.( -15) +20.( -120)\\
=\dfrac{-50}{2} +\dfrac{50}{5} -\dfrac{50}{25} -120.( 15+20)\\
=-25+10-2-120.35=-4217\\
c/\ 162.\left(\dfrac{\dfrac{1}{3} -\dfrac{1}{5} +\dfrac{1}{7}}{\dfrac{7}{3} -\dfrac{7}{5} +1} +\dfrac{\dfrac{6}{5} +\dfrac{6}{11} -\dfrac{6}{13}}{\dfrac{7}{5} +\dfrac{7}{11} -\dfrac{7}{13}}\right) :\dfrac{818181}{797979}\\
=162.\left(\dfrac{\dfrac{1}{3} -\dfrac{1}{5} +\dfrac{1}{7}}{7\left(\dfrac{1}{3} -\dfrac{1}{5} +\dfrac{1}{7}\right)} +\dfrac{6\left(\dfrac{1}{5} +\dfrac{1}{11} -\dfrac{1}{13}\right)}{7\left(\dfrac{1}{5} +\dfrac{1}{11} -\dfrac{1}{13}\right)}\right) :\dfrac{81.10101}{79.10101}\\
=162.\left(\dfrac{1}{7} +\dfrac{6}{7}\right) :\dfrac{81}{79} =162.\dfrac{79}{81} =158\\
d/\ \left(\dfrac{1}{2} -1\right)\left(\dfrac{1}{3} -1\right) ...\left(\dfrac{1}{2003} -1\right)\\
=\dfrac{-1}{2} .\dfrac{-2}{3} ....\dfrac{-2002}{2003} =( -1) .\dfrac{-2}{2} .\dfrac{-3}{3} ...\dfrac{-2002}{2002} .\dfrac{1}{2003}\\
=( -1)( -1) ...( -1) .\dfrac{1}{2003} =( -1)^{2002} .\dfrac{1}{2003} =\dfrac{1}{2003}\\
e/\ \left(\dfrac{13}{24} -\dfrac{29}{30}\right) :\left(\dfrac{-51}{3}\right)\\
=\dfrac{130-232}{240} .\dfrac{-3}{51} =\dfrac{-102}{240} .\dfrac{-3}{51} =\dfrac{102}{51} .\dfrac{3}{240}\\
=2.\dfrac{1}{80} =\dfrac{1}{40}\\
f/\ \dfrac{5}{31} .\dfrac{21}{25} .+\dfrac{5}{31} .\dfrac{-7}{16} -\dfrac{9}{20} .\dfrac{5}{31}\\
=\dfrac{5}{31} .\left(\dfrac{21}{25} -\dfrac{7}{16} -\dfrac{9}{20}\right) =\dfrac{5}{31} .\dfrac{336-175-180}{400}\\
=\dfrac{5}{31} .\dfrac{-19}{400} =\dfrac{-19}{2480}
\end{array}$
Hungoccho
25/07/2023
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