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a,\(=\frac{-5}{9}+\frac{8}{15}+\frac{-2}{11}+\frac{-4}{9}+\frac{7}{15}\)
\(\left(\frac{-5}{9}+\frac{-4}{9}\right)+\left(\frac{8}{15}+\frac{7}{15}\right)+\frac{-2}{11}\)
=-1+1+-2/11
=0+-2/11
=-2/11
b,\(=\left(\frac{5}{13}+\frac{8}{13}\right)+\left(\frac{-20}{41}+\frac{-21}{40}\right)+\frac{-5}{17}\)
=1+-1+-5/17
=0+-5/17
=-5/17
c,\(=\left(\frac{1}{5}+\frac{4}{5}\right)+\left(\frac{-2}{9}+-\frac{7}{9}\right)+\frac{16}{17}\)
=1+-1+16/17
=0+16/17
=16/17
d,\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{99}-\frac{1}{101}\)
\(=\frac{1}{3}-\frac{1}{101}=\frac{98}{303}\)
a.\(\frac{-5}{9}\)+\(\frac{8}{15}\)+\(\frac{-2}{11}\)+\(\frac{4}{-9}\)+\(\frac{7}{15}\)
=\(\frac{-5}{9}\)+\(\frac{4}{-9}\)+\(\frac{8}{15}\)+\(\frac{7}{15}\)+\(\frac{-2}{11}\)
=(\(\frac{-5}{9}\)+\(\frac{-4}{9}\))+(\(\frac{8}{15}\)+\(\frac{7}{15}\))+\(\frac{-2}{11}\)
=(-1)+1+\(\frac{-2}{11}\)
=0+\(\frac{-2}{11}\)
=\(\frac{-2}{11}\).
p) \(\frac{-5}{9}+\frac{8}{15}+\frac{-2}{11}+\frac{4}{-9}+\frac{7}{15}\)
\(=\left(\frac{-5}{9}+\frac{-4}{9}\right)+\left(\frac{8}{15}+\frac{7}{15}\right)+\frac{-2}{11}\)
\(=-1+1+\frac{-2}{11}\)
\(=-\frac{2}{11}\)
q) \(\frac{5}{13}+\frac{-5}{17}+\frac{-20}{41}+\frac{8}{13}+\frac{-21}{41}\)
\(=\left(\frac{5}{13}+\frac{8}{13}\right)+\left(\frac{-20}{41}+\frac{-21}{41}\right)+\frac{-5}{17}\)
\(=1+\left(-1\right)+\frac{-5}{17}=\frac{-5}{17}\)
r) \(\frac{1}{5}+\frac{-2}{9}+\frac{-7}{9}+\frac{4}{5}+\frac{16}{17}\)
\(=\left(\frac{1}{5}+\frac{4}{5}\right)+\left(\frac{-2}{9}+\frac{-7}{9}\right)+\frac{16}{17}\)
\(=1+\left(-1\right)+\frac{16}{17}=\frac{16}{17}\)
\(A=\frac{5}{13}+\left(-\frac{5}{7}\right)+\left(-\frac{20}{41}\right)+\frac{8}{13}+\left(-\frac{21}{41}\right)\)
\(A=\left(\frac{5}{13}+\frac{8}{13}\right)+\left[\left(-\frac{20}{41}\right)+\left(-\frac{21}{41}\right)\right]+\left(-\frac{5}{7}\right)\)
\(A=1+\left(-1\right)+\left(-\frac{5}{7}\right)\)
\(A=-\frac{5}{7}\)
\(B=-\frac{5}{9}+\frac{8}{15}+\left(-\frac{2}{11}\right)+\left(\frac{4}{-9}\right)+\frac{7}{15}\)
\(B=\left[\left(-\frac{5}{9}\right)+\left(-\frac{4}{9}\right)\right]+\left(\frac{8}{15}+\frac{7}{15}\right)+\left(-\frac{2}{11}\right)\)
\(B=-1+1+\left(-\frac{2}{11}\right)\)
\(B=-\frac{2}{11}\)
\(A=\frac{5}{13}+\frac{-5}{7}+\frac{-20}{41}+\frac{8}{13}+\frac{-21}{41}\)
\(=\left(\frac{5}{13}+\frac{8}{13}\right)-\left(\frac{20}{41}+\frac{21}{41}\right)-\frac{5}{7}\)
\(=1-1-\frac{5}{7}\)
\(=0-\frac{5}{7}=-\frac{5}{7}\)
\(B=-\frac{5}{9}+\frac{8}{15}+\frac{-2}{11}+\frac{4}{-9}+\frac{7}{15}\)
\(=\left(\frac{8}{15}+\frac{7}{15}\right)-\left(\frac{5}{9}+\frac{4}{9}\right)-\frac{2}{11}\)
\(=1-1-\frac{2}{11}\)
\(=0-\frac{2}{11}=-\frac{2}{11}\)