a: \(A=\dfrac{1}{3}+\dfrac{-13}{21}+\dfrac{5}{7}+\dfrac{1}{6}+\dfrac{1}{14}+\dfrac{-1}{2}\)
\(=\left(-\dfrac{13}{21}+\dfrac{1}{14}+\dfrac{5}{7}\right)+\left(\dfrac{1}{3}+\dfrac{1}{6}-\dfrac{1}{2}\right)\)
\(=\dfrac{-26+3+35}{42}+\dfrac{2+1-3}{6}\)
\(=\dfrac{38-26}{42}=\dfrac{12}{42}=\dfrac{2}{7}\)
b: \(B=\dfrac{25}{31}+\dfrac{-3}{17}+\dfrac{6}{31}+\dfrac{5}{9}+\dfrac{-14}{17}+\dfrac{-1}{12}\)
\(=\left(\dfrac{25}{31}+\dfrac{6}{31}\right)+\left(-\dfrac{3}{17}-\dfrac{14}{17}\right)+\dfrac{5}{9}-\dfrac{1}{12}\)
\(=\dfrac{31}{31}+\dfrac{-17}{17}+\dfrac{20-3}{36}\)
\(=1-1+\dfrac{17}{36}=\dfrac{17}{36}\)
c: \(C=\dfrac{-5}{46}+\dfrac{-7}{25}+1\dfrac{16}{19}+\dfrac{5}{46}+\dfrac{-16}{19}+\dfrac{7}{25}\)
\(=\left(-\dfrac{5}{46}+\dfrac{5}{46}\right)+\left(-\dfrac{7}{25}+\dfrac{7}{25}\right)+\left(1+\dfrac{16}{19}-\dfrac{16}{19}\right)\)
\(=0+0+1=1\)
d: \(D=\dfrac{-2}{11}+\dfrac{-1}{6}+\dfrac{52}{264}+\dfrac{3}{22}+\dfrac{5}{24}+\dfrac{-7}{8}\)
\(=\left(-\dfrac{2}{11}+\dfrac{52}{264}+\dfrac{3}{22}\right)+\left(-\dfrac{1}{6}+\dfrac{5}{24}+\dfrac{-7}{8}\right)\)
\(=\left(\dfrac{-12}{66}+\dfrac{13}{66}+\dfrac{9}{66}\right)+\dfrac{-4+5-21}{24}\)
\(=\dfrac{10}{66}+\dfrac{-20}{24}=\dfrac{5}{33}-\dfrac{5}{6}=-\dfrac{15}{22}\)
