a: \(-\dfrac{5}{7}+\dfrac{11}{13}+\dfrac{5}{7}=\left(-\dfrac{5}{7}+\dfrac{5}{7}\right)+\dfrac{11}{13}=0+\dfrac{11}{13}=\dfrac{11}{13}\)
b: \(2+\left(\dfrac{8}{11}+\dfrac{3}{11}\right)=2+\dfrac{11}{11}=2+1=3\)
c: \(\dfrac{-5}{21}+\dfrac{-2}{21}+\dfrac{8}{24}\)
\(=\dfrac{-5-2}{21}+\dfrac{1}{3}\)
\(=-\dfrac{7}{21}+\dfrac{1}{3}=\dfrac{1}{3}-\dfrac{1}{3}=0\)
d: \(\dfrac{1}{3}+\dfrac{-2}{6}+\dfrac{-3}{9}=\dfrac{1}{3}-\dfrac{1}{3}-\dfrac{1}{3}=-\dfrac{1}{3}\)
e: \(\dfrac{5}{12}+\dfrac{5}{3}+\dfrac{2}{12}+\dfrac{2}{3}\)
\(=\left(\dfrac{5}{12}+\dfrac{2}{12}\right)+\left(\dfrac{5}{3}+\dfrac{2}{3}\right)\)
\(=\dfrac{7}{12}+\dfrac{7}{3}\)
\(=\dfrac{7+28}{12}=\dfrac{35}{12}\)
f: \(\dfrac{4}{7}+\dfrac{3}{4}+\dfrac{2}{7}+\dfrac{5}{4}+\dfrac{1}{7}\)
\(=\left(\dfrac{4}{7}+\dfrac{2}{7}+\dfrac{1}{7}\right)+\left(\dfrac{3}{4}+\dfrac{5}{4}\right)\)
\(=\dfrac{7}{7}+\dfrac{8}{4}=2+1=3\)
g: \(\dfrac{1}{28}+\dfrac{-1}{14}+\dfrac{3}{28}+\dfrac{-1}{7}+\dfrac{3}{14}\)
\(=\left(\dfrac{1}{28}+\dfrac{3}{28}\right)+\left(-\dfrac{1}{14}+\dfrac{3}{14}\right)+\dfrac{-1}{7}\)
\(=\dfrac{1}{7}-\dfrac{1}{7}+\dfrac{2}{14}=\dfrac{1}{7}\)
h: \(\dfrac{5}{13}+\dfrac{-5}{7}+\dfrac{-20}{41}+\dfrac{8}{13}+\dfrac{-21}{41}\)
\(=\left(\dfrac{5}{13}+\dfrac{8}{13}\right)+\left(-\dfrac{20}{41}-\dfrac{21}{41}\right)+\dfrac{-5}{7}\)
\(=1-1-\dfrac{5}{7}=-\dfrac{5}{7}\)
i: \(\dfrac{-4}{12}+\dfrac{18}{45}+\dfrac{-6}{9}+\dfrac{24}{30}\)
\(=\left(-\dfrac{1}{3}-\dfrac{2}{3}\right)+\left(\dfrac{2}{5}+\dfrac{4}{5}\right)\)
\(=\dfrac{6}{5}-1=\dfrac{1}{5}\)
