\(a)\)
\(\dfrac{2}{5}+\dfrac{6}{11}+\left(-\dfrac{2}{5}\right)\)
\(=\dfrac{6}{11}+\left[\dfrac{2}{5}+\left(-\dfrac{2}{5}\right)\right]\)
\(=\dfrac{6}{11}+0\)
\(=\dfrac{6}{11}\)
\(b)\)
\(-\dfrac{4}{15}+\dfrac{6}{15}+\left(-\dfrac{2}{15}\right)+\dfrac{11}{2}\)
\(=\dfrac{11}{2}+\left[-\dfrac{4}{15}+\dfrac{6}{15}+\left(-\dfrac{2}{15}\right)\right]\)
\(=\dfrac{11}{2}+0\)
\(=\dfrac{11}{2}\)
\(c)\)
\(\dfrac{5}{13}+\dfrac{-5}{7}+\dfrac{-20}{41}+\dfrac{8}{13}+\dfrac{21}{-41}\)
\(=\dfrac{5}{13}+\dfrac{-5}{7}+\dfrac{-20}{41}+\dfrac{8}{13}+\dfrac{-21}{41}\)
\(=\dfrac{-5}{7}+\left(\dfrac{5}{13}+\dfrac{8}{13}\right)+\left(\dfrac{-20}{41}+\dfrac{-21}{41}\right)\)
\(=\dfrac{-5}{7}+1+\left(-1\right)\)
\(=\dfrac{2}{7}+\left(-1\right)\)
\(=\dfrac{-5}{7}\)
\(d)\)
\(\dfrac{-3}{8}+\dfrac{12}{25}+\dfrac{5}{-8}+\dfrac{2}{-5}+\dfrac{13}{25}\)
\(=\dfrac{-3}{8}+\dfrac{12}{25}+\dfrac{-5}{8}+\dfrac{-2}{5}+\dfrac{13}{25}\)
\(=\dfrac{-2}{5}+\left(\dfrac{-3}{8}+\dfrac{-5}{8}\right)+\left(\dfrac{12}{25}+\dfrac{13}{25}\right)\)
\(=\dfrac{-2}{5}+\left(-1\right)+1\)
\(=\dfrac{-7}{5}+1\)
\(=\dfrac{-2}{5}\)
