\(\dfrac{1}{2}+\dfrac{13}{19}-\dfrac{4}{9}+\dfrac{6}{19}+\dfrac{5}{18}\)
\(=\dfrac{1}{2}+\left(\dfrac{13}{19}+\dfrac{6}{19}\right)+\left(\dfrac{5}{18}-\dfrac{4}{9}\right)\)
\(=\dfrac{1}{2}+\dfrac{19}{19}+\left(\dfrac{5}{18}-\dfrac{8}{18}\right)\)
\(=\dfrac{1}{2}+1+\dfrac{-3}{18}\)
\(=\dfrac{1}{2}+1-\dfrac{1}{6}\)
\(=\dfrac{3}{6}+\dfrac{6}{6}-\dfrac{1}{6}\)
\(=\dfrac{8}{6}=\dfrac{4}{3}\)