\(\frac{5}{9}+\frac{2}{3}+\frac{1}{-2}\)
\(=\frac{5}{9}\times1+\frac{2}{3}\times1+\frac{1}{-2}\times1\)
\(=\frac{5}{9}\times\frac{2}{2}+\frac{2}{3}\times\frac{6}{6}+\frac{1}{-2}\times\frac{-1}{-1}\)
\(=\frac{5\times2}{9\times2}+\frac{2\times6}{3\times6}+\frac{1\times\left(-1\right)}{-2\times\left(-1\right)}\)
\(=\frac{10}{18}+\frac{12}{18}+\frac{-1}{2}\)
\(=\left(\frac{10}{18}+\frac{12}{18}\right)+\frac{-1}{2}\)
\(=\frac{10+12}{18}+\frac{-1}{2}\)
\(=\frac{22}{18}+\frac{-1}{2}\)
\(=\frac{22}{18}+\frac{-9}{18}\)
\(=\frac{13}{18}\)
\(\frac{5}{9}+\frac{2}{3}+\frac{1}{-2}\)
\(=\frac{5}{9}+\frac{6}{9}+\frac{1}{-2}\)
\(=\frac{5+6}{9}+\frac{1}{-2}\)
\(=\frac{11}{9}+\frac{1}{-2}=\frac{(-22)+9}{-18}=\frac{-13}{-18}\)
\(\frac{5}{9}+\frac{2}{3}+\frac{1}{-2}\)
\(=\frac{5}{9}+\frac{2}{3}+\frac{-1}{2}\)
\(=\frac{15+18}{27}+\frac{-1}{2}\)
\(=\frac{11}{9}+\frac{-1}{2}=\frac{22+(-9)}{18}=\frac{13}{18}\)