\(\dfrac{5}{9}:\dfrac{12}{9}+\dfrac{1}{2}=\dfrac{5}{12}+\dfrac{1}{2}=\dfrac{5}{12}+\dfrac{6}{12}=\dfrac{11}{12}\)
\(\dfrac{5}{9}:\dfrac{12}{9}+\dfrac{1}{2}=\dfrac{5}{9}x\dfrac{9}{12}+\dfrac{1}{2}=\dfrac{5}{12}+\dfrac{1}{2}=\dfrac{5}{12}+\dfrac{6}{12}=\dfrac{11}{12}\)
\(\dfrac{5}{9}:\dfrac{12}{9}+\dfrac{1}{2}=\dfrac{5}{9}\times\dfrac{9}{12}+\dfrac{1}{2}=\dfrac{5}{12}+\dfrac{1}{2}=\dfrac{5}{12}+\dfrac{6}{12}=\dfrac{11}{12}\)
\(= (\dfrac59 + \dfrac{12}9) x \dfrac21\)
\(= \dfrac{15}{9} x \dfrac21 = \dfrac{30}9\)