[tex]\displaystyle \frac{1}{2} +0,(2):\left(- \frac{2}{3} \right)+ \frac{1}{6} = \frac{1}{2} + \frac{2}{9} \cdot \left(- \frac{3}{2} \right)+ \frac{1}{6} = \frac{1}{2} - \frac{6}{18} + \frac{1}{6} = \\ \\ = \frac{9}{18} - \frac{6}{18} + \frac{3}{18} = \frac{3}{18} + \frac{3}{18} = \frac{6}{18} =\boxed{ \frac{1}{3} }[/tex]
