[tex]\frac{1}{2} \times - 2 + \frac{1}{3} \times - 5 \\ \\ = \frac{1}{ \cancel2} \times \cancel{- 2} + \frac{1}{3} \times - 5 \\ \\ = 1 \times - 1 + \frac{1}{3} \times - 5 \\ \\ = - 1 + ( - \frac{5}{3} ) \\ \\ = - 1 - \frac{5}{3} \\ \\ = \frac{ - 3 - 5}{3} \\ \\ = \frac{ - 8}{3} = - 2 \frac{2}{3} [/tex]