math rational numbers

what is six and one over three -four and five over six 

 

$$6\frac{1}{3}-4\frac{5}{6}\\\\
=6+\frac{1}{3}-4-\frac{5}{6}\\\\
=2+\frac{1*2}{3*2}-\frac{5}{6}\\\\
=2+\frac{2}{6}-\frac{5}{6}\\\\
=2+\frac{2-5}{6}\\\\
=2+\frac{-3}{6}\\\\
=2+\frac{-1}{2}\\\\
=2+-\frac{1}{2}\\\\
=2-\frac{1}{2}\\\\
=1\frac{1}{2}\\\\$$