[tex]1\dfrac{1}{3}+2\dfrac{2}{3}=1+\dfrac{1}{3}+2+\dfrac{2}{3}=(1+2)+\left(\dfrac{1}{3}+\dfrac{2}{3}\right)=3+\dfrac{1+2}{3}\\\\=3+\dfrac{3}{3}=3+1=4[/tex]
1-1/3 = 4/3
2-2/3 = 8/3
(4/3) + (8/3) = 12/3
But 12/3 = 4 .
The only way to make a mixed number out of 4 is to call it "4 and 0/3".
