John, Karen, and Luke collected cans of vegetables for a food drive. The number of cans that John collected was ~$\frac{1}{2}$~ the number of cans that Karen collected and ~$\frac{1}{3}$~ the number of cans that Luke collected. The number of cans that Luke collected was what fraction of the total number of cans that John, Karen, and Luke collected?
~$\frac{1}{5}$~
~$\frac{1}{3}$~
~$\frac{2}{5}$~
~$\frac{1}{2}$~
~$\frac{2}{3}$~