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?

~$\frac{1}{5}$~

~$\frac{1}{3}$~

~$\frac{2}{5}$~

~$\frac{1}{2}$~

~$\frac{2}{3}$~