*This is what is easiest for me. I hope it helps you.*
1.) First I would turn the mixed fraction into an improper fraction. 2 2/3 turns into 8/3.
2.) I would get the fractions over with. So 8/3+1/3. Lucky you. You don't have to find the Least Common Factor. Add the numerators and you get 9/3.
3.) Next do 9 divide 3 and you get 3.
4.) 3•3 and you get back to 9.
5.) The volume of your bed would be 9 inches.