John made 1/4 of a pound of fudge and Mary made 1/3 of a pound of fudge. Ricky takes the sum of the two amounts of fudge and divides it into three equal portions, planning to keep one portion for himself. How much fudge does Ricky keep?
The sum of the amount of fudge John and Mary made is 1/4 + 1/3 = 3/12 + 4/12 = <<1/4+1/3=7/12>>7/12 of a pound of fudge.
Ricky keeps 1/3 of this amount, or (1/3)*(7/12) =7/36 of a pound of fudge. Answer: \boxed{\frac{7}{36} \text{ pounds}}.