2009 AMC 12A Problem 3

The gap is $\dfrac{3}{4} - \dfrac{1}{4} = \dfrac{1}{2}.$ One third of the way adds $\dfrac{1}{3} \cdot \dfrac{1}{2} = \dfrac{1}{6}.$ So the number is $\dfrac{1}{4} + \dfrac{1}{6} = \dfrac{3}{12} + \dfrac{2}{12} = \dfrac{5}{12}.$ Thus, the correct answer is B.