Which fraction sits exactly halfway between 1/3 and 1/2?

The midpoint of two numbers is their average: (1/3 + 1/2) ÷ 2 = (2/6 + 3/6) ÷ 2 = (5/6) ÷ 2 = 5/12 ≈ 0.4167. The trap is 2/5: adding the tops and the bottoms gives (1+1)/(3+2) = 2/5 = 0.4, which does lie between the two but is not the midpoint. 3/8 = 0.375 also lies between them, and 1/12 is merely the gap 1/2 − 1/3.