To solve this expression, we need to find a common denominator for the fractions involved.

First, let's simplify the fractions:
1/3 + 1/4 = (4/12) + (3/12) = 7/12
1/6 + 0.5 = (1/6) + (3/6) = 4/6 = 2/3

Now we can divide the sum of the first set of fractions by the sum of the second set:
(7/12) / (2/3)

To divide fractions, we multiply the first fraction by the reciprocal of the second:
(7/12) * (3/2) = 21/24 = 7/8

Therefore, (1/3 + 1/4) : (1/6 + 0.5) = 7/8