To add these fractions, we need to find a common denominator.

The prime factorization of 15 is 3 x 5, and the prime factorization of 25 is 5^2. The common denominator is the least common multiple of the two denominators, which is 3 x 5^2 = 75.

1/15 can be rewritten with a denominator of 75 as (1 5)/(15 5) = 5/75
7/25 can be rewritten with a denominator of 75 as (7 3)/(25 3) = 21/75

Now, we can add the two fractions:

5/75 + 21/75 = (5 + 21)/75 = 26/75

Therefore, the sum of 1/15 + 7/25 is 26/75.