To add these two fractions, we need to find a common denominator. The least common multiple of 7 and 4 is 28.
So, we convert both fractions to have a denominator of 28:
4/7 = 16/28
1/4 = 7/28
Now that the fractions have the same denominator, we can add them:
16/28 + 7/28 = 23/28
Therefore, 4/7 + 1/4 in its simplest form is 23/28.