1/2 and 1/4 are not the same size pieces.
Adding them directly would be like saying 1 half + 1 quarter = 2 something. But what something?
Rename the half as 2/4. Now both fractions are in quarters.
Once the denominators match, you can add: 2/4 + 1/4 = 3/4.
1 / 4
/ + /