Start from zero — the basic math you need before everything else
You can only add fractions directly when the pieces are the same size, meaning the same denominator. Then it's easy: keep the denominator and add the tops. 1/4 + 2/4 = 3/4. Never add the bottoms. The piece size doesn't change just because you have more pieces.
If the denominators are different, the pieces are different sizes and you can't add them yet. First rewrite both over a common denominator so the pieces match, then add the tops. Subtraction works exactly the same way.
Baking shows why the denominators must match. A 1/2 cup of flour plus a 1/4 cup is easy to picture, but you can't just add 1/2 and 1/3 — the cups are different sizes. Rewrite them with the same-size measure (sixths): 1/2 = 3/6 and 1/3 = 2/6, and now they combine to 5/6 of a cup.
▶ Adding & Subtracting Fractions