Adding Fractions
Same-size pieces before you can count them.
Concept
You can only add matching pieces
Thirds and quarters are different-sized pieces, so 1/3 + 1/4 is not 2/7. First rewrite both with a common denominator.
Multiplying the two denominators always gives a workable common denominator — it may not be the smallest, but you can simplify at the end.
a/b + c/d = (ad + cb) / bd