The sum of two fractions is 19 2/5. Their difference is 11 2/3. What are the two fractions?

Simple: 19 2/5 = 97/5 or 291/15 and 11 2/3 = 35/3 or 175/15

(291/15)/2 = 291/30 and (175/15)/2 = 175/30

The smaller number = (291–175)/30 = 116/30 or 58/15 and the larger = (291+175)/30 = 466/30 or 233/15