Fortunately for me, a wonderful 3rd grade teacher gave us the solution. It helped that he was male, and my 8-year-old daughter had a major crush on him. She ate up every word that man said, so when he taught her to skip count to some familiar tunes she came home singing her math just for fun.
If the two values being subtracted are mixed fractions, it is often easier to turn them into improper fractions to perform the subtraction. This avoids any kind regrouping or borrowing from the minuend fraction if the numerator in the subtrahend is larger.