|Most people prewash at least some of their fabrics, and there's always an inch or more fabric that's ruined by the fraying. This little trick has worked on every kind of fabric I've tried it on.
Simply sew a straight stitch close to the raw edges of the fabric before you wash it. the stitching will limit how far the fabric can fray and waste less. After it's dry, simply cut the stitching off!