You all may not like me for this but I will NOT tear. It does not straighten the fabric and as the others have said, they have to trim anyhow. What a waste of fabric!
Here is what I do. I unfold the fabric and press out the fold line. Then bring your cut edges together, keeping your selvedges even (sometimes I have to pin every so often) fold to a manageable length, cut off your selvedge then cut the width you need for your borders.