There are actually many fine uses for sentence fragments. Here’s a brief scene from an imaginary Greek tragedy composed entirely of fragments:Menelaus: Aha! Helen!Helen (startled): Beloved husband!Menelaus: Slut!Paris (entering, seeing Menelaus): Oops. ’Bye.Menelaus: Not so fast! (stabs Paris).Paris: Arrggh!Some people get into trouble by breaking a perfectly good sentence in two: “We did some research in newspapers. Like the National Inquirer.” The second phrase belongs in the same sentence with the first, not dangling off on its own.A more common kind of troublesome fragment is a would-be sentence introduced by a word or phrase that suggests it’s part of some other sentence: “By picking up the garbage the fraternity had strewn around the street the weekend before got the group a favorable story in the paper.” Just lop off “by” to convert this into a proper complete sentence.