In the past year, Alton Middle School auditorium has begun to fall apart, yet our drama class enrollments have steadily increased.
This is a Sentence fragment because it isn't complete and does not convey a meaning. It is also not a run on sentence because it isn't just incorrectly connected two independent sentences. Therefore it is a fragment.
The king was in debt because of a war, and needed to get out, so he decided to tax the citizens who he didn't think could rebel, but he was wrong. Hope I helped!