He broke the glass carelessly.

His carelessness caused the accident.

That information is unnecessary.

That information is completely unnecessary.

I learned how to solve inequalities in math class.

His behavior was thought to be an anomaly.

His behavior is completely abnormal.

He was punished for his disobedience to the rules.

This liquid is nonfreezing, so it does not freeze even in winter.

His feelings are in the realm of the unknowable.