A fragment is a group of words without a subject or verb; it can also be a dependent clause that is not attached to an independent clause.
 
Example: Went to the store.
Who went to the store? This has no subject.
 
Example: Paul.
What about him? This has no verb.
 
Example: After surveying the landscape for forty-five minutes and deciding that the area was secure enough to walk through.
What happened? This thought is incomplete because “After” indicates a dependent clause, but the clause gives no resolution. This clause needs an independent clause.
 
Example: To follow in the path of righteousness.
This noun phrase needs a verb or needs to be grouped behind a subject and a verb.
 
To correct a fragment, add the necessary components to make an independent clause or attach the words to another sentence to complete the thought.
 
Example: After surveying the landscape for forty-five minutes and deciding that the area was secure enough to walk through, Paul went to the store.
 
Example: To follow in the path of righteousness is wise.