Which sentence is a run-on sentence? A. Alaska is the largest state in the U.S., but it has the fewest people. B. Some foods are canned; others are frozen. C. Fencers wear metal helmets, these have wire face guards. D. Sarah swam quickly across the lake and back again.

C. "Fencers wear metal helmets, these have wire face guards." 

This sentence incorrectly connects two independent clauses with just a comma, which leads to a run-on sentence, also known as a comma splice. An independent clause is a group of words that can stand alone as a sentence because it contains a subject and a verb and expresses a complete thought. In this case, "Fencers wear metal helmets" and "these have wire face guards" are both independent clauses. To fix this run-on sentence, the writer could use a period, a semicolon, or a coordinating conjunction with a comma to properly connect them.

A run-on sentence occurs when two or more independent clauses are not joined correctly. There are a few ways to fix run-on sentences:

1. Use a period to separate the clauses into two sentences: "Fencers wear metal helmets. These have wire face guards."

2. Use a semicolon to connect the independent clauses: "Fencers wear metal helmets; these have wire face guards."

3. Use a coordinating conjunction (for, and, nor, but, or, yet, so) with a comma to join the two clauses: "Fencers wear metal helmets, and these have wire face guards."

Understanding run-on sentences is important because they can make your writing hard to understand and can obscure the meaning of what you're trying to communicate. Run-on sentences are common mistakes but can easily be corrected with proper punctuation and conjunctions. It's worth noting that compound and complex sentences are grammatically correct ways to connect clauses, as long as they are punctuated correctly.