A sentence is a group of words that contains three things:
A sentence fragment is a group of words that lacks one or more of these three things. While there are many ways to end up with a fragment, almost every fragment is simply a result of one of the following three problems:
Fragments are no big deal in conversation; spoken English is full of them. In fact, if you spoke in complete sentences for one entire day, you would probably get some strange looks. But English conventions require that you avoid writing fragments (except in very rare instances), so you must be able to identify them in your writing and fix them.
To begin to identify fragments in your writing, read a sentence aloud. Does it sound complete? If you walked up to a stranger and said it to him, would it sound like a complete thought to him? Or would he be waiting expectantly for you to finish? Even if it sounds okay to you (because you already know what you mean), look at it and identify the subject (who or what did the action) and the verb (what the subject did) to make sure they're there. (For help identifying subjects and verbs, see the TIP Sheet Parts of Sentences.) If you think a subject is missing, or the verb sounds a little strange, or the thought is left hanging, refer to the tips below.
Some fragments are missing subjects. Often the subject appears nearby, perhaps in the preceding sentence; however, each sentence must have a subject of its own. The following fragment lacks a subject:
Was running late that day.
Who was running late? The instructor? The train? The simplest (but by no means only) way to correct this fragment is to add a subject:
I was running late that day.
Phrases which include words ending in -ing often appear as fragments:
Biking and swimming after work on Thursday.
What about biking and swimming? Who is biking and swimming? Are you proposing that we all go biking and swimming? Add both a subject and a verb to correct this (again, not the only solution):
Mitchell went biking and swimming after work on Thursday.
Another suspect in the missing subject category is a phrase like this one:
To register for class before the deadline.
Who wants to register? Or failed to register? Or plans to register? This fragment lacks both subject and verb. ("To register" is not really a verb, but another thing entirely; see the TIP Sheet Other Phrases: Verbal, Appositive, Absolute). The simplest fix is to add a subject and verb:
Stan hopes to register for class before the deadline.
(Avoid the mistake of thinking that a command, demand, or request lacks a subject. This kind of sentence has an unstated subject, you. So the subject of "Turn in your schedule changes at the counter" is you: "[You] turn in your schedule changes at the counter.")
Some fragments are fragments because they are missing a verb or an essential part of a verb. Any phrase, no matter how long, is a fragment if the verb is missing:
The birch trees with their rattling yellow leaves.
What about the birch trees? Adding a verb makes this fragment complete:
The birch trees with their rattling yellow leaves swayed in the wind.
Some verbs require helpers in order to be complete. Words ending in -ing, for example, must include helpers such as is, are, was, were, will be, or has been to be real verbs; without these helpers, they are not verbs. (If you want to know more about verb look-alikes, see the TIP Sheet Other Phrases: Verbal, Appositive, Absolute.) The fragment below contains an incomplete verb:
Caroline studying her sociology tonight at Moxie's downtown.
Did your ear hear the strangeness? Add helpers to make the verb complete and repair the fragment:
Caroline will be studying her sociology tonight at Moxie's downtown.
A very common type of fragment is the unfinished thought fragment. While other kinds of fragments require you to add something--a subject, or a verb, or both--you can often fix unfinished thought fragments simply by joining them to a preceding or following sentence. The following example, while it contains a subject and a verb, fails to complete the thought:
Because tuition increased again this semester.
The word to blame for making this thought incomplete is because. (Contrary to rumor, it's perfectly okay to start a sentence with because; you just have to finish what you're saying--in the same sentence.) If you find a fragment of this kind, see if the sentence before or the sentence after it would complete it:
Because tuition increased again this semester, Kou got a second job as a Student Assistant.
Kou must take fewer units because tuition increased again this semester.
If the preceding or following sentence does not complete the unfinished thought, add the missing information to the fragment to make it complete. There are many words that, by their mere presence, make a clause incomplete, for example, since, while, when, unless, although. For more about these words, see the TIP Sheet Independent & Dependent Clauses.
In spite of the rules of grammar, language is plastic and can be shaped a great many ways, so for any fragment problem, many solutions exist. The more you practice writing, the more you will be able to spot fragments and fix them. And the more you learn about English, the more ways you will find to make your grammatically correct sentences say exactly what you mean.