What, exactly, is dangling in a dangling modifier, and how does it differ from what dangles in a dangling participle? Most important, how does one go about undangling these sentence elements?
A modifier is an optional word or phrase that is associated with a noun or noun phrase and provides a further detail about that noun or noun phrase and the sentence in which it appears, such as bright in “She shielded her eyes from the bright light.” Omit bright, and the sentence is still valid. The same is true of the phrase that follows light in “She shielded her eyes from the bright light, which lit up the entire chamber”; it is informative, but it is not essential to the sentence.
Modifiers can appear at the beginning or end of a sentence, or in the middle. Sometimes, when a modifying phrase begins a sentence, it is erroneously written in such a way that it applies not to the subject of the sentence but to another noun or noun phrase. Such a phrase is called a dangling modifier.
In the sentence “The youngest team in the sailing competition, Smith and Jones’s record-breaking performance was their goal heading into the event,” the introductory phrase pertains to “Smith and Jones,” but “Smith and Jones” is not the subject; that phrase is itself a modifier that provides additional information about the subject “(A) record-breaking performance.” To make the modifier work—to undangle it—the sentence must be revised so that “Smith and Jones” is the subject: “The youngest team in the sailing competition, Smith and Jones, had a record-breaking performance as their goal heading into the event.”
A dangling participle is simply a type of dangling modifier; a participle is a type of verb, such as having in this sentence: “Having known this man for seven years, I would like to think that you have had a chance to observe him in many situations.” At first glance, nothing may seem amiss, but the point of the sentence is that the person identified as you is the one who has known the man for seven years, but the sentence construction implies that the writer is the one who has been acquainted with the third person. This confusion is remedied by explicitly referring in the modifying phrase to the second person: “Because you have known this man for seven years, I would like to think that you have had a chance to observe him in many situations.”