Today, I'm going to tackle the proper use of which vs. that. Before we get started, commit this to memory: Which needs a comma(s). That does not.
Ex: My first car, which is in the driveway, is red.
Ex: The dog that stole my hotdog ran away.
Next, you need to understand the difference between a restrictive clause and a nonrestrictive clause. A restrictive clause is essential to the meaning of the sentence. If you took it out, the sentence wouldn't make sense or its meaning would change. A nonrestrictive clause is one that adds additional information, but could be left out without losing anything vital. *Nonrestrictive clauses are set off with commas. Restrictive ones are not.
Let's apply this to our examples...
Ex: My first car, which is in the driveway, is red.
Ex: The dog that stole my hotdog ran away.
In the first example, 'which is in the driveway' is additional information. We already know which car—my first car. In the second example, the clause must be restrictive, because removing 'that stole my hotdog' takes essential information from the sentence.
Now add 2 + 2...
If 'which' needs a comma, and nonessential information is set off with commas, then 'which' is used for nonessential clauses and 'that' is used for essential ones. Simple. :)
Grammar Girl does a nice job of explaining this.
Grammarbook does a fair job, too.
One last tip:
'Which' and 'that' refer to things. 'Who' refers to people.*
*Grammarians disagree on this one. Some say using 'that' for people is also correct. Ex: The people that vandalized the school were all students there. However, you would definitely be correct using 'that' when referring to collective nouns such as jury, committee, audience, crowd, class, troop, mob, family, and couple. Ex. The jury that found the defendant not guilty was biased in his favor. On the other hand, references to specific people like 'Mary,' 'the president,' and 'my mom' would use the pronoun 'who,' not 'that.'
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