In the following sentence, should I say "could care less" or "could not care less"?
I could not care less of what you think.
Sometimes I have seen written "could care less" and sometimes "could not care less." Since it happens in informal contexts, I am not sure if "could not care less" is the right phrase, or if both are correct and they have slightly different meanings.
The vast majority of British speakers would say
I could not care less
In my experience, its mostly only US speakers who would say
I could care less
The omission of the word "not" completely changes the (literal) meaning of the sentence, but you should understand them to mean the same thing. The "I could care less" version is probably my single most disliked phrase/idiom---its just plain wrong, IMO---but its too late to stop it now :(
The correct way to say this is "I could not care less about what you think.", meaning that "I care so little about what you think, that it is impossible for me to care less than I do now".
I believe over time, people have shortened it, similar to the way people shorted words into contractions ("I can not" becomes "I can't), but the shortened form does not really mean what they intend it to mean.
As a British english speaker, I would say "I couldn't care less".
I would consider them distinct though, as if you "couldn't care less" you are unable to care about something. "I could care less" implies a certain non-zero level of care in the first place:
In the following sentence, should I say "could care less" or "could not care less"?
That would depend on if you are using American English or not. If you are, then use "could care less". If you are not, then use could not care less.
The use of "could care less" seems to be just in American English. It does not make any sense because it actually says the opposite of what is meant, when it is used. What is meant is that the person saying it does not care about something. It actually contradicts the meaning because it means that you currently care but have the possibility of caring even less, at some point in the future.
In England and the rest of the UK, people use could not care less.
"I could not care less" implies that you must care at least some amount no matter how small that amount is. I do not care means you have zero care or without any care for the subject matter.
:)