rather · adverb /ˈræð.ər/Full view
rather (SMALL AMOUNT)
B1 slightly or to a small degree
Dictionary examples:

That's rather a difficult question to answer.

I thought he was rather nice.

It was rather strange to invite me and then not come himself.

She answered the telephone rather sleepily.

Learner example:

I can't come because I feel rather sick. (Preliminary English Test; B1; Czech)

rather than
B1 instead of
Dictionary example:

I think I'd like coffee rather than tea, if that's okay?

Learner example:

When the weather is to[o] hot to wear jeans, I usually wear a swimsuit rather than shorts. (Preliminary English Test; B1; Spanish)

would rather
B1 used to show that you prefer to have or do one thing more than another
Dictionary examples:

I'd much rather go out to dinner than stay in and watch TV.

I would rather not tell him.

Learner example:

I'd rather watch something funny, like a sitcom. (Preliminary English Test; B1; Russian)

rather (MORE EXACTLY)
B2 used to change something you have just said and make it more correct
Dictionary example:

She'll go shopping on Thursday, or rather, she will if she has to.

Learner example:

The food - or rather, leftovers - that she gave him was barely enough to feed a baby. (First Certificate in English; B2; Chinese)

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