I can imagine someone saying, "At least she's got half a brain, which is more than can be said of her friends." That would be very unflattering to her friends, of course. It would mean she is smarter than her friends, but not necessarily as smart as one should, at least, be.
Now, if someone said, "She's got a brain and a half", that would mean she's extra intelligent.
Of course, for this to be practical she would have to have one quarter extra of the right brain, and one quarter extra of the left brain. Otherwise, there might be a certain imbalance.
Student or Learner