1. I don't even know where she is half the time.---- Here "Half" used as a predeterminer.
2. I don't even know where she is half of the time.---- Here "Half" used as a pronoun.
Now my question is that do the two examples above carry the same meaning when "half" used as a predeterminer and as a pronoun?
source: http://dictionary.cambridge.org/dictionary/english/half
Yes, they have the same meaning. Your second example is a partitive 'fused-head' construction, meaning "half of x, where x = some length of time". Incidentally, despite what most dictionaries say, "half" belongs to the category (part of speech) noun.
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Yes, they have the same meaning.
Your second example is a partitive 'fused-head' construction, meaning "half of x, where x = some length of time".
Incidentally, despite what most dictionaries say, "half" belongs to the category (part of speech) noun. Evidence for the analysis of fractions as nouns comes from the fact that they take determiners ("a half") and they inflect for num