The distributive determiner half is used to talk about a whole group divided in two. Half can be used as a distributive in several different patterns. Other fractions can be used in the same patterns, although they are less frequent.
Half can be used with measurements preceeded by an indefinite article (a or an). In this usage, it refers to a measurement.
- I had half a cup of milk left.
- I bought half a kilo of flour.
- He ran half a mile this morning.
- I will be back in half a minute.
Half can be used with nouns preceeded by the, a, a demonstrative, or a possessive pronoun. In this case, the meaning refers to a concrete, physical divison. The word of can be added just after half with no change in meaning.
- Half the people have already left.
- Half of an apple isn't very much lunch.
- Did you use half my sugar?
- I will need half of the flour for my cake.
- I earned half of that money last summer.
- She found half these frogs in the river.
- I spent half that time on my project.
- You can take half of those books back.
- I've invited half my friends to the party.
- I've used up half of our eggs.
- You wasted half your money on that!
Half can be used with plural pronouns preceeded by of.
- Half of us are going.
- He scolded half of you but he let the rest off.
- You couldn't find half of them?