1.8 Predeterminers

The predeterminers are all, both, half, the fractions (one third, one fifth, etc.), and the multipliers (double, twice, three times, etc.). They occur before determiners and other premodifiers in the noun phrase, e.g.:

All/Both/Half/One third the men arrived on time
Double/Twice/Three times that number arrived late

Of is optional with all, both, half, and the fractions, except when the head noun is a-pronoun, in which case it is obligatory:

All/Both/Half/One third (of) the men.
All/Both/Half/One third of them.