It may be used with of.

• Half the eggs = Half of the eggs

• Half our money = Half of our money

But with you, us, it them we must use of

• Half of them live here. half them live here
• Half of it is enough. half it

• Half (of) the class are Spanish.
• She invited a lot of people to the party but half of them didn’t turn up.
• Half (of) this cake is yours.
• Almost half (of)the India’s population do not have access to safe, clean, drinking water.
• Half of them actually completed the race.
• The Japanese recycle more than half (of) their waste paper.
• Half (of) my speech was devoted to the issue of education.