Don’t use a or the before half or half of:
✗ Nearly a half of the programmes included advertising.
✓ Nearly half of the programmes included advertising.
✗ Girls constitute the half of the population of universities.
✓ Girls constitute half of the population of universities.
You can use the definite article (the) before half with an adjective such as first, second, or next when you are referring to something that has been mentioned before:
The second half of the film is not as good as the first.
The movement gathered impetus during the next half century.
When half forms part of a number, the most common structure is one and a half, two and a half, three and a half etc.
✗ Tourists can visit any of these sites within one and half hours.
✓ Tourists can visit any of these sites within one and a half hours.
✗ They made us wait for two hours and a half for our visa.
✓ They made us wait two and a half hours for our visa.
Always use a plural noun in this structure:
✗ A 90-minute film might last two and a half hour with commercials.
✓ A 90-minute film might last two and a half hours with commercials.