The words like "half" , "part" etc are singular or plural according to the meaning of the sentence. When these words refer to a mass or a section, they are singular. When they refer to a number of individuals or things, they are plural.
1. Half of the boys are in camp. (number -- plural)
2. Half of the pie is left. (mass or section -- singular)
3. Part of the roof was destroyed. (mass or section -- singular)
4. Part of the guests have arrived. (number -- plural)