Say you have in front of you three marbles, one of which is red, another blue, and the last one yellow. Is the sentence "A third of these marbles is blue." grammatically correct?
Edit:
The reason I chose this particular setup is because 3/3=1. So "a third" represents a single object. If I said "half of the strips of the US banner are white", "half" represents 25 objects, so it seems natural to use the plural "are". But if the fraction only covers one object, the justification for using a plural becomes less clear.