Should I use
What fraction of the residents are married?
What fraction of the residents is married?
Technically, as fraction is singular, I would use the latter version. Am I correct?
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No doubt, it should be 'are'. Fraction is not commonly used in the mathematical sense ('technically' refers to 'mathematically'). For eg, A small fraction of voters will abstain from voting due to the boycott call. It can be seen in other usages as well - http://www.azadvocacy.org/press-a-media/media/253-just-a-fraction-of-voters-meet-id-deadline - Just a Fraction of Voters Meet I.D. Deadline. (not 'meets' if we want to use 'singular').