"Half" is the nominal subject of those sentences. There is no easy way to get the right number of the verb, but it tends to go for the nearest noun, partly because "half" has something of the pronoun about it, and the object of "of" is its referent. You could say that half were on sale.
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drdmt2013Could you determine if the verb-noun agreement is correct by referring to the noun/subject of the sentence and negating the rest of the sentence including modifiers?I don't see that your method involves the negation of anything. It's much simpler to remember that when it comes to expressions like X of Y as a subject, the verb agrees with X mo