Half of the polar glaciers have melted.
In such cases as fractions / percentages, the verb will be singular or plural depending on whether the object of the preposition is singular or plural.
Here, since glaciers is plural, the correct verb is have.
See the contrast with -
Half of the carrot has been eaten by the rabbit. (singular has for singular carrot)
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Source: Beat The GMAT — Sentence Correction |