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prorate (v.)

also pro-rate, "divide or distribute proportionally, assess pro rata," 1860, American English, verb derived from Latin pro rata (parte); see pro rata. Related: Prorated; prorating.

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Definitions of prorate from WordNet

prorate (v.)
make a proportional settlement or distribution;
prorate (v.)
divide or assess proportionally;
The rent was prorated for the rest of the month
From wordnet.princeton.edu