To prorate is to divide something in a proportional way, based on time. If your new landlord prorates your first month's rent, she only charges you for the days you've actually lived in your apartment.

The word prorate comes from the Latin pro rata, "according to the calculated share," and when someone prorates a bill or payment, they only charge you for a certain share. Instead of billing you for a fixed rate, they calculate the price based on how much you've used the service: "The electric company will prorate August's bill, since you moved out mid-month."

Definitions of prorate
  1. verb
    make a proportional settlement or distribution
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    type of:
    dispose of; make a financial settlement
  2. verb
    divide or assess proportionally
    “The rent was prorated for the rest of the month”
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    type of:
    calculate, cipher, compute, cypher, figure, reckon, work out
    make a mathematical calculation or computation
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