Tagged proration

Split an amount into the part used and the part unused over a billing period, losing nothing.

Days two date ranges have in common, with the end of each range stated as inclusive or exclusive.

Split an amount across ratios without losing or inventing a single minor unit.

Rent for part of a month from the monthly rent, by the annual-daily or the calendar-month method.

Mid-cycle plan change: credit for unused time on the old plan and charge for the rest of the period on the new one.