What is an example of how to prorate something?

A pro rated refund of an annual membership might be paid back according to how many months have not expired, so a pro rated return after 6 months would be half the annual rate, after 10 months only 1/6 would be refunded, etc. Property taxes (t) of a property being sold are pro rated by the number of days (x) of the tax year up to the transfer date, so the seller pays the share accrued before the sale (x/365)t and the buyer pays the remainder ((365-x)/365)t.