Open Question: how do you calculate prorated amount for rent?

I am living in an appartment where the rent is (or its supposed to be) $ 705 per month, I moved in on december 3rd and the prorated amount was $ 659.52, and we also had to pay for january which they charged us $ 705.00 and they said that all other charges like pest control and trash where included in the rent. but today I got a bill charging me for about $ 790 in rent, and when i went to complain they said that the $ 705 is not including pest control which is $ 4.99, trash which is $

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