Rent Proration - First Rental!

[Kyle M.]

So I have received applications from two tenants who meet all requirements.  More than 3x income, no evictions, and clean records.  I also called employers to check on their employment status.  The only thing is they have a young son who was sliding around on the floors at the time that they were signing the applications.  I will have "tenants responsible for all floors" in the lease. 

Questions:

1.  Are their any additional things that I can do to limit the risk for myself?  I obviously cannot deny them because of their kid.

2. Also, how do I prorate the rent? I know to prorate on the second month, not on the initial rent collection.  Lets say hypothetically the rent is $1000, and they move in on the 8th of January (which is a month with 31 days).  What is the equation that I will use to calculate the amount that they pay?