I'm about to sign a lease on an apartment.
I was told if I sign a 7 month lease I will get 1 month free and I can prorate that out over the 7 months.
The rent on the apartment will be $770.00
If I prorate my 1 month free over the 7 month lease.
How much should my rent be per month?

If you are prorating the "free month" its not free, it's just spread out.

So if I spread it out what will my rent be over 7 months.
$770.00 is what the apt is renting for.
What will my rent be over 7 months if I spread out the free rent?

How do you caculate that?

Divide the monthly rent by 7 (110), now add that to each month. So 880; but again, I want to address something. It's not a free month if you are still paying for it.

I think you would actually get to pay 7 months rent over the course of 8 months.

So, 770 x 7 = 5390
5390 / 8 = 673.75

That's how I would interpret it.

I get $660 per month.

770 per month x 7 month = 5390 total for the term
5390 - 770 (1 month free rent) = 4620 total for the term
4620 divided by 7 months = 660 per month

I get $660 per month.

770 per month x 7 month = 5390 total for the term
5390 - 770 (1 month free rent) = 4620 total for the term
4620 divided by 7 months = 660 per month

I think you're right. I was trying to make the 8th month free, not the 7th month!