Splitting lot - how to do 1031?

[David Sisson]

I own a SFR on a double lot. I'd like to split the lot, keep the SFR, and sell the (new) empty lot.

After I pay expenses, I'd net something like $45K from the empty lot. 

I'd like to avoid capital gains on this $45K. I'd like to do a 1031 exchange, putting this $45K as a down payment on another property. 

Since I'm not selling the entire original property, can I do a 1031? If yes, how? 

If I can't do a 1031, can I use the $45K to pay down the mortgage on the SFR and avoid cap gains that way?