Accept partial rent, then serve a 3 day notice?

[Roy Lam]

I have a tenant that in the past few months she has been late on paying rent. She would pay a portion first, then more later during the month. This has been going on for the last six months and I am getting tired of this.  I know she is having a hard time to come up with the full rent since her roommate moved out.  This coming month I am planning to take whatever she gives me first, and give her until the 15th to pay all of it.  Otherwise, I will give her a 3 day notice, then evict her.

My question is, if I take part of the rent , can I still give her the 3 day notice?