Time Machine Backups & Reformatting TM Drive

[Caralvarez24]

I have an external drive that I have had partitioned half for TM and Half as just an external drive. I want to commit more space to TM because I hardly ever put anything on the external and I am running out of room on the TM half. Problem is if I reformat the drive I'll obviously lose all my backups and I cannot copy the backups to my internal HD because its too small ( I have a MBA with 80GB HDD and TM backups are 115GB.) My question is can I select the folders with the most recent backups and then put them into the new TM folder once it creates one after it formats. Will TM just recognize those folders as older backups? Thank you for any help you can offer!