Can I use the free space on an NTFS Hard Drive to make a "Mac OS Journaled" partition to use as a backup space? I have a 1 TB NTFS HDD which has 350GB free space, how would I format that 350GB to use it as a backup space for my MacBook?

diskutil list output:

/dev/disk1 (external, physical):
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:     FDisk_partition_scheme                        *1.0 TB     disk1
   1:               Windows_NTFS ADATA HD710             1.0 TB     disk1s1
If you've already got GParted, use ´GParted /dev/disk1´ to resize your NTFS partition.  It has a nice Graphical front-end, and just in case you need it, here is the manual.
As David Anderson said a couple times, above, then you can open the OSX application Disk Utility, which is under /Applications/Utilities, and then you will see empty space on that disk:
Create a partition of the type HFS+ (journaled), and you'll be ready to use it as your Time Machine disk.


I think you'll be finished in no time, since you personally already found Gparted, and sound like you have good information about this.  You would also be able to do this all on the command-line is OSX with diskutil.