While LVM makes it simple to add space, shrinking existing space becomes harder. You'll need to do all this while booted from a live CD because you cannot shrink a filesystem while it is mounted. I suggest the
gparted 0.23.0 live CD.
While running from that CD, start a terminal with root permissions and shrink your /home filesystem and LV:
Code:
lvresize --size=350G --resizefs /dev/fedora/home
Now, refresh the devices in
gparted (Ctrl+R), and it should show that sda3 is no longer completely used. Click on "Resize/Move" and adjust that partition to the minimum allowed size. You should now have 50GB of unallocated space for a new partition. This assumes that fedora-home is physically located at the end of the PV. If not, resizing the partition is going to be harder.
Resizing filesystems is always a risky operation. I strongly recommend that you have a full backup before doing this.