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You could use a LiveCD or LiveUSB (maybe the one you used to install Fedora), and get gparted (su -c 'yum install gparted') to resize the partitions you assigned for / and /home. Shrink first /home by 7 GB, then grow / by those 7GB.

In my experience 12 GB is an affordable size for / and don't worry too much for applications installed.

Gparted is going to take a while, but not too much.