Please try with 'mount'. Fdisk doesn't show the partition types.
The problem with type is that older versions of parted didn't support ext3 directly. New ones should handle it, however (at least the manual is saying so).
In the meantime, you may find the parted manual useful. You can find it here: http://www.gnu.org/software/parted/m...no/parted.html
Make sure you have parted installed.
Now, the whole resize operation has, in your case, minimum 3 steps:
1. resize /var; you'll get free space after /var
2. move /var at the end of disk
3. resize /home to add the free space to it
Now, the exact commands depends on the fact how much space you want to add to /home. You need two 'resize' and one 'move' in parted.