No, a fractional patent is not what you have left over after the PTAB gets a hold of your patent. Fractional patents are actually patents with fractional numbers.  The practice started back when the USPTO was trying to reassemble the collection of patents issued before the Office numbered patents.  These pre-number era patents are known as the “X” patents, and as the Office was assigning these patents numbers, they would occasionally come across patents whose issue  dates were between already numbered patents.  In order to keep the chronological sequence, the USPTO needed to issue fractional numbers.

In fact the USPTO even created a letter code system to identify the fractions:

The surprising thing is that the fractional number scheme continued from time to time even after the USPTO began numbering patents.  126½, 1400½, RE1217½, RE1242½, D1093½, 2712152½, 3262124½, 

and D90793½.