What is the X in X-mas?
early 15c., from Latin fragmentum "a fragment, remnant," literally "a piece broken off," from root of frangere "to break" (see fraction).
by 1788 (implied in fragmented), from fragment (n.). Related: Fragmenting.
fragment frag·ment (frāg'mənt)n.
A small part broken off or detached.
An incomplete or isolated portion; a bit.