fraction

shred, tatter

end, leftover, oddment, remainder, remnant, stub

portion, section, segment

chip, flake, shard, shatter, shiver, sliver, splinter

clipping, paring, shaving

atom, crumb, dribble, fleck, flyspeck, grain, granule, molecule, morsel, mote, nubbin, nugget, particle, patch, scruple, snip, snippet, speck, tittle