Etymology
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groats (n.)
"hulled grain coarsely ground or crushed; oatmeal," early 14c., from grot "piece, fragment," from Old English grot "particle," from same root as grit (n.). The word also meant "excrement in pellets" (mid-15c.).
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slice (n.)
c. 1300, "a fragment," from Old French escliz "splinter, fragment" (Modern French éclisse), a back-formation from esclicier "to splinter, shatter, smash," from Frankish *slitan "to split" or some other Germanic source (compare Old High German slihhan; see slit (v.)). Meaning "piece cut from something" emerged early 15c. Meaning "a slicing stroke" (in golf, tennis) is recorded from 1886. Slice of life (1895) translates French tranche de la vie, a term from French Naturalist literature.
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gobbet (n.)
late 13c., "a fragment," from Old French gobet "piece, mouthful," diminutive of gobe "mouthful, lump," related to gober "to gulp, swallow down," probably from Gaulish *gobbo- (compare Irish gob "mouth," Gaelic gob "beak").
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fraction (n.)
late 14c., originally in the mathematical sense, from Anglo-French fraccioun (Old French fraccion, "a breaking," 12c., Modern French fraction) and directly from Late Latin fractionem (nominative fractio) "a breaking," especially into pieces, in Medieval Latin "a fragment, portion," noun of action from past participle stem of Latin frangere "to break (something) in pieces, shatter, fracture," from Proto-Italic *frang-, from a nasalized variant of PIE root *bhreg- "to break." Meaning "a breaking or dividing" in English is from early 15c.; sense of "broken off piece, fragment," is from c. 1600.
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merrythought (n.)

"wishbone of a fowl's breast," c. 1600, from merry (adj.) + thought. So called from the sport of breaking it between two persons pulling each on an end to determine who will get a wish he made for the occasion (the winner getting the longer fragment). Also see wishbone.

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screed (n.)

early 15c., "fragment, piece torn off," also "strip of cloth," a northern England dialectal variant of Old English screade (see shred (n.)). Meaning "lengthy speech" is by 1812, from the notion of reading from a long list or simply a "long strip" of speaking.

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darn (v.)

"to mend (fabric) by interweaving yarn or thread to fill a rent or hole," c. 1600, of unknown origin. Perhaps from French darner "mend," from darne "a piece, a slice," from Breton darn "piece, fragment, part." Alternative etymology is from obsolete dern "secret, hidden." Related: Darned; darning.

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exuviae (n.)
"cast-off skins, shells, or other coverings of animals," 1650s, Latin, literally "that which is stripped off," hence "slough, skin," also "clothing, equipment, arms, booty, spoils," from stem of exuere "to doff," from ex "off" (see ex-) + from PIE root *eu- "to dress" (also found in Latin induere "to dress," reduvia "fragment").
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crumb (n.)

Middle English crome, crumme, from Old English cruma "fragment of bread or other food, a morsel, small fragment," from a West Germanic root of obscure origin (compare Middle Dutch crume, Dutch kruim, German Krume); perhaps from a PIE word for "small particle of bread" and cognate with Greek grumea "bag or chest for old clothes" (Beekes writes: "In origin, the word probably denoted small things of little value, later also the chest, etc.), Albanian grime.

The unetymological -b- appeared mid-15c., in part by analogy with words like dumb. Slang meaning "lousy person" is 1918, from crumb, U.S. slang for "body-louse" (1863), which were so called from resemblance.

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morsel (n.)

late 13c., "a bite, mouthful; small piece of food, fragment," from Old French morsel (Modern French morceau) "small bite, portion, helping," diminutive of mors "a bite," from Latin morsum, neuter of morsus  "biting, a bite," past participle of mordēre "to bite," which is perhaps from an extended form of PIE root *mer- "to rub away, harm."

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