early 15c., divident, "that which serves as a barrier;"c. 1500, "act of dividing;" from Latin dividendum "thing to be divided," neuter gerundive of dividere "to force apart; to distribute" (see divide (v.)).
From late 15c. as "portion or share of anything to be divided." Sense of "sum to be divided into equal parts" is from 1620s, hence "portion of interest on a loan, stock, etc." Mathematical sense "number or quantity which is to be divided by another" is from 1540s (perhaps immediately from French dividende "a number divided by another"). Related: Dividends.
"to divide (up)," 1877, American English, originally a noun (1865), a slang shortening of dividend. The verb is primary now (the noun is not in "Webster's New World Dictionary"), leading some (such as "Webster's") to think the word is a slang alteration of divide. Related: Divvying. In early 20c. British slang the same word was a shortening of divine (adj.).
1540s, in mathematics, "that term of a fraction which indicates the value of the fractional unit" (commonly the number written below the numerator or dividend), from Medieval Latin denominator, agent noun from past-participle stem of denominare "to name," from de- "completely" (see de-) + nominare "to name," from nomen "name" (from PIE root *no-men- "name"). As "one who or that which gives a name," 1570s.
also lagnappe, "dividend, something extra, present or extra item given by a dealer to a customer to encourage patronage," 1849, from New Orleans creole, of unknown origin though much speculated upon. Originally a bit of something given by New Orleans shopkeepers to customers. Said to be from American Spanish la ñapa "the gift." Klein says this is in turn from Quechua yapa "something added, gift."
We picked up one excellent word — a word worth travelling to New Orleans to get; a nice, limber, expressive, handy word — 'lagniappe.' They pronounce it lanny-yap. It is Spanish — so they said. ["Mark Twain," "Life on the Mississippi," 1883]