quotient

Etymology

It is inherited from Middle English quocient, also quociens,^[2][3] borrowed from Latin quotiēns (“how many times, how often”),^{[4][5][6][7][8]} from quot (“how many”),^[4][8][7] which is akin to quis (“who”),^[9][6] from Proto-Indo-European *kwo-, the stem of relative and interrogative pronouns.^[5][8] The final -t is a mistake: the Latin adverb was taken for a present participle, whose stem ends in -ent-.^{[4][6][10][11][12]} Klein describes this as treating it like a third-declension adjective or noun.^[13] Other languages have the same altered form: French quotient, from Middle French quotiens (1484), Spanish cociente (about 1527), Italian quoziente (1533) and German Quotient (second half of the 15th century).^[4]

Earliest recorded meaning

The result of dividing one number by another: about 1450, in the Art Nombryng, an arithmetic treatise.^[4][2]

Semantic evolution

The word was a term of arithmetic from the start,^[4][2] and Johnson (1755) still defined it only so, citing Cocker.^[14] In the 17th century it was briefly a share or proportion (1621–1641), a use the OED compares with the slightly later quotum, and once a number or total (1659).^[4] A later sense is a ratio between a test score and the measure on which the score should depend, usually multiplied by 100, as in intelligence quotient.^[9][10] From 1935, a word placed before quotient could name the amount of any quality that something has.^[4]

Timeline

• c. 1450 – the result of a division, as quocient.^[4][2][6]
• 1621 – a proportion, a share (rare, obsolete by 1641).^[4]
• 1659 – number, total (rare, obsolete).^[4]
• 1935 – with a preceding word, the degree to which a quality is present.^[4]

Meanings

Noun

1. (mathematics) The number obtained by dividing one number by another: Divide twenty by four and the quotient is five.^[15][9][4]
2. (mathematics) The whole-number part of the result of a division.^[15]
3. A ratio, especially between a test score and the measure on which it should depend, usually multiplied by 100.^[15][9]
4. With a preceding word, the degree to which a quality is present: The film has a high charm quotient.^[4]
5. (obsolete, 1621–1641) A proportion or share; a quota.^[4][10]

Word family

• intelligence quotient
• quotient group

Related words

• quota
• quote
• who

References

1. ^ a b Wiktionary, the free dictionary, https://en.wiktionary.org
2. ^ a b c d Kurath, Hans; Kuhn, Sherman M.; Lewis, Robert E., eds. (1952–2001), Middle English Dictionary, Ann Arbor: University of Michigan Press; online edition ed. Frances McSparran et al. (2000–2018)
3. ^ Dictionary.com Unabridged (2016), based on the Random House Unabridged Dictionary, New York: Random House
4. ^ a b c d e f g h i j k l m n o Oxford English Dictionary Online (accessed March 2026), Oxford: Oxford University Press
5. ^ a b Harper, Douglas. Online Etymology Dictionary, https://www.etymonline.com
6. ^ a b c d Barnhart, Robert K. (1988), The Barnhart Dictionary of Etymology
7. ^ a b Hoad, T. F., ed. (1986), The Concise Oxford Dictionary of English Etymology, Oxford: Clarendon Press
8. ^ a b c The American Heritage Dictionary of the English Language (online 2024), 5th ed., Boston: Houghton Mifflin Harcourt
9. ^ a b c d Merriam-Webster Unabridged Dictionary (2024), online ed., Springfield, Mass.: Merriam-Webster
10. ^ a b c Shorter Oxford English Dictionary on Historical Principles (2002), 5th ed., ed. William R. Trumble and Angus Stevenson, Oxford: Oxford University Press
11. ^ Stevenson, Angus, ed. (2010), Oxford Dictionary of English, 3rd ed., Oxford: Oxford University Press
12. ^ Weekley, Ernest (1921), An Etymological Dictionary of Modern English, London: John Murray
13. ^ Klein, Ernest. A Comprehensive Etymological Dictionary of the English Language. 2 vols. Amsterdam: Elsevier, 1966–1967.
14. ^ Johnson, Samuel (1755), A Dictionary of the English Language, London; 4th ed. 1773; Johnson's Dictionary Online, ed. Beth Rapp Young et al.
15. ^ a b c Collins English Dictionary (2023), Glasgow: HarperCollins