quotient

See also: Quotient and quotiënt

English

Etymology

From Latin quotiēns, from quotiēs.

Pronunciation

• (UK) IPA^(key): /ˈkwəʊʃənt/
• (US) enPR: kwōʹshənt, IPA^(key): /ˈkwoʊʃənt/

• Audio (US):

  (file)

• Rhymes: -oʊʃənt

Noun

quotient (plural quotients)

1. (arithmetic) The number (either a fraction or an integer) resulting from the division of one number by another.

   Dividing 12 by 4 yields a quotient of 3.

2. (mathematics) By analogy, the result of any process that is the inverse of multiplication as defined for any mathematical entities other than numbers.
3. (obsolete, rare) A quotum or quota.
4. (cricket) The number of runs scored per wicket lost when batting, divided by the number of runs conceded per wicket taken when bowling — used as a league table tiebreaker in some first-class tournaments.

   Coordinate term: net run rate

5. (mathematics, group theory) A mathematical structure formed by identifying elements within a larger one.

Derived terms

• accomplishment quotient
• achievement quotient
• artificial intelligence quotient
• biquotient
• difference quotient
• encephalization quotient
• Horowitz quotient
• intelligence quotient
• pseudoquotient
• Q quotient
• quotient group
• quotient map
• quotient ring
• quotient set
• quotient space
• Rayleigh quotient
• subquotient
• truth quotient

Related terms

• quotientive
• quotiety

Translations

number resulting from division

• Arabic: خَارِج قِسْمَة m (ḵārij qisma), خَارِج m (ḵārij), حاصِل الْقِسْمَة m (ḥāṣil al-qisma)
• Armenian: քանորդ (hy) (kʻanord)
• Asturian: cociente m
• Azerbaijani: qismət (az)
• Belarusian: дзель f (dzjelʹ)
• Bulgarian: ча́стно (bg) n (částno)
• Burmese: စားလဒ် (my) (ca:lad)
• Catalan: quocient m
• Cebuano: lapa
• Chinese:

  Mandarin: 商 (zh) (shāng), 商數 / 商数 (zh) (shāngshù)

• Czech: podíl (cs) m
• Danish: kvotient c
• Dutch: quotiënt (nl) n
• Finnish: osamäärä (fi)
• French: quotient (fr) m, rapport (fr) m
• Galician: cociente (gl) m
• Georgian: განაყოფი (ganaq̇opi)
• German: Quotient (de) m
• Greek: πηλίκο (el) n (pilíko)
• Hebrew: מָנָה (he) f (maná)
• Hindi: भगफल m (bhagphal), विभाग (hi) (vibhāg), लब्धि (hi) (labdhi), बाँटफल (bā̃ṭphal), फल (hi) (phal), भजनफल (bhajanphal)
• Hungarian: hányados (hu)
• Icelandic: kvóti (is) m, hlutatala f
• Ido: quociento (io)
• Indonesian: kuosien (id), hasil bagi (id)
• Italian: quoziente (it) m
• Japanese: 商 (ja) (しょう, shō)
• Khmer: ផលចែក (phɑl caek)
• Korean: 몫 (ko) (mok)
• Macedonian: ко́личник m (kóličnik)
• Māori: otinga, otinga wehe
• Norwegian:

  Bokmål: kvotient m

  Nynorsk: kvotient m

• Persian: خارج قسمت, بهر (fa) (bahr)
• Polish: iloraz (pl) m
• Portuguese: quociente (pt) m
• Romanian: cât (ro) n
• Russian: ча́стное (ru) n (částnoje)
• Serbo-Croatian:

  Cyrillic: ко̀личнӣк m

  Latin: kòličnīk (sh) m

• Slovak: podiel m
• Slovene: kolíčnik (sl) m
• Spanish: cociente (es) m, cuociente m
• Swedish: kvot (sv) c
• Tagalog: kahatian
• Telugu: భాగఫలము (bhāgaphalamu)
• Turkish: bölüm (tr)
• Ukrainian: ча́стка (uk) f (částka)
• Vietnamese: thương số (vi), thương (vi)

result of inverse of multiplication defined for non-numerical mathematical entities

• Asturian: cociente m
• Bulgarian: коефицие́нт (bg) m (koeficiént)
• Catalan: quocient m
• Dutch: quotiënt (nl) n
• Finnish: osamäärä (fi)
• French: quotient (fr) m, rapport (fr) m
• Galician: cociente (gl) m
• Italian: quoziente (it) m
• Portuguese: quociente (pt) m
• Russian: результат (ru) m (rezulʹtat)
• Spanish: cociente (es) m, cuociente m
• Swedish: kvot (sv) c
• Tagalog: kahatian

quotum or quota

• Bulgarian: квота (bg) f (kvota)
• Dutch: quotum (nl) n
• Portuguese: cota (pt) m
• Russian: часть (ru) f (častʹ), до́ля (ru) f (dólja)
• Swedish: kvot (sv) c

Verb

quotient (third-person singular simple present quotients, present participle quotienting, simple past and past participle quotiented)

1. (mathematics, group theory) To identify elements within a mathematical structure so as to create a quotient.
   • 2015, Valerio Astuti, Laurent Freidel, “Lorentz invariant deformations of momentum space”, in arXiv‎^[1]:

     We show that such deformations still exists after quotienting out by diffeomorphisms only if the non linear addition is non associative.

   • 2019, James Chapman, Tarmo Uustalu, Niccolò Veltri, “Quotienting the delay monad by weak bisimilarity”, in Mathematical Structures in Computer Science‎^[2], volume 29, number 1, page 67:

     In type theory, one commonly replaces quotients with setoids. In this approach, the delay datatype quotiented by weak bisimilarity is still a monad–a constructive alternative to the maybe monad.

See also

Other terms used in arithmetic operations:

• successor
• addition, summation:

  (augend) + (addend) = (total)

  (summand) + (summand) + (summand)... = (sum)

• subtraction:

  (minuend) − (subtrahend) = (difference)

• multiplication, factorization:

  (multiplier) × (multiplicand) = (product)

  (factor) × (factor) × (factor)... = (product)

• division:

  (dividend) ÷ (divisor) = (quotient)

  (numerator) / (denominator) = (quotient)

  Or sometimes = (quotient) with (remainder) remaining

• exponentiation:

  (base) ^(exponent) = (power)

• root extraction:

  ^(degree) √ (radicand) = (root)

• logarithmization:

  log_(base) (antilogarithm) = (logarithm)

Advanced hyperoperations: tetration, pentation, hexation

Anagrams

• not quite

French

Etymology

From Latin quotientem, from quotiēs.

Pronunciation

• IPA^(key): /kɔ.sjɑ̃/

• Audio (Paris):

  (file)

• Audio (Switzerland (Valais)):

  (file)

• Audio (France (Toulouse)):

  (file)

• Audio (France (Vosges)):

  (file)

Noun

quotient m (plural quotients)

1. quotient (result of a division)

Derived terms

• quotient intellectuel

Further reading

• “quotient”, in Trésor de la langue française informatisé [Digitized Treasury of the French Language], 2012