Multiplication

  

Copyright © Philip M. Parker, INSEAD. Terms of Use.

Multiplication

Definition: Multiplication

Multiplication

Noun

1. An arithmetic operation that is the inverse of division; the product of two numbers is computed; "the multiplication of four by three gives twelve"; "four times three equals twelve".

2. The act of propagating.

3. The process of multiplying; "this multiplication of cells is a natural correlate of growth".

Source: WordNet 1.7.1 Copyright © 2001 by Princeton University. All rights reserved.
 

Date "multiplication" was first used in popular English literature: sometime before 1350. (references)


Synonyms: Multiplication

Synonyms: generation (n), propagation (n), times (n). (additional references)

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Specialty Definition: Multiplication

(From Wikipedia, the free Encyclopedia)

Multiplication is a quick way of adding identical numbers. The result of multiplying numbers is called a product. The numbers being multiplied are called coefficients or factors, and individually as the multiplicand and multiplicator.

Notation

Multiplication can be denoted several different ways, and for all real numbers the different notations are equivalent. All of the following mean, "5 times 2":

The asterisk is often used on computers because it is a symbol on every keyboard, but it is never used when writing math by hand, and should only be used when there are no other alternatives. (This usage originated in the FORTRAN programming language). Frequently, multiplication is implied rather than specifically noted. This arises in Algebra and looks like:

This should only be done with variables that have one letter; with variable that have multiple letters (it is possible, and often less confusing, to write out the name of a variable rather than using a single letter, i.e. using "mass" instead of "m") it can become confusing as to where one variable ends and the other begins. It is also confusing to use this notation with just numbers because 52 could then mean fifty-two or five times two.

If the terms are not written out individually, then the product may be written with an ellipsis to mark out the missing terms. Thus, the product of all the natural numbers from 1 to 100 is 1 · 2 · ... · 99 · 100.

Alternatively, the product can be with the product symbol, which is a capital Pi from the Greek alphabet. This is defined as:

The subscript gives the symbol for a dummy variable (i in our case) and its lower value (m); the superscript gives its upper value. So for example:

One may also consider products of infinitely many terms; these are called infinite products. Notationally, we would replace n above by the infinity symbol (∞). The product of such a series is defined as the limit of the product of the first n terms, as n grows without bound. That is:
One can similarly replace m with negative infinity, and
for some integer m, provided both limits exist.

Definition

As for what multiplication means, the product of two whole numbers n and m is:

This is just a shorthand for saying, "Add m to itself n times." Expanding the above to make its meaning more clear:

m×n = m + m + m +...+ m

such that there are n m's added together. So for instance:

Using this definition, it is easy to prove some interesting properties of multiplication. As the first two examples above hint at, the order in which to numbers are multiplied does not matter. This is called the commutative property and it turns out to be true in general that for any two numbers x and y:

x·y = y·x

Multiplication also has what is called the associative property. The associative property means that for any three numbers x, y, and z:

(x·y)z = x(y·z)

Note from algebra: the parentheses mean that the operations inside the parentheses must be done before anything outside the parentheses is done.

Multiplication is also has what is called a distributive property because:

x(y + z) = xy + xz

Also of interest is that any number times 1 is equal to itself, thus:

1·x = x

and this is called the identity property

What about zero? The initial definition above is little help because 1 is greater than zero. It is actually easier to define multiplication by zero using the second definition. So:

m·0 = m + m + m +...+ m

where there are zero m's added together. The sum of zero m's is zero, so

m·0 = 0

no matter what m is (as long as it is finite).

Multiplication with negative numbers also requires a little thought. First consider negative 1. For any positive integer m:

(-1)m = (-1) + (-1) +...+ (-1) = -m

This is an interesting fact that shows that any negative number is just negative one multiplied by a positive number. So multiplication with any integers can be represented by multiplication of whole numbers and (-1)'s. All that remains is to explicitly define (-1)(-1):

(-1)(-1) = -(-1) = 1

In this way, the multiplication of any two integers is defined. The definitions can be extended to larger and larger sets of numbers: first to fractions called the rational numbers, then to infinitely long decimals called real numbers, and then to the complex numbers.

Students are sometimes mystified when told that the result of multiplying no numbers is 1.

A formal recursive definition of multiplication can be given by the rules:

x.0 = 0
x.y = x + x.(y-1)

where x is an arbitrary quantity, and y is a natural number. Once multiplication has been defined for natural numbers, it can be extended to include integers, and then to real and complex numbers.

Computation

For fast ways to compute products of large numbers, see multiplication algorithms.

To multiply numbers using pencil and paper, you need to have a multiplication table (either in your head or on paper). You also need to know a "multiplication algorithm" (a way to multiply numbers) such as lattice multiplication.

See also:

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Multiplication."

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Synonyms within Context: Multiplication

ContextSynonyms within Context (source: adapted from Roget's Thesaurus).

Multitude

Greater number, majority; multiplication, multiple.

Numeration

Notation, addition, subtraction, multiplication, division, rule of three, practice, equations, extraction of roots, reduction, involution, evolution, estimation, approximation, interpolation, differentiation, integration.

Productiveness

Regnancy, pullulation, fructification, multiplication, propagation, procreation; superfetation.

Reproduction

Generation; (production); multiplication.

Source: adapted from Roget's Thesaurus.

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Crosswords: Multiplication

English words defined with "multiplication": Algebraic function, anaplasiaBible Societycarry, Cell cleavage, Cell developmentDistributive operation, divisionEndogeny, EquimultiplefieldGeometrical progression, Gunter's linehistiocytosisidempotent, identity, identity element, identity operator, Irrelative repetitionLeptothrixmanifold, mathematical product, matrix multiplication, Multiplicate flower, multiplied, multiply, MycothrixNapier's bones, Napier's rodsPhthiriasis, Polysyndetic, product, proliferationSarcina, Sectional boiler, slide rule, Superfecunditytimes. (references)
Specialty definitions using "multiplication": abstract interpretation, Algebraic formula, Algebraic identity, amplifying semiconductor detector, Arithmetic and Logic Unit, arithmetic operator, arithmetical operator, Auxins, average calculating operationBacillus cereus, Balantidium, bill clerk, biller, billing clerk, BILLING-MACHINE OPERATOR, binary fissioncollected current, collector current, criticality factor, cytostaticDS levelElectronic Numerical Integrator and Computerfloating-point acceleratorGeiger region, Geiger-Mueller regionimpact ionisation, impact ionization, Interferons, invoicing-machine operatorlinear space, logical shiftMark 1, Microbial Growth, Motorola 6809, multiplication-reversed rectificationnucleus herdprojective plane, proportional regionshadow factor, Slow Virus Diseases, standardized variable, systolic arrayTownsend avalanche, Townsend ionisation, Townsend ionization, transformation of data valuesunobstructed capacityVirus Replicationzero key. (references)
Non-English Usage: "Multiplication" is also a word in the following language with English translations in parentheses.

French (breed, multiplication).

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Modern Usage: Multiplication

DomainUsage

Clever

Civilization is a limitless multiplication of unnecessary necessities. (references; author: Mark Twain)

Source: compiled by the editor from various references; see credits.

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Commercial Usage: Multiplication

DomainTitle

Books

  • Math by All Means: Multiplication (reference)

  • Multiplication Unplugged-Times Tables to 12 (reference)

  • The Amazing Pop-Up Multiplication Book (reference)

  • Times Tables the Fun Way: Book for Kids: A Picture Method of Learning the Multiplication Facts (reference)

    (more book examples)

  

Theater & Movies

  • Rock 'N Learn - Multiplication Rock (reference)

  • Schoolhouse Rock! - Multiplication Rock (reference)

    (more DVD examples; more video examples)

  

Music

  

High Tech

Source: compiled by the editor from various references; see credits.

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Image Slideshow: Multiplication

Illustrations:
Multiplication

More pictures...

Computer Images:
Multiplication

More pictures...

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Photo Album: Multiplication

ThumbnailDescription & CreditThumbnailDescription & Credit

A microgametocyte, a product of the erythrocytic cycle, is shown in an oval RBC. The ingestion of the gametocytes by an Anopheles sp. mosquito begins the parasitic multiplication process during the Sporogonic Cycle. Credit: CDC.

Malarial parasites undergo asexual multiplication in the erythrocytes, i.e. erythrocytic schizogony. During the ring stage, these three trophozoites will mature into schizonts, which will rupture releasing more merozoites. Credit: CDC.

The malarial parasite Plasmodium falciparum is seen in multiple stages of development. An immature schizont is centrally located. Malarial parasites undergo asexual multiplication in the erythrocytes, i.e. erythrocytic schizogony. Credit: CDC.

  

Source: pictures compiled by the editor from various references; see picture credits.

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Use in Literature: Multiplication

TitleAuthorQuote

Grapes of Wrath

Steinbeck, John

Only a little multiplication now, and this land, this tractor are ours.

Source: compiled by the editor from various references.

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Non-Fiction Usage: Multiplication

SubjectTopicQuote

Health

Malaria generally occurs in areas where environmental conditions allow parasite multiplication in the vector. (references)

In the tubercles, TB bacilli may persist within macrophages, but further multiplication and spread of M. tuberculosis are confined. (references)

After this initial replication in the liver (exo-erythrocytic schizogony ), the parasites undergo asexual multiplication in the erythrocytes (erythrocytic schizogony ). Merozoites infect red blood cells . The ring stage trophozoites mature into schizonts, which rupture releasing merozoites . Some parasites differentiate into sexual erythrocytic stages (gametocytes) . Blood stage parasites are responsible for the clinical manifestations of the disease. (references)

Children

Pakistan

In August a former provincial official reported that a survey revealed that half of the third grade teachers at one school in Punjab did not know their multiplication tables. (references)

Source: compiled by the editor from ICON Group International, Inc.; see credits.

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Speeches: Multiplication

SpeakerTermPhrase(s)

Andrew Jackson

1829-1837To extend the circuit courts equally throughout the different parts of the Union, and at the same time to avoid such a multiplication of members as would encumber the supreme appellate tribunal, is the object desired.

Martin van Buren

1837-1841Certain danger was foretold from the extension of our territory, the multiplication of States, and the increase of population.

Source: compiled by the editor from various references.

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Usage Frequency: Multiplication

"Multiplication" is generally used as a noun (singular) -- approximately 100.00% of the time. "Multiplication" is used about 250 times out of a sample of 100 million words spoken or written in English. Its rank is based on over 700,000 words used in the English language. Some parts-of-speech are not covered due to the samples used by the British National Corpus. (note: percents less than one-hundredth of one percent have been omitted)
Parts of SpeechPercentUsage per
100 Million Words
Rank in English
Noun (singular)100%25018,796

Source: compiled by the editor from several corpora; see credits.

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Expressions: Multiplication

Expressions using "multiplication": Endogenous multiplication matrix multiplication multiplication sign multiplication table multiplication tables. Additional references.

Hyphenated Usage

Beginning with "multiplication": multiplication-reversed.

Source: compiled by the editor from various references; see credits.

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Frequency of Internet Keywords: Multiplication

The following statistics estimate the number of searches per day across the major English-language search engines as identified by various trade publications. Hyperlinks lead to commercial use of the expression at Amazon.com.
 
ExpressionFrequency
per Day

multiplication table

643

multiplication

343

multiplication worksheets

137

multiplication chart

109

multiplication fact

77

multiplication worksheet

21

fraction multiplication

14

multiplication test timed

9

multiplication time table

7

lattice multiplication

6

experimental fringe mechanics moire multiplication

6

chart multiplication table time

5

fuzzy logic multiplication

5

16 bit multiplication x86

3

associative multiplication property

3

card flash multiplication table

3

distributive multiplication property

3

multiplication timed

2

digit multiplication two

2
Source: compiled by the editor from various references; see credits.

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Modern Translation: Multiplication

Language Translations for "multiplication"; alternative meanings/domain in parentheses.

Albanian

  

shumëzim (increase), shtim (accession, accretion, addition, augment, augmentation, build up, enhancement, extension, gain, growth, inclusion, increase, increment, insertion, intensification, interest, proliferation, rise). (various references)

   

Arabic 

  

‏مضاعفة (reduplication), ‏تضاعف (expand, geminate, multiplicity, multiply, redouble), ‏ضرب (batter, battery, beat, beat off, belabour, biff, buffet, chastise, connect, curry, description, drub, drubbing, fib, flap, flapping, form, galvanize, genre, go getter, grain, hit, hitting, impact, jabbing, kidney, kind, lace, lace into smb., lam, larrup, let out, lock out, manner, multiply, order, overtake, paddle, paste, pasting, patter, poke, pommel, pound, pummel, slash, slosh, sock, sort, stamp, strike, stripe, tan, tanning, thrash, thrashing, thresh, variety, wallop, whip). (various references)

   

Bulgarian 

  

умножение, размножаване (breeding, generation, increase, procreation, propagation, reproduction, spawning), плодене (procreation, propagation, reproduction, spawning). (various references)

   

Chinese 

  

乘法 , 增殖. (various references)

   

Czech

  

množení, násobení. (various references)

   

Danish

  

opformering (multiplying). (various references)

   

Dutch

  

vermeerdering (accession, increase). (various references)

   

Finnish

  

lisääntyminen (increase, propagation, reproduction). (various references)

   

French

  

multiplication (multiplying). (various references)

   

German

  

multiplikation, vermehrung (accession, accretion, aggrandizement, augmentation, breeding, enlargement, growth, increase, multiplying, proliferation, propagation, reproduction). (various references)

   

Greek 

  

πολλαπλασιασμός (multiplying, propagation), αναπαραγωγή (breeding, reproduction). (various references)

   

Hebrew 

  

כפל (duplicate), "תרבות (increase, proliferation), "כפל" (duplication, gemination, reduplication), "רבי" (multiplying), "'י", רביון (satisfaction). (various references)

   

Hungarian

  

szorzás (multiplying), szaporodás (accretion, proliferation, prolification, propagation, reproduction, rise). (various references)

   

Indonesian

  

pergandaan (reduplication), perbanyakan, darab. (various references)

   

Italian

  

moltiplicazione (propagation). (various references)

   

Japanese Kanji 

  

増殖 (increase, propagation). (various references)

   

Japanese Katakana 

  

ぞうしょく (increase, propagation), そうじょう (disturbance, high Buddhist priest, report to the Emperor, riot, stratified, synergism), かけざ", じょうざ". (various references)

   

Korean 

  

곱셈. (various references)

   

Manx

  

ymmodaghey (multiply), yl-raghey (multiply), mooadaghey (aggravation, amplify, augment, develop, developing, enlarge, escalate, escalation, exaggerate, exaggeration, exaggerator, expand, expansion, extend, extension, gain, grow, increase, increment, magnification, magnify, maximize, mount, multiply, swell), filltaghey, bishaghey (accession, accession of funds, accrue, develop, development, expand, expansion, growth, increase, multiply, prosper, thrive, wax, wax as moon). (various references)

   

Pig Latin

  

ultiplicationmay

   

Portuguese

  

multiplicação. (various references)

   

Romanian

  

multiplicare (reproduction), înmulţire (increase, propagation). (various references)

   

Russian 

  

умножение (generation). (various references)

   

Serbo-Croatian

  

množenje (breeding, reproduction), umnožavanje, porast (accretion, boost, increase, jump, mark up, pickup, rise, upgrowth, upsurge). (various references)

   

Spanish

  

multiplicación (proliferation). (various references)

   

Swedish

  

multiplikation. (various references)

   

Turkish

  

çoğaltma (aggrandizement, augmentation, increase), çoğalma (accrual, increase, increment, proliferation, propagation, reproduction), çarpma (beat, blip, brunt, bump, impact, jolt, lash, percussion, stroke). (various references)

   

Ukrainian

  

розмножування (pullulation), множення. (various references)

   

Vietnamese 

  

bảng cửu chương (multiplication table). (various references)

   

Welsh

  

lluosogiad, lluosiad. (various references)

Source: compiled by the editor from various translation references.

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Ancestral Language Translations: Multiplication

LanguagePeriodTranslations
Latin500 BCE-Modern

conplicationem, multiplicatione, multiplicationem. (various references)

Source: compiled by the editor from various references.

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Derivations & Misspellings: Multiplication

Derivations

Words beginning with "multiplication": multiplications. (additional references)


Misspellings

"Multiplication" is suggested in spellcheckers for the following: multipication, multiplacation, multiplicate, multiplicational, multiplycation. (additional references)

Source: compiled by the editor, based on several corpora (additional references).

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Rhyming with "Multiplication"

# of Phoneme MatchesPronunciationWord(s) rhyming with "multiplication" (pronounced mu'ltuplukā"shun)
8-p l u k ā" sh u napplication, complication, duplication, explication, implication, misapplication, replication.
7-l u k ā" sh u nallocation, misallocation, reallocation.
6-u k ā" sh u nacidification, adjudication, advocation, amplification, authentication, avocation, certification, classification, codification, communication, convocation, decertification, dedication, deification, desiccation, disqualification, diversification, domestication, edification, education, equivocation, eradication, excommunication, falsification, fortification, gasification, gratification, identification, indication, intensification, intoxication, invocation, magnification, medication, miscommunication, modification, notification, nullification, ossification, pacification, personification, pontification, prefabrication, prognostication, provocation, purification, qualification, quantification, ramification, ratification, recertification, reclassification, rectification, rededication, reunification, revocation, sanctification, saponification, suffocation, unification, verification, vilification, vindication.
5-k ā" sh u nabdication, altercation, bifurcation, clarification, confiscation, demarcation, detoxication, detoxification, disembarkation, dislocation, echolocation, electrification, embarkation, evocation, fabrication, gentrification, glorification, indemnification, justification, location, lubrication, misidentification, mummification, obfuscation, publication, relocation, simplification, sophistication, specification, syndication, telecommunication, vacation, vocation.
4-ā" sh u nabbreviation, aberration, abomination, abrogation, acceleration, acclimation, accommodation, accreditation, accumulation, accusation, activation, adaptation, administration, admiration, adoration, adulation, affectation, affiliation, affirmation, agglomeration, aggravation, agitation, alienation, allegation, alleviation, alphabetization, alteration, amalgamation, amelioration, amortization, amputation, animation, annexation, annihilation, annotation, anticipation, antidiscrimination, appellation, appreciation, approbation, appropriation, approximation, arbitration, argumentation, articulation, aspiration, assassination, assimilation, association, augmentation, authorization, automation, aviation, balkanization, calculation, calibration, cancellation, cannibalization, capitalization, capitulation, carnation, castration, categorization, causation, celebration, centralization, cessation, cetacean, characterization, citation, civilization, coagulation, cogeneration, cogitation, cohabitation, collaboration, collectivization, colonization, coloration, colorization, combination, commemoration, commendation, commercialization, communization, compensation, compilation, computation, computerization, concatenation, concentration, conciliation, condemnation, condensation, confabulation, confederation, configuration, confirmation, conflagration, confrontation, conglomeration, congratulation, congregation, conjugation, connotation, consecration, conservation, consideration, consolation, consolidation, constellation, consternation, constipation, consultation, consummation, contamination, contemplation, continuation, conversation, cooperation, coordination, coronation, corporation, correlation, corroboration, creation, cremation, criminalization, crustacean, culmination, cultivation, dalmatian, damnation, decaffeination, decapitation, deceleration, decentralization, declaration, decontamination, decoration, decriminalization, defamation, deflation, deforestation, deformation, degeneration, degradation, dehumanization, dehydration, deinstitutionalization, delegation, deliberation, delineation, demilitarization, demobilization, democratization, demodulation, demonization, demonstration, demoralization, denationalization, denomination, denuclearization, denunciation, depopulation, deportation, depravation, depreciation, depredation, deprivation, deregulation, derivation, desalination, desalinization, desecration, desegregation, designation, desolation, desperation, destabilization, destination, determination, detonation, devaluation, devastation, deviation, dictation, differentiation, dilatation, dilation, discoloration, discontinuation, discrimination, disinclination, disinflation, disinformation, disintegration, disorganization, disorientation, dispensation, disputation, dissemination, dissertation, dissipation, dissociation, distillation, divination, documentation, domination, donation, dramatization, duration, ejaculation, elaboration, elation, elevation, elimination, elongation, emanation, emancipation, emigration, emulation, enumeration, equalization, equitation, escalation, estimation, evacuation, evaluation, evaporation, exacerbation, exaggeration, examination, exasperation, excavation, excitation, exclamation, exfoliation, exhalation, exhilaration, exhortation, exhumation, exoneration, expatriation, expectation, experimentation, expiration, explanation, exploitation, exploration, expropriation, extermination, extrapolation, facilitation, fascination, federation, fermentation, fertilization, fibrillation, figuration, filtration, fixation, flirtation, flotation, fluctuation, fluoridation, foliation, formation, formulation, foundation, fragmentation, frustration, fumigation, gastrulation, generalization, generation, germination, gestation, glaciation, globalization, gradation, graduation, granulation, gravitation, gyration, habitation, hallucination, harmonization, hesitation, hibernation, hospitalization, humiliation, hybridization, hydration, hydrogenation, hyperinflation, illumination, illustration, imagination, imitation, immigration, immunization, impersonation, implantation, implementation, importation, impregnation, improvisation, imputation, inactivation, inauguration, incantation, incapacitation, incarceration, incarnation, inclination, incoordination, incorporation, incrimination, incrustation, incubation, indentation, indexation, indignation, indoctrination, industrialization, infatuation, infestation, infiltration, inflammation, inflation, information, inhabitation, inhalation, initiation, innovation, inoculation, insemination, insinuation, inspiration, installation, instigation, institutionalization, instrumentation, insubordination, insulation, integration, internationalization, interpretation, interrogation, intimation, intimidation, intonation, inundation, invalidation, investigation, invitation, ionization, irradiation, irrigation, irritation, isolation, jubilation, laceration, lactation, legalization, legislation, levitation, liberalization, liberation, libration, ligation, limitation, liquidation, litigation, localization, machination, magnetization, malformation, manifestation, manipulation, marginalization, masturbation, maturation, maximization, mechanization, mediation, meditation, menstruation, migration, mineralization, miniaturization, ministration, misappropriation, miscalculation, mischaracterization, miscreation, misinformation, misinterpretation, misrepresentation, mitigation, mobilization, moderation, modernization, modulation, molestation, monopolization, motivation, mutation, mutilation, narration, nation, nationalization, naturalization, navigation, negation, negotiation, neutralization, nitration, nomination, nondiscrimination, nonproliferation, normalization, notation, nucleation, obligation, observation, occupation, operation, optimization, oration, orchestration, ordination, organisation, organization, orientation, origination, ornamentation, oscillation, ostentation, ovation, overpopulation, overregulation, overvaluation, ovulation, oxidation, pagination, palpitation, participation, pasteurization, penetration, perforation, permutation, perpetuation, personalization, perspiration, perturbation, pigmentation, plantation, polarization, politicization, pollination, popularization, population, precipitation, predestination, premeditation, preoccupation, preparation, presentation, preservation, pressurization, privation, privatization, probation, proclamation, procrastination, procreation, profanation, proliferation, pronunciation, propagation, proration, prostration, protestation, punctuation, quotation, radiation, radicalization, rationalization, reaffirmation, realization, reauthorization, recalculation, recantation, recapitalization, recitation, reclamation, recommendation, reconciliation, reconfiguration, reconfirmation, reconsideration, recreation, recrimination, recuperation, redecoration, reevaluation, reexamination, reflation, reforestation, reformation, refrigeration, refutation, regeneration, regimentation, registration, regulation, rehabilitation, rehydration, reincarnation, reincorporation, reinterpretation, reinvigoration, reiteration, rejuvenation, relation, relaxation, remediation, remuneration, renationalization, renegotiation, renomination, renovation, renunciation, reorganization, reparation, repatriation, representation, repudiation, reputation, reregulation, reservation, resignation, respiration, restoration, resuscitation, retaliation, retardation, revaluation, revelation, reverberation, revitalization, rotation, rumination, salvation, sanitation, saturation, securitization, sedation, sedimentation, segmentation, segregation, sensation, separation, sequestration, simulation, situation, socialization, solicitation, specialization, speculation, stabilization, stagflation, stagnation, standardization, starvation, station, sterilization, stimulation, stipulation, strangulation, subluxation, subordination, subsidization, substantiation, suburbanization, summation, superstation, tabulation, taxation, temptation, termination, titillation, toleration, transformation, transillumination, translation, transplantation, transportation, trepidation, triangulation, tribulation, undervaluation, unionization, urbanization, usurpation, utilization, vaccination, vacillation, validation, valuation, vaporization, variation, vegetation, ventilation, vibration, victimization, violation, visitation, visualization, vulgarization, westernization.
3-sh u nabduction, abolition, abortion, absolution, absorption, abstraction, academician, accession, accretion, acquisition, action, addiction, addition, admission, admonition, adoption, advection, affection, affliction, aggression, alliteration, alternation, ambition, ammunition, antiabortion, anticorruption, apparition, apportion, apprehension, ascension, ashen, assertion, assumption, attention, attraction, attribution, attrition, auction, audition, beautician, benediction, brutalization, caption, carburetion, caution, circulation, circumspection, clinician, coalition, coercion, cognition, collection, commission, commotion, compassion, competition, completion, complexion, composition, comprehension, compression, compulsion, compunction, conception, conceptualization, concession, concoction, concussion, condescension, condition, conduction, confection, confession, conjunction, connection, conniption, conscription, constitution, constriction, construction, consumption, contention, contortion, contraception, contraction, contradiction, contraption, contribution, contrition, convection, convention, conviction, convolution, convulsion, correction, corruption, counterrevolution, crucifixion, cushion, deception, decimation, decommission, decomposition, decompression, deconstruction, deduction, defection, definition, deletion, demolition, demotion, dentition, depiction, depletion, deposition, depression, dereliction, description, desertion, destitution, destruction, detection, detention, deterioration, devolution, devotion, diction, dietitian, diffraction, digression, dilution, dimension, diminution, direction, disaffection, disconnection, discretion, discussion, disinfection, disposition, disruption, dissatisfaction, dissection, dissension, dissolution, distinction, distortion, distraction, distribution, dysfunction, edition, egyptian, ejection, election, electrician, electrocution, elocution, emission, emotion, emulsion, encryption, erection, erudition, eruption, eviction, evolution, exaction, exception, excoriation, excretion, execution, exemption, exertion, exhibition, expansion, expedition, exposition, expression, expulsion, extension, extinction, extortion, extraction, extradition, faction, fashion, fiction, fission, flexion, formalization, fraction, freshen, friction, fruition, function, gentian, geriatrician, gumption, hessian, homogenization, hypertension, hypotension, ignition, impassion, imperfection, imposition, impression, inaction, inception, incineration, indiscretion, induction, infarction, infection, inflection, infliction, infraction, inhibition, injection, injunction, inquisition, inscription, insertion, inspection, institution, instruction, insurrection, interaction, interception, intercession, interconnection, interdiction, interjection, intermission, interruption, intersection, introduction, introspection, intuition, invention, junction, jurisdiction, juxtaposition, lilliputian, liposuction, liquefaction, locomotion, logician, lotion, magician, malfunction, malnutrition, mansion, martian, mathematician, mention, midsection, misapprehension, misconception, misimpression, misperception, mission, mortician, motion, munition, musician, nonaggression, nonfiction, nonprescription, notion, nutrition, objection, obsession, obstetrician, obstruction, ocean, omission, opposition, oppression, optician, option, overconsumption, overexpansion, overproduction, overprotection, overreaction, oversimplification, partition, passion, patrician, pediatrician, pension, perception, percussion, perfection, permission, persecution, petition, physician, politician, pollution, portion, position, possession, potion, precaution, precession, preconception, precondition, prediction, predilection, predisposition, preelection, preemption, preignition, premonition, prescription, presumption, presupposition, pretension, prevention, procession, production, profession, progression, prohibition, projection, promotion, proportion, proposition, propulsion, proscription, prosecution, prostitution, protection, ration, reaction, reassertion, reception, recession, recognition, recollection, recondition, reconstruction, redefinition, redemption, redirection, redistribution, reduction, reeducation, reelection, reflection, regression, reimposition, reinspection, reintegration, reintroduction, reinvention, rejection, remission, rendition, repercussion, repetition, reposition, repossession, repression, reproduction, requisition, resolution, restitution, restriction, resumption, resurrection, retention, retraction, retransmission, retribution, revolution, revulsion, rhetorician, sanction, satisfaction, secession, secretion, section, sedition, seduction, selection, session, solution, statistician, submission, subscription, subsection, substation, substitution, subtraction, succession, suction, superstition, supposition, suppression, suspension, suspicion, syncopation, tactician, technician, tension, theoretician, titian, traction, tradition, transaction, transcription, transection, transgression, transition, transmission, tuition, venetian, volition, workstation.

Source: compiled by the editor (additional references); see credits.

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Anagrams: Multiplication

Scrabble® Enable2K-Verified Anagrams

Words within the letters "a-c-i-i-i-l-l-m-n-o-p-t-t-u"

-3 letters: implication, impolitical, unpolitical.

-4 letters: ampicillin, illuminati, imputation, limitation, multiplant, mutilation, politician.

-5 letters: ciliation, complaint, compliant, imitation, impaction, impolitic, limonitic, manicotti, multipion, municipal, plication, political, pollinium, pollutant, punctilio, tuitional.

 Words containing the letters "a-c-i-i-i-l-l-m-n-o-p-t-t-u"
 

+1 letter: multiplications.

Source: compiled by the editor from various references; see credits.

SCRABBLE® is a registered trademark. All intellectual property rights in and to the game are owned in the U.S.A and Canada by Hasbro Inc., and throughout the rest of the world by J.W. Spear & Sons Limited of Maidenhead, Berkshire, England, a subsidiary of Mattel Inc. Mattel and Spear are not affiliated with Hasbro.

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Alternative Orthography: Multiplication


Hexadecimal (or equivalents, 770AD-1900s) (references)

4D 75 6C 74 69 70 6C 69 63 61 74 69 6F 6E

Leonardo da Vinci (1452-1519; backwards) (references)

American Sign Language (origins from 1620-1817 in Italy and, especially, France) (references)

=

Semaphore (1791, in France) (references)

Braille (1829, in France) (references)

Morse Code (1836) (references)

--    ..-    .-..    -    ..    .--.    .-..    ..    -.-.    .-    -    ..    ---    -.

Dancing Men (Sir Arthur Conan Doyle, 1903) (references)

Binary Code (1918-1938, probably earlier) (references)

01001101 01110101 01101100 01110100 01101001 01110000 01101100 01101001 01100011 01100001 01110100 01101001 01101111 01101110

HTML Code (1990) (references)

&#77 &#117 &#108 &#116 &#105 &#112 &#108 &#105 &#99 &#97 &#116 &#105 &#111 &#110

ISO 10646 (1991-1993) (references)

004D 0075 006C 0074 0069 0070 006C 0069 0063 0061 0074 0069 006F 006E

British Sign Language (Fingerspelling, BSL; 1992, British Deaf Association Dictionary of British Sign Language) (references)

Encryption (beginner's substitution cypher): (references)

4787788675827875696786758180

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INDEX

1. Definition
2. Synonyms
3. Crosswords
4. Usage: Modern
5. Usage: Commercial
6. Images: Slideshow
7. Images: Photo Album
8. Quotations: Fiction
9. Quotations: Non-fiction
10. Quotations: Speeches
11. Usage Frequency
12. Expressions
13. Expressions: Internet
14. Translations: Modern
15. Translations: Ancient
16. Derivations
17. Rhymes
18. Anagrams
19. Orthography
20. Bibliography


  

Copyright © Philip M. Parker, INSEAD. Terms of Use.