Tamazight-NLP/NLLB-Seed_Tamasheq-Latin-Script huggingface dataset:
English: Taken literally, the above definition is an application of the recursion theorem on the partially ordered set N2.
Tamasheq: Adakal wan taɣare, aliɣi wa ilan sider eqal igitan ən tekanite tan asimuduɣil fal dǎɣ tartite nafala toɣadat N2.
English: If either a or b is zero, treat it as an identity.
Tamasheq: Afal a meɣ b egal wala, aytawaga sund atwizay iyan.
English: Here, the semigroup is formed by the natural numbers and the group is the additive group of integers.
Tamasheq: Diya, təzune ən tartit taqal ayertayan fal maɗinan imanasan əd tartit taqalat tartit tan asiwid ən entiertan.
English: The commutativity and associativity of real addition are immediate; defining the real number 0 to be the set of negative rationals, it is easily seen to be the additive identity.
Tamasheq: Əmilahawan əd sirtayan wən asiwid itawanhayan eqalan agudendǎɣ; dǎɣ aliɣi ən amaɗin itawanhayan 0 sund asirtay rationneltan wi ifnaznen, hanayan nariqisan eqalan atiwasaknan ən təwaƭ.
English: One must prove that this operation is well-defined, dealing with co-Cauchy sequences.
Tamasheq: Nanihaga anisikin as adabara wen eqalan ahusken dǎɣ asikin, dǎɣ igitan ən ulkam wan cob-Cauchy.
English: The set of integers modulo 2 has just two elements; the addition operation it inherits is known in Boolean logic as the "exclusive or" function.
Tamasheq: “Tartit tan entiertan modulo 2 wadila ad əsin haratan; adabara wen naśiwiɗ amosan adogaz eqalan atiwazan dǎɣ uqud ən booléen daw əsim ən əšiɣil ""wan ukis meɣ"".
English: These give two different generalizations of addition of natural numbers to the transfinite.
Tamasheq: Awen ihaku əsin generalisationtan abdanen dǎɣ təwaƭ ən maɗinan imanas dǎɣ transfini.
English: There are even more generalizations of multiplication than addition.
Tamasheq: Ilanti harwa iyogarnen generalisationtan ən asinimi ƭif wan asiwid.
English: In fact, if two nonnegative numbers a and b are of different orders of magnitude, then their sum is approximately equal to their maximum.
Tamasheq: Dǎɣ atwig, afal əsin maɗinan winan eqel aygadam a meɣ b aqalan dǎɣ təmɣire tabdat, mašan hadi nasan eqal ohazan adiqil wa samando nasan.
English: It includes the idea of the sum of a single number, which is itself, and the empty sum, which is zero.
Tamasheq: Itawaga dǎɣas anizgum ən hadi niyandǎɣ amaɗin, eqalan inta emanes, əd hadi wan banan, eqalan wala.
English: Integration is a kind of "summation" over a continuum, or more precisely and generally, over a differentiable manifold.
Tamasheq: Ugiš eqalan iyan azagar ən "atwiqal" fal əontinuum, meɣ ogaran asinihig əd amosan, fal umaɣ ebdanen.
English: Linear combinations are especially useful in contexts where straightforward addition would violate some normalization rule, such as mixing of strategies in game theory or superposition of states in quantum mechanics.
Tamasheq: Ənsirtayan anilkamnen aqalnen amosnen ayfan dǎɣ əmik ɣur təwa ƭ toɣadat tihaɣnen tabarat ən asisiɣid, sund asirtay wan əmikan ən tekanit tan adal meɣ tihusay ən taɣimit taqalat dǎɣ mécanique quantique.
English: Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers.
Tamasheq: Tuzant taqal iyat dǎɣ tinikozat adabarat ən santo wan arithmétique, atamosan əmik wamosan əmaɗinan aqalnen ayertayan fal igi ən maɗinan aynaynen.
English: Those in which a Euclidean division (with remainder) is defined are called Euclidean domains and include polynomial rings in one indeterminate (which define multiplication and addition over single-variabled formulas).
Tamasheq: Widǎɣ amosnen təbiɗawt euclidien (awa diqiman) eqal atiwalaɣen aqalan asitawana tabarat tan euəlidien əd tila anneautan polynomiaux dǎɣ awinan atwasan (waytalaɣen animtafan əd təwaɗen fal əmikan ən aytimutuyan).
English: This division sign is also used alone to represent the division operation itself, as for instance as a label on a key of a calculator.
Tamasheq: Ašikel wen ən tuzant taqalat amitkalan intaɣas fal asiknin adabara ən tibidawt iman nasan, sund dǎɣ asikin sund étique ƭe fal ades ən calculatrice.
English: Distributing the objects several at a time in each round of sharing to each portion leads to the idea of 'chunking' a form of division where one repeatedly subtracts multiples of the divisor from the dividend itself.
Tamasheq: Tazune ən haratan ajotnen fal ajit ən hak aɣalay ən təzune dǎɣ hak aɣil nagay ən anuzgum ən "əhunking", əmik wan təzune ɣur itakas awadim dǎɣ əmik amidǎɣalan ən anmitif ən amazan ən diɣidende imanes.
English: A person can use logarithm tables to divide two numbers, by subtracting the two numbers' logarithms, then looking up the antilogarithm of the result.
Tamasheq: Awadim adobat adtiqil tabarat tan logarithme fal tazant nəsin maɗinan, dǎɣ afanaz ən logarithme wasisin maɗinan, izar dǎɣ umaɣ ən antilogarithme awatwagrawan.
English: Some programming languages, such as C, treat integer division as in case 5 above, so the answer is an integer.
Tamasheq: Əmigridan iyad ən asinihigi, sund C, taganen tuzant dak sund dǎɣ əmik wan 5 tan afala, aliɣi eqalan amosan aymdan.
English: Similarly, right division of b by a (written ) is the solution y to the equation .
Tamasheq: Dǎɣ sundawen, tazune toɣadat ən b fal a (iktab) eqalan adabara dǎɣ iha équation.
English: Examples include matrix algebras and quaternion algebras.
Tamasheq: Algebretan ən matriəetan əd algebretan ən quaterniontan dǎɣ aqalan sund dolahan.
English: Entry of such an expression into most calculators produces an error message.
Tamasheq: Ugiš ən magrad dǎɣ iyadak dǎɣ əaləulatriəetan iganen isalan winan oɣed.
English: Since this replacement reduces the larger of the two numbers, repeating this process gives successively smaller pairs of numbers until the two numbers become equal.
Tamasheq: Sund asimutiy ifnazan ogaran təmɣire wi nisin imaɗinan, tanalist ən tabarat tatiwafat ən əsin maɗinan ogarnen dǎɣ ugur ən timidrit hawendǎɣ har əsin maɗinan aqalnen ogdahan.
English: The fact that the GCD can always be expressed in this way is known as Bézout's identity.
Tamasheq: Igi was GCD adobat harkuk adiqil aygan dǎɣ əmik wendǎɣ eqalan atiwazay sund amuzuy ən Bézout.
English: With this improvement, the algorithm never requires more steps than five times the number of digits (base 10) of the smaller integer.
Tamasheq: Fal təmotayen tən, algorithme winan eqel atiwasan ogaran simos handagan wi amaɗin ən edanan (dǎɣ santo ən 10) wa ogaran təmidrit əmdan.
English: The Euclidean algorithm has many theoretical and practical applications.
Tamasheq: Algorithme euclidien ən iyajotnen igitan ən tabarat əd tawaganen.
English: The Euclidean algorithm may be used to solve Diophantine equations, such as finding numbers that satisfy multiple congruences according to the Chinese remainder theorem, to construct continued fractions, and to find accurate rational approximations to real numbers.
Tamasheq: Algorithme euclidien adoben adiqil amitkalan fal kanan ən taqinen dioɗhantiennetan, dǎɣ milahaw fal adigriwan imaɗinan wi sagdahnen ən əongruenəetan animatafnen dǎɣ tabarat tan əhinoistan wi dakimanen , fal adiqinan inamawarnen okaynen əd fal adigriwan ahazan ən rationnelletan təɣidnen imaɗinan atiwasanen.
English: The greatest common divisor is often written as gcd(a, b) or, more simply, as (a, b), although the latter notation is ambiguous, also used for concepts such as an ideal in the ring of integers, which is closely related to GCD.
Tamasheq: Wa ogaran təmɣire amazan ən tərtit eqalan agudiyan ayiktaban sund gəd (a, b) meɣ, ogaran tarɣise, sund (a, b), ahuskat as tatilkamat tən aytakasan eqalan atiwasan dǎɣ ašrutan, ogdahan dǎɣ amitkal fal əonəeɗtan amosan iyan anuzgum dǎɣ anneau ən wi əmdanen, eqalan oɣadan ertayan dǎɣ GCD.
English: For example, neither 6 nor 35 is a prime number, since they both have two prime factors: 6 = 2 × 3 and 35 = 5 × 7.
Tamasheq: Dǎɣ olahan, wade 6 wala 35 wadeqel amaɗin wazaran, falas ilan daknasan əsin faəteurtan wi azarnen: 6= 2 × 3 əd 35 = 5 × 7.
English: Factorization of large integers is believed to be a computationally very difficult problem, and the security of many widely used cryptographic protocols is based upon its infeasibility.
Tamasheq: Ifanazan wi wimaqornen imaɗinan əmdanen eqalan atiwagan sund asibab aśohen hulen dǎɣ alɣisab, əd uguz ən ɗrotoəoletan ən cryptographique harawnen dǎɣ amitkal eqalan ayhan fal iba nigines.
English: The set of all integral linear combinations of a and b is actually the same as the set of all multiples of g (mg, where m is an integer).
Tamasheq: Tartite nimirtayan dak anilkamnen ahanen dǎɣ a əd b eqalan dǎɣ igi ən asirtay wan nəmitifan kul ən g (mg, ɣur m eqalan amaɗin əmdan).
English: In other words, multiples of the smaller number rk−1 are subtracted from the larger number rk−2 until the remainder rk is smaller than rk−1.
Tamasheq: Dǎɣ iyad əmikan, ənimtifan wi ogarnen təmidrit amaɗin rk-1 aqalnen adigmadan wa ogaran təmɣire amaɗin rk-2 hawendǎɣ har awa diqiman rk amosan ogaran təmidrit ən rk-1.
English: Therefore, c divides the initial remainder r0, since r0 = a − q0b = mc − q0nc = (m − q0n)c.
Tamasheq: Dǎɣ aɣašad, ə tazun awadiqiman insanto r0, falas r0 = a - q0b = mə - q0nc = (m - q0n)c.
English: We first attempt to tile the rectangle using b-by-b square tiles; however, this leaves an r0-by-b residual rectangle untiled, where r0 < b. We then attempt to tile the residual rectangle with r0-by-r0 square tiles.
Tamasheq: Nitirim izar ye asisigdah ən reətangle dǎɣ tadhil ən əarreautan ogdahnen b fal b ; agudendǎɣ, awen itiyu reətangle résiduel r0 ɗar b winan eqel amisasaran, ɣur r0 < b. Nitirim agudiyan ye asisigdah ən reətangle résiduel dər ən əarreautan ogdahnen r0-fal-r0.
English: The theorem which underlies the definition of the Euclidean division ensures that such a quotient and remainder always exist and are unique.
Tamasheq: Təmusne tan winan tifles aliɣi wan tazune tan euəlidien ikanu iyandǎɣ quotient əd iyamosan adiqiman atilan harkuk əd aqalnen iyadǎɣ.
English: At the end of the loop iteration, the variable b holds the remainder rk, whereas the variable a holds its predecessor, rk−1.
Tamasheq: Dǎɣ samando ən asimusuɣil wan tisifil, təbidaw ƭ ən b tataf awadiqiman rk, mašan tamotayt tan a tataf way han edag, rk-1.
English: The mathematician and historian B. L. van der Waerden suggests that Book VII derives from a textbook on number theory written by mathematicians in the school of Pythagoras.
Tamasheq: Əmasaɗinan əd awtifust B. L. Ɣan der Waerden aɣelan alkitab ƔII adigmaɗan manuel fal ən tabarat tan maɗinan iktaban fal əmasaɗinan wən taɣare ən Pythagore
English: Centuries later, Euclid's algorithm was discovered independently both in India and in China, primarily to solve Diophantine equations that arose in astronomy and making accurate calendars.
Tamasheq: Təmaɗ nelan darat awen, algorithme Euclidien eqal atiwagrawan dǎɣ Inde əd dǎɣ Chine, aqalnen fal kanan ən tidas diophantienne ti nasanen dǎɣ astronomie əd fal igi ən calendriertan itbatnen.
English: The Euclidean algorithm was first described numerically and popularized in Europe in the second edition of Bachet's Problèmes plaisants et délectables (Pleasant and enjoyable problems, 1624).
Tamasheq: Algorithme Euclidien eqal ayktaban numeriquement fal wadazaran ehandag əd atiwasanan dǎɣ Euroɗe dǎɣ tasanatat tədiwt ən asibaban atiwarhanen əd atiwarhan ən Bachet (1624).
English: In the 19th century, the Euclidean algorithm led to the development of new number systems, such as Gaussian integers and Eisenstein integers.
Tamasheq: Dǎɣ 19 temede nawatay, algorithme Euclidien ilway dǎɣ təwa ƭ nəmikan aynaynen ən numérique, atamosan aymdan dǎɣ Gauss əd əmdanen wi Eisenstein.
English: Peter Gustav Lejeune Dirichlet seems to have been the first to describe the Euclidean algorithm as the basis for much of number theory.
Tamasheq: Peter Gustaɣ Lejeune Dirichlet olahnen dagaraw eqalan wadazaran dǎɣ atwiktab ən algorithme euəlidienne sund santo maqaran aɣil wa tabarat tan maɗinan.
English: For example, Dedekind was the first to prove Fermat's two-square theorem using the unique factorization of Gaussian integers.
Tamasheq: Dǎɣ olahan, Dedekind eqalan wa dazaran asikna tabarat ən əsin sisigdihan ən Fermat dǎɣ amitkil ən fanaz iyandǎɣ dǎɣ wəmdanen ən Eisenstein.
English: Other applications of Euclid's algorithm were developed in the 19th century.
Tamasheq: Iyad igitan ən algorithme wan Euclide aqalan adiɗan dǎɣ19e temede nawatay
English: Several novel integer relation algorithms have been developed, such as the algorithm of Helaman Ferguson and R.W. Forcade (1979) and the LLL algorithm.
Tamasheq: Ajotnen aynaynen algorithmetan ən ilanen gar əmdanen aqalnen awidan, amosan algorithme wan Helaman Ferguson əd R.W. Forəade (1979) əd algorithme LLL.
English: The players take turns removing m multiples of the smaller pile from the larger.
Tamasheq: Imadalan irkaban dǎɣ aɣalay ən əšiɣil m animatafan wən tuhunt tadirat togarat təmɣire.
English: By allowing u to vary over all possible integers, an infinite family of solutions can be generated from a single solution (x1, y1).
Tamasheq: Dǎɣ taganen dǎɣ u ən atimutiy fal əmdanen adobatnen, terwe winan təminda dǎɣ adabaratan adobatnen adiqilan anelasan fal adabara iyandǎɣ (x1, y1).
English: In this field, the results of any mathematical operation (addition, subtraction, multiplication, or division) is reduced modulo 13; that is, multiples of 13 are added or subtracted until the result is brought within the range 0–12.
Tamasheq: Dǎɣ tabarat ten, igarawan ən tədas ən maɗinan (asiwiɗ, ukis, asinimi ƭif meɣ tizune) aqalan ayfnazan modulo 13, atamosan anmitif ən 13 aqalan awiɗan meɣ ukis hawendǎɣ har agaraw eqal aditiwawayan dǎɣ efay 0-12.
English: Now assume that the result holds for all values of N up to M − 1.
Tamasheq: Nasinihiget amaradǎɣ as agaraw eqal atiwagrawan fal ɣaleurtan dak ən N hawendǎɣ M - 1.
English: For illustration, the probability of a quotient of 1, 2, 3, or 4 is roughly 41.5%, 17.0%, 9.3%, and 5.9%, respectively.
Tamasheq: Dǎɣ kanan, asinihigi ən awadiqiman ən 1, 2, 3 əd 4 eqal ihomiši 41,5 %, 17,0%, 9,3% əe 5,9%, dǎɣ anilkam.
English: One inefficient approach to finding the GCD of two natural numbers a and b is to calculate all their common divisors; the GCD is then the largest common divisor.
Tamasheq: Ahaz winan aśohat fal agaraw ən GCD ən əsin maɗinan imanasan a əd b itagan alɣisab ən mazanan oharnen ; GCD eqalan adiš ogaran təmɣire amazan oharan.
English: As noted above, the GCD equals the product of the prime factors shared by the two numbers a and b. Present methods for prime factorization are also inefficient; many modern cryptography systems even rely on that inefficiency.
Tamasheq: Sund atiwaɗaqen daw ider, ən GCD eqalan ogdahan dǎɣ alil ən faəteurtan wi dazarnen azunen fal wi nəsin imaɗinan a əd b. Tabaraten ti amaradǎɣ ən afanaz ən maɗinan wi dazarnen aqalan intanedǎɣ winan aśohat; ajotnen əmikan ən əryɗtograɗhiquetan amutaynen taɣaymen dǎɣ fal iba naśahat wen.
English: Lehmer's GCD algorithm uses the same general principle as the binary algorithm to speed up GCD computations in arbitrary bases.
Tamasheq: Algorithme GƏD ən Lehmer amitkalan dǎɣ iyandǎɣ oɣadan atiwazay dǎɣ algorithme nəsin fal atrub ən alɣisab GCD dǎɣ winsanto imahadan.
English: The Euclidean algorithm can be used to solve linear Diophantine equations and Chinese remainder problems for polynomials; continued fractions of polynomials can also be defined.
Tamasheq: Algorithme euclidien adobat adiqil amitkalan fal adiqin alɣisaban dioɗhantienne anilkamnen əd aśibaban wi daqimanen ən chinois fal polynômetan ; fractiontan okaynen dǎɣ polynômetan adobatnen deɣqanen eqalan atiwalaɣen.
English: Any Euclidean domain is a unique factorization domain (UFD), although the converse is not true.
Tamasheq: Tabaraten dak ti euclidien eqalan tabarat tan fanazan iyadǎɣ (UFD), ahuskat as amšiliq winan eqel aduten.
English: A Euclidean domain is always a principal ideal domain (PID), an integral domain in which every ideal is a principal ideal.
Tamasheq: Tabarat tan euclidien eqal harkuk ən tabarat nanizgum itbatan (DIP), tabarat tanugiš dǎɣ tas amosan hak anizgum atiwasanan.
English: Numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals.
Tamasheq: Imasaɗinan əd malaɣatan aqalnen intanedǎɣ amitkalan dǎɣ fractiontan winan eqel oharnen, amosnen fractiontan artaynen, fractiontan aśohatnen əd minéraux artaynen.
English: The term was originally used to distinguish this type of fraction from the sexagesimal fraction used in astronomy.
Tamasheq: Əmik eqalan amosnen amitkalan fal təbiɗawt ən əmik wan fraətion ən fraətion sexagésimale amitkalan dǎɣ astronomie.
English: This was explained in the 17th century textbook The Ground of Arts.
Tamasheq: Awen eqal atiwalaɣen dǎɣ edes ən 17e temede nawatay sitawana The Ground of Arts.
English: The product of a fraction and its reciprocal is 1, hence the reciprocal is the multiplicative inverse of a fraction.
Tamasheq: Asinimitif ən fraction əd ən amliliy eqalan ogdahan dǎɣ 1. Amliliy eqal adiš animašrayan ən nimitafan ən fraction.
English: The remainder becomes the numerator of the fractional part.
Tamasheq: Awadiqiman eqal wanafala ən tasaga ən fractionnaire.
English: Since 5×17 (= 85) is greater than 4×18 (= 72), the result of comparing is .
Tamasheq: Falas 5×17 (=85) eqal ayzwayan dǎɣ 4×18 (= 72), agaraw ən təbiɗawen aqalan.
English: Since one third of a quarter is one twelfth, two thirds of a quarter is two twelfth.
Tamasheq: Falas was karaɗ ən ikoz eqal was maraw ən diyan, wa əsin ən karaɗ dǎɣ ikoz aqalnen wasisin dǎɣ maraw ən disin.
English: Sometimes an infinite repeating decimal is required to reach the same precision.
Tamasheq: Agudiyan, mariaw elan anilkamnen dǎɣ samando eqal ayfan fal agad ən aytbatan wendǎɣ.
English: The Egyptians used Egyptian fractions  BC.
Tamasheq: Égyptientan amitkalnen dǎɣ fractiontan ən égyɗtienne BC.
English: Their methods gave the same answer as modern methods.
Tamasheq: Tabarat nasan haku aliɣi imanes ən tabaraten amutaynen.
English: A modern expression of fractions known as bhinnarasi seems to have originated in India in the work of Aryabhatta, Brahmagupta, and Bhaskara.
Tamasheq: Əsalan amutaynen dǎɣ fractiontan atiwazaynen daw əsim ən bhinnarasi olahan adiqil aywan dǎɣ Inde dǎɣ əšiɣilan ən Aryabha ƭa, Brahmaguɗta əd Bhaskara.
English: In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus.
Tamasheq: Dǎɣ maɗinan, algorithme modulaire eqal əmik iyan ən arithmétique fal əmdanen, ɣur maɗinan ""tikmikimiten"" ugud waɗiwadan iyan ɣaleur, sitawana module."
English: A very practical application is to calculate checksums within serial number identifiers.
Tamasheq: Igi itawagen harkuk aytagu alɣisab ən hadi ən tanhat dǎɣ atwizayan ən numéro ən anilkaman.
English: RSA and Diffie–Hellman use modular exponentiation.
Tamasheq: RSA ən Diffie–Hellman mǎgrǎd exponentiation.modulaire
English: It is used by the most efficient implementations of polynomial greatest common divisor, exact linear algebra and Gröbner basis algorithms over the integers and the rational numbers.
Tamasheq: Taqal ayšɣalan daɣ imɗlémentationtan wi ogarnen aśuhu ən wagaran asirtay daɣ tazune ən ɗolynomial, wən tabarat tan maɗine anilkaman oɣad əd algorithmetan wən santo far entiertan əd maɗinan ətbatnen.
English: The modulo operation, as implemented in many programming languages and calculators, is an application of modular arithmetic that is often used in this context.
Tamasheq: Asəmusudiw wan modulo, atamosan igines daɣ məgridan ajotnen ən almaɣnatan əd alɣisaban, eqalan aytawagen daɣ maɗinan wən adabaratan aqalnen agudiyan amitkalan daɣ almaɣna wen.
English: The method of casting out nines offers a quick check of decimal arithmetic computations performed by hand.
Tamasheq: Daɣ əmik wan agamad daɣ asostanan aynaynen ukisnašak irmaɗan daɣ alɣisab ən maɗinan animawarnen tawaganen safus.
English: A linear system of congruences can be solved in polynomial time with a form of Gaussian elimination, for details see linear congruence theorem.
Tamasheq: Almaɣna anilkaman daɣ awa ilan gar maɗinan sihomiši ikna sund ɗolynomial dər əmik wan ukis ən gaussienne, fal ibaɗan wi ogarne inhiy tanhat tan awa ilan gar maɗinan anilkamnen.
English: The multiplication of integers (including negative numbers), rational numbers (fractions) and real numbers is defined by a systematic generalization of this basic definition.
Tamasheq: Asinmitif ən maɗinan əmdanen (atomosan wi ifnaznen), maɗinan animawarnen (franctintan) əd maɗinan tawanhaynen aqalnen atiwazayan səmik wan atwizay wan təmusne tan santo.
English: The product of two measurements is a new type of measurement.
Tamasheq: Anmitaf nəsin makatan eqal aynayan əmik wan akot.
English: The inverse operation of multiplication is division.
Tamasheq: Alzawaɗ wan amlalay ən ninmitif eqal tazune.
English: The division of a number other than 0 by itself equals 1.
Tamasheq: Tazuner namaɗin iyan winan amos 0 sinta emanes eqal iyandǎɣ.
English: This implicit usage of multiplication can cause ambiguity when the concatenated variables happen to match the name of another variable, when a variable name in front of a parenthesis can be confused with a function name, or in the correct determination of the order of operations.
Tamasheq: Igitan winDǎɣ okayan dǎɣ anmitaf adobat adiqil tabarat naylan gar əsin haratan ugud tə timutuynen amisadawnen dǎɣ əmawan ahanat olahan dǎɣ əsim wan təbiɗawen tiyad, hak əsim ən atimutuyan dat dǎɣ ɗarenthèse eqal sihomiši olahan ən əsim nəšiɣil, meɣ dǎɣ asikin oɣadan ən anilkaman ən tidas.
English: The numbers to be multiplied are generally called the "factors".
Tamasheq: "Maɗinan wi tənmitifnen aqalan intanedǎɣ asitawan ““facteurs””.”
English: Also as the result of a multiplication does not depend on the order of the factors, the distinction between "multiplicand" and "multiplier" is useful only at a very elementary level and in some multiplication algorithms, such as the long multiplication.
Tamasheq: "Olahan dadabara wan asinimitaf warilkem ye anilkam ən wi sənmititnen, awa tan ebdan garesan ““multiɗliəande”” et ““way sinmitifan”” wareqel ayfan aswade hadi izwayan əd dǎɣ algorithmetan wən asinmitaf, sund asinmitaf wa zigren.
English: The result of a multiplication is called a product.
Tamasheq: Aljawaban wən asinmitaf as itawanen asirtay.
English: The slide rule allowed numbers to be quickly multiplied to about three places of accuracy.
Tamasheq: Almaɣna wan alɣisab itagu asinmitaf irmaɗan ən maɗinan dər asidutu naywaɗan idagan karaɗ.
English: The general theory is given by dimensional analysis.
Tamasheq: Tanhat tan tətiwazayat ataqal atiwafan səmik wan akotan.
English: The complex numbers do not have an ordering.
Tamasheq: Maɗinan wi asohatnen warilen anilkaman.
English: Here we have identity 1, as opposed to groups under addition where the identity is typically 0.
Tamasheq: Nila diha əsiknitan 1, aybdan dǎɣ tisdaw tən daw asiwid ɣur asikin eqal atamosan 0.
English: To see this, consider the set of invertible square matrices of a given dimension over a given field.
Tamasheq: Dǎɣ təmusne, atiwaga tartit tan matriəetan ogdahan əs tisigwen ən nakot ən huk dǎɣ edag atiwafan.
English: Another fact worth noticing is that the integers under multiplication is not a group—even if we exclude zero.
Tamasheq: Iyan tagu anihagan aɗiqil ayktaban eqalan entiertan wi daw sənmitifan wareqel adiwan, indar tigmaɗ wala.
English: In mathematics, a percentage (from Latin per centum "by a hundred") is a number or ratio expressed as a fraction of 100.
Tamasheq: "Dǎɣ maɗinan, ɗourəentage iyan (wan latin ɗer əentum ““ɗar cent””) eqal amaɗin meɣ iyad ikan asikin ən daw təniɣruf tan anmiwir wan 100.”
English: Computation with these fractions was equivalent to computing percentages.
Tamasheq: Tidas dər anmiwarnasnat eqal ogdahan ən tidas tən pourcentagetan.
English: Whenever communicating about a percentage, it is important to specify what it is relative to (i.e., what is the total that corresponds to 100%).
Tamasheq: Ugud wan salan ən ɗourəentage, ahuskat adisikin nawa amos (atamosan əndeki hadi nawaɗan 100%).