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For example, digital computers can reuse existing adding-circuitry and save additional circuits for implementing a subtraction, by employing the method of two's complement for representing the additive inverses, which is extremely easy to implement in hardware (negation). | Sund, ordinatertan ən edanən adoben atkul ən taberaten ən assiwəd aɣlaknen ad assəməsədu ən taberaten awednen as sanatən ye assəkən ən imliliyan awednen, awa iknan təraɣse ən iji dǎɣ ašəɣəl dǎɣ harat (tamətki). |
Multiplication also combines two numbers into a single number, the product. | Asjət asertay deɣ assin edan as iyan dǎɣ, asənətfəs. |
If the numbers are imagined as lying in a line, multiplication by a number greater than 1, say x, is the same as stretching everything away from 0 uniformly, in such a way that the number 1 itself is stretched to where x was. | As aznazjamat awadəm as imaɗinan ilan ɣor tassaret,asjət as adin ojarən 1, nənna x, eqalid as anərkəb olahən awa itijəjan kul 0, as alməɣna as adin 1 imanes adəqəl anərkab ɣor edag ɣor ila x. |
Any dividend divided by zero is undefined. | Amazun kul azunən as wala war atwəssən. |
The fundamental theorem of arithmetic was first proven by Carl Friedrich Gauss. | Tamkare maqarat ən edan tatiwasəkna as tizarat as Carl Friedrich Gauss. |
"Positional notation (also known as ""place-value notation"") refers to the representation or encoding of numbers using the same symbol for the different orders of magnitude (e.g., the ""ones place"", ""tens place"", ""hundreds place"") and, with a radix point, using those same symbols to represent fractions (e.g., the ""tenths place"", ""hundredths place"")." | "Akatab ibdadən (tatiwazayat fal issəm ən ""akatab tamɣar ən edag(""itirək as assəkən meɣ aɣafal ən maɗinan dǎɣ atkul ən iyan ešwal ən mezlayən anilkamnen ən tamɣar (sund,""edag ən iyad""""edag ən təmərwen(""izar, ad edag ən radix, dǎɣ atkul ən ešwalan olahnen ye assəkən ən ikərumatan (sund,""edag ən tamara """"edagən timad".("" |
The use of 0 as a placeholder and, therefore, the use of a positional notation is first attested to in the Jain text from India entitled the Lokavibhâga, dated 458 AD and it was only in the early 13th century that these concepts, transmitted via the scholarship of the Arabic world, were introduced into Europe by Fibonacci using the Hindu–Arabic numeral system. | Atkul ən wala sund harat ən assəmutiy ad,as alkum,atkul ən akatab azuken eqal taguhe ye tizarat dǎɣ akatab jaïn ən Inde atiwəɣran as Lokaɣibhâga, intan ɣor 458 darat J.-C. izar ɣor sənto ən 13e awatay as muziyaten, atiwəfanen as torhajət ən musnat ən adunya ən tarabt,agašən ɣor Europe as Fibonacci dǎɣ atkul ən mertay ən adin hindu-tarabt. |
The result is calculated by the repeated addition of single digits from each number that occupies the same position, proceeding from right to left. | Agaraw atiwassedan as assiwad amissaɣalan ən adinan iyadǎɣ ən maɗin kul ikrašən edag iyan ,as atkul ɣor aɣil as tašalje. |
The rightmost digit is the value for the current position, and the result for the subsequent addition of the digits to the left increases by the value of the second (leftmost) digit, which is always one (if not zero). | Adin iknan ugiš ən aɣil edagar ən edaj namaradǎɣ, ad agaraw ən assiwad adimalan ən edanan dǎɣ tašalje tiwadan as talət ən edan wasəsin (ihan tašalje),ogdahən harkuk ad iyan (as warogdeh as wala). |
A multiplication table with ten rows and ten columns lists the results for each pair of digits. | Tabalt ən assənətfəs təlat maraw laytan ad marawat təzunawen issakna igarawən ən assin edanən kul. |
Similar techniques exist for subtraction and division. | Timkarawen olahnen aɣlaknat ye afanaz ad tazunt . |
In mathematical terminology, this characteristic is defined as closure, and the previous list is described as . | Dǎɣ saməndo ən maɗin, tamezlayt tatiwatkal sund aɣəfal, akatab okayan tatiwalaɣat sund. |
The total in the pence column is 25. | Amsədu ən tazunt ən pence taqal 25. |
This operation is repeated using the values in the shillings column, with the additional step of adding the value that was carried forward from the pennies column. | Assedən wen amissaɣəl dǎɣ atkul edan ən ehan ən šillings, ad ašrut awedan təfat asiwad ən adin izjarən ihan wan pennies. |
"One typical booklet that ran to 150 pages tabulated multiples ""from one to ten thousand at the various prices from one farthing to one pound""." | "Alkad olahan ilan 150 ɗageten issakna tijutawen ""ɣor iyan as maraw efdan ɣor hebutan abdanen əlanen ɣor farthing as alkad"". |
This study is sometimes known as algorism. | Aləmad wen atiwəssan agud iyan fal issəm ən algorisme. |
Also, arithmetic was used by Islamic Scholars in order to teach application of the rulings related to Zakat and Irth. | Edanən atiwətkal deɣ as imusanən ən inəsləman ye assaɣar ən iji tənaten adəkalen Tanaqast ad Irth. |
Addition (usually signified by the plus symbol ) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. | Assiwad (atiwətkal as ešwal ən assiwad) taqal iyan dǎɣ akoz sidinən ən amas ən madin, karad wiyadnen aqalan afanaz, assənətfəs ad tazunt. |
In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces and subgroups. | Dǎɣ assedin, edag iyan ən imaɗinan, assiwəd adobat atwəj fal haratan əfarnen sund ɣeəteurtan, matrices, tidəgaten ad təmsədawen. |
"Using the gerundive suffix -nd results in ""addend"", ""thing to be added""." | Atkul ən səmdo gérondif -nd ihaku edag ye ""addenadde”", “”harat ən assiwad""." |
"""Sum"" and ""summand"" derive from the Latin noun summa ""the highest, the top"" and associated verb summare." | ""Sum"ad ""Summand""izjarənid issəm latin summa ""iknan azaway,afəla""ad magrad ertayan summare". |
"The later Middle English terms ""adden"" and ""adding"" were popularized by Chaucer." | "Tənaten ən tədabit-təglizit təknat tahajit "adden"ad “"adding"”atwəzayan as Chaucer." |
As an example, should the expression a + b + c be defined to mean (a + b) + c or a + (b + c)? | As təlat ən milhaw,akatab a + b + c as atwətkəl sund adərtidila ( a + b) + c meɣ a + (b + c)? |
Even some nonhuman animals show a limited ability to add, particularly primates. | Iyad imudaran imanes waren eqel adinat saknen assahat ən assiwad ibdadən, atamosən aytedim. |
"With additional experience, children learn to add more quickly by exploiting the commutativity of addition by counting up from the larger number, in this case, starting with three and counting ""four, five.""" | "Ad aləmad, aratən lamədan assiwəd šikanen as dakalan asəmələliy ən assiwad as sadanən ɣor maɗin wa iknan təmɣare,dǎɣ edag wen, dǎɣ assənt as karad as isadan ""akoz, səmos.""" |
Zero: Since zero is the additive identity, adding zero is trivial. | Wala: falas wala eqal muzyat tawedat, assiwad ən wala eqal raqis. |
One aligns two decimal fractions above each other, with the decimal point in the same location. | Nəzimzizer assin ikərumatən decimales iyan fal iyan, ad edag décimal ɣor iyan edag. |
If the addends are the rotation speeds of two shafts, they can be added with a differential. | As issiwedan aqalan azalən ən ɣalayan ən assin ihəškan, nadobat assərtay ad ebadi. |
It made use of a gravity-assisted carry mechanism. | Exdm s mekaniz idhal gravite |
To subtract, the operator had to use the Pascal's calculator's complement, which required as many steps as an addition. | Fal agamad, adabara anihaga adamatkal talɣa ən əaləulatriəe wan Pascal, awa amosan hadi ən hadagan ən asiwid. |
Both XOR and AND gates are straightforward to realize in digital logic allowing the realization of full adder circuits which in turn may be combined into more complex logical operations. | Išar wi XOR əd AND aqalan fal asinanesan banan ye aritwigin dǎɣ oɣadan ən numérique dǎɣ adabaratan oɣadnen ogarnen aśuhu. |
Many implementations are, in fact, hybrids of these last three designs. | Ajotnen isiqtitan aqalan, dǎɣ aygan, abdanen əd wi karad ilkamnen təmoɣgrazen. |
Unanticipated arithmetic overflow is a fairly common cause of program errors. | Isusukayan ən arithmétique fal iba nigi eqal harat amosan atiwazayan dǎɣ qaɣadan ən asinihigi. |
Taken literally, the above definition is an application of the recursion theorem on the partially ordered set N2. | Adakal wan taɣare, aliɣi wa ilan sider eqal igitan ən tekanite tan asimuduɣil fal dǎɣ tartite nafala toɣadat N2. |
If either a or b is zero, treat it as an identity. | Afal a meɣ b egal wala, aytawaga sund atwizay iyan. |
Here, the semigroup is formed by the natural numbers and the group is the additive group of integers. | Diya, təzune ən tartit taqal ayertayan fal maɗinan imanasan əd tartit taqalat tartit tan asiwid ən entiertan. |
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. | 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. |
One must prove that this operation is well-defined, dealing with co-Cauchy sequences. | Nanihaga anisikin as adabara wen eqalan ahusken dǎɣ asikin, dǎɣ igitan ən ulkam wan cob-Cauchy. |
"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." | “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"". |
These give two different generalizations of addition of natural numbers to the transfinite. | Awen ihaku əsin generalisationtan abdanen dǎɣ təwaƭ ən maɗinan imanas dǎɣ transfini. |
There are even more generalizations of multiplication than addition. | Ilanti harwa iyogarnen generalisationtan ən asinimi ƭif wan asiwid. |
In fact, if two nonnegative numbers a and b are of different orders of magnitude, then their sum is approximately equal to their maximum. | Dǎɣ atwig, afal əsin maɗinan winan eqel aygadam a meɣ b aqalan dǎɣ təmɣire tabdat, mašan hadi nasan eqal ohazan adiqil wa samando nasan. |
It includes the idea of the sum of a single number, which is itself, and the empty sum, which is zero. | Itawaga dǎɣas anizgum ən hadi niyandǎɣ amaɗin, eqalan inta emanes, əd hadi wan banan, eqalan wala. |
"Integration is a kind of ""summation"" over a continuum, or more precisely and generally, over a differentiable manifold." | "Ugiš eqalan iyan azagar ən ""atwiqal"" fal əontinuum, meɣ ogaran asinihig əd amosan, fal umaɣ ebdanen." |
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. | 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. |
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. | Tuzant taqal iyat dǎɣ tinikozat adabarat ən santo wan arithmétique, atamosan əmik wamosan əmaɗinan aqalnen ayertayan fal igi ən maɗinan aynaynen. |
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). | 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). |
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. | Ašikel wen ən tuzant taqalat amitkalan intaɣas fal asiknin adabara ən tibidawt iman nasan, sund dǎɣ asikin sund étique ƭe fal ades ən calculatrice. |
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. | 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. |
A person can use logarithm tables to divide two numbers, by subtracting the two numbers' logarithms, then looking up the antilogarithm of the result. | Awadim adobat adtiqil tabarat tan logarithme fal tazant nəsin maɗinan, dǎɣ afanaz ən logarithme wasisin maɗinan, izar dǎɣ umaɣ ən antilogarithme awatwagrawan. |
Some programming languages, such as C, treat integer division as in case 5 above, so the answer is an integer. | Əmigridan iyad ən asinihigi, sund C, taganen tuzant dak sund dǎɣ əmik wan 5 tan afala, aliɣi eqalan amosan aymdan. |
Similarly, right division of b by a (written ) is the solution y to the equation . | Dǎɣ sundawen, tazune toɣadat ən b fal a (iktab) eqalan adabara dǎɣ iha équation. |
Examples include matrix algebras and quaternion algebras. | Algebretan ən matriəetan əd algebretan ən quaterniontan dǎɣ aqalan sund dolahan. |
Entry of such an expression into most calculators produces an error message. | Ugiš ən magrad dǎɣ iyadak dǎɣ əaləulatriəetan iganen isalan winan oɣed. |
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. | 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. |
The fact that the GCD can always be expressed in this way is known as Bézout's identity. | Igi was GCD adobat harkuk adiqil aygan dǎɣ əmik wendǎɣ eqalan atiwazay sund amuzuy ən Bézout. |
With this improvement, the algorithm never requires more steps than five times the number of digits (base 10) of the smaller integer. | Fal təmotayen tən, algorithme winan eqel atiwasan ogaran simos handagan wi amaɗin ən edanan (dǎɣ santo ən 10) wa ogaran təmidrit əmdan. |
The Euclidean algorithm has many theoretical and practical applications. | Algorithme euclidien ən iyajotnen igitan ən tabarat əd tawaganen. |
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. | 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. |
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. | 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. |
For example, neither 6 nor 35 is a prime number, since they both have two prime factors: 6 = 2 × 3 and 35 = 5 × 7. | Dǎɣ olahan, wade 6 wala 35 wadeqel amaɗin wazaran, falas ilan daknasan əsin faəteurtan wi azarnen: 6= 2 × 3 əd 35 = 5 × 7. |
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. | 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. |
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). | 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). |
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. | 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. |
Therefore, c divides the initial remainder r0, since r0 = a − q0b = mc − q0nc = (m − q0n)c. | Dǎɣ aɣašad, ə tazun awadiqiman insanto r0, falas r0 = a - q0b = mə - q0nc = (m - q0n)c. |
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. | 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. |
The theorem which underlies the definition of the Euclidean division ensures that such a quotient and remainder always exist and are unique. | Təmusne tan winan tifles aliɣi wan tazune tan euəlidien ikanu iyandǎɣ quotient əd iyamosan adiqiman atilan harkuk əd aqalnen iyadǎɣ. |
At the end of the loop iteration, the variable b holds the remainder rk, whereas the variable a holds its predecessor, rk−1. | Dǎɣ samando ən asimusuɣil wan tisifil, təbidaw ƭ ən b tataf awadiqiman rk, mašan tamotayt tan a tataf way han edag, rk-1. |
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. | 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 |
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. | 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. |
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). | Algorithme Euclidien eqal ayktaban numeriquement fal wadazaran ehandag əd atiwasanan dǎɣ Euroɗe dǎɣ tasanatat tədiwt ən asibaban atiwarhanen əd atiwarhan ən Bachet (1624). |
In the 19th century, the Euclidean algorithm led to the development of new number systems, such as Gaussian integers and Eisenstein integers. | Dǎɣ 19 temede nawatay, algorithme Euclidien ilway dǎɣ təwa ƭ nəmikan aynaynen ən numérique, atamosan aymdan dǎɣ Gauss əd əmdanen wi Eisenstein. |
Peter Gustav Lejeune Dirichlet seems to have been the first to describe the Euclidean algorithm as the basis for much of number theory. | Peter Gustaɣ Lejeune Dirichlet olahnen dagaraw eqalan wadazaran dǎɣ atwiktab ən algorithme euəlidienne sund santo maqaran aɣil wa tabarat tan maɗinan. |
For example, Dedekind was the first to prove Fermat's two-square theorem using the unique factorization of Gaussian integers. | Dǎɣ olahan, Dedekind eqalan wa dazaran asikna tabarat ən əsin sisigdihan ən Fermat dǎɣ amitkil ən fanaz iyandǎɣ dǎɣ wəmdanen ən Eisenstein. |
Other applications of Euclid's algorithm were developed in the 19th century. | Iyad igitan ən algorithme wan Euclide aqalan adiɗan dǎɣ19e temede nawatay |
Several novel integer relation algorithms have been developed, such as the algorithm of Helaman Ferguson and R.W. Forcade (1979) and the LLL algorithm. | Ajotnen aynaynen algorithmetan ən ilanen gar əmdanen aqalnen awidan, amosan algorithme wan Helaman Ferguson əd R.W. Forəade (1979) əd algorithme LLL. |
The players take turns removing m multiples of the smaller pile from the larger. | Imadalan irkaban dǎɣ aɣalay ən əšiɣil m animatafan wən tuhunt tadirat togarat təmɣire. |
By allowing u to vary over all possible integers, an infinite family of solutions can be generated from a single solution (x1, y1). | Dǎɣ taganen dǎɣ u ən atimutiy fal əmdanen adobatnen, terwe winan təminda dǎɣ adabaratan adobatnen adiqilan anelasan fal adabara iyandǎɣ (x1, y1). |
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. | 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. |
Now assume that the result holds for all values of N up to M − 1. | Nasinihiget amaradǎɣ as agaraw eqal atiwagrawan fal ɣaleurtan dak ən N hawendǎɣ M - 1. |
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. | Dǎɣ kanan, asinihigi ən awadiqiman ən 1, 2, 3 əd 4 eqal ihomiši 41,5 %, 17,0%, 9,3% əe 5,9%, dǎɣ anilkam. |
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. | 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. |
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. | 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. |
Lehmer's GCD algorithm uses the same general principle as the binary algorithm to speed up GCD computations in arbitrary bases. | Algorithme GƏD ən Lehmer amitkalan dǎɣ iyandǎɣ oɣadan atiwazay dǎɣ algorithme nəsin fal atrub ən alɣisab GCD dǎɣ winsanto imahadan. |
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. | 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. |
Any Euclidean domain is a unique factorization domain (UFD), although the converse is not true. | Tabaraten dak ti euclidien eqalan tabarat tan fanazan iyadǎɣ (UFD), ahuskat as amšiliq winan eqel aduten. |
A Euclidean domain is always a principal ideal domain (PID), an integral domain in which every ideal is a principal ideal. | Tabarat tan euclidien eqal harkuk ən tabarat nanizgum itbatan (DIP), tabarat tanugiš dǎɣ tas amosan hak anizgum atiwasanan. |
Numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals. | Imasaɗinan əd malaɣatan aqalnen intanedǎɣ amitkalan dǎɣ fractiontan winan eqel oharnen, amosnen fractiontan artaynen, fractiontan aśohatnen əd minéraux artaynen. |
The term was originally used to distinguish this type of fraction from the sexagesimal fraction used in astronomy. | Əmik eqalan amosnen amitkalan fal təbiɗawt ən əmik wan fraətion ən fraətion sexagésimale amitkalan dǎɣ astronomie. |
This was explained in the 17th century textbook The Ground of Arts. | Awen eqal atiwalaɣen dǎɣ edes ən 17e temede nawatay sitawana The Ground of Arts. |
The product of a fraction and its reciprocal is 1, hence the reciprocal is the multiplicative inverse of a fraction. | Asinimitif ən fraction əd ən amliliy eqalan ogdahan dǎɣ 1. Amliliy eqal adiš animašrayan ən nimitafan ən fraction. |
The remainder becomes the numerator of the fractional part. | Awadiqiman eqal wanafala ən tasaga ən fractionnaire. |
Since 5×17 (= 85) is greater than 4×18 (= 72), the result of comparing is . | Falas 5×17 (=85) eqal ayzwayan dǎɣ 4×18 (= 72), agaraw ən təbiɗawen aqalan. |
Since one third of a quarter is one twelfth, two thirds of a quarter is two twelfth. | Falas was karaɗ ən ikoz eqal was maraw ən diyan, wa əsin ən karaɗ dǎɣ ikoz aqalnen wasisin dǎɣ maraw ən disin. |
Sometimes an infinite repeating decimal is required to reach the same precision. | Agudiyan, mariaw elan anilkamnen dǎɣ samando eqal ayfan fal agad ən aytbatan wendǎɣ. |
The Egyptians used Egyptian fractions BC. | Égyptientan amitkalnen dǎɣ fractiontan ən égyɗtienne BC. |
Their methods gave the same answer as modern methods. | Tabarat nasan haku aliɣi imanes ən tabaraten amutaynen. |
A modern expression of fractions known as bhinnarasi seems to have originated in India in the work of Aryabhatta, Brahmagupta, and Bhaskara. | Əsalan amutaynen dǎɣ fractiontan atiwazaynen daw əsim ən bhinnarasi olahan adiqil aywan dǎɣ Inde dǎɣ əšiɣilan ən Aryabha ƭa, Brahmaguɗta əd Bhaskara. |
"In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers ""wrap around"" when reaching a certain value, called the modulus." | Dǎɣ maɗinan, algorithme modulaire eqal əmik iyan ən arithmétique fal əmdanen, ɣur maɗinan ""tikmikimiten"" ugud waɗiwadan iyan ɣaleur, sitawana module." |
A very practical application is to calculate checksums within serial number identifiers. | Igi itawagen harkuk aytagu alɣisab ən hadi ən tanhat dǎɣ atwizayan ən numéro ən anilkaman. |