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href="http://dbpedia.org/resource/Multiplication">Multiplication</a> </h1> </div> </div> <div class="row"> <div class="col"> <div class="text-muted"> An Entity of Type: <a href="http://www.w3.org/2002/07/owl#Thing">Thing</a>, from Named Graph: <a href="http://dbpedia.org">http://dbpedia.org</a>, within Data Space: <a href="http://dbpedia.org">dbpedia.org</a> </div> </div> </div> <div class="row pt-2"> <div class="col-xs-9 col-sm-10"> Multiplication (often denoted by the cross symbol ×, by the mid-line ⋅, by juxtaposition, or, on computers, by an asterisk *) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product. For example, 4 multiplied by 3, often written as and spoken as "3 times 4", can be calculated by adding 3 copies of 4 together: Here, 3 (the multiplier) and 4 (the multiplicand) are the factors, and 12 is the product. </div> <div class="col-xs-3 col-sm-2"> <a href="#" class="thumbnail"> <img src="http://commons.wikimedia.org/wiki/Special:FilePath/Multiply_4_bags_3_marbles.svg?width=300" alt="thumbnail" class="img-fluid" /> </a> </div> </div> </div> </section>   <section> <div class="container-xl"> <div class="row"> <div class="table-responsive"> <table class="table table-hover table-sm table-light"> <thead> <tr> <th class="col-xs-3 ">Property</th> <th class="col-xs-9 px-3">Value</th> </tr> </thead> <tbody> <tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/abstract">dbo:abstract</a> </td><td class="col-10 text-break"><ul> <li style="display:none;">Násobení je vedle sčítání, odčítání a dělení jedna ze čtyř základních početních operací v aritmetice. Symbol násobení je , × nebo *, vstupní hodnoty se nazývají činitelé, výsledek násobení součin. Opakovaným násobením získáváme umocňování. Například 3 · 4 se čte „tři krát čtyři“ a je násobení činitelů 3 a 4, jejich součin je 12: 3 · 4 = 12 Násobení je stejně jako sčítání komutativní, nezáleží na pořadí činitelů: 3 · 4 = 4 · 3 = 12 (cs)</li> <li style="display:none;">La multiplicació és una operació aritmètica resultat d'un cas particular de la suma. Quan tots els sumands d'una suma són iguals, es pot simplificar. Així, si el nombre m se suma n vegades, es diu que es multiplica el nombre m pel nombre n. Els nombres que es multipliquen en una multiplicació, s'anomenen factors, i el resultat de la multiplicació s'anomena producte. La multiplicació s'indica amb una creu, ×, o un punt, ⋅. En computació s'acostuma a utilitzar l'asterisc * (ús originari en el llenguatge FORTRAN). En un monomi, es considera que tots els components del monomi es multipliquen sense necessitat d'indicar cap símbol de multiplicació. Exemples: 5⋅2 = 5 +5 = 102⋅5 = 2 +2 +2 +2 +2 = 104⋅3 = 4 +4 +4 = 12m⋅6 = m +m +m +m +m +m Igual que la suma, la multiplicació és una operació interna dins els nombres naturals, els enters, els racionals, els reals i els complexos. També es poden multiplicar altres entitats matemàtiques, com polinomis, vectors o matrius. (ca)</li> <li style="display:none;">Ο πολλαπλασιασμός (συχνά συμβολίζεται με το εγκάρσιο σύμβολο "×") είναι η μαθηματική πράξη της κλιμάκωσης ενός αριθμού από έναν άλλο. Είναι μία από τις τέσσερις βασικές πράξεις στη στοιχειώδη αριθμητική (οι άλλες είναι η πρόσθεση, η αφαίρεση και η διαίρεση). Επειδή το αποτέλεσμα της κλιμάκωσης από ακέραιους αριθμούς μπορεί να θεωρηθεί ως αποτέλεσμα πρόσθεσης κάποιου αριθμού αντιγράφων του αρχικού, το ακέραιο γινόμενο που είναι μεγαλύτερο από 1 μπορεί να υπολογιστεί από επαναλαμβανόμενη πρόσθεση. Για παράδειγμα το 3 πολλαπλασιασμένο με το 4 (συχνά λέμε και "4 φορές το 3") μπορεί να υπολογιστεί προσθέτοντας 4 αντίγραφα του 3: Εδώ το 3 και το 4 είναι οι "παράγοντες" και το 12 είναι το "γινόμενο". Οι εκπαιδευτικοί διαφωνούν ως προς το ποιος αριθμός θα πρέπει κανονικά να θεωρηθεί ως ο αριθμός των αντιγράφων, και κατά πόσον ο πολλαπλασιασμός πρέπει ακόμη να παρουσιαστεί ως επαναλαμβανόμενη πρόσθεση. Για παράδειγμα το 3 πολλαπλασιασμένο με το 4, μπορεί επίσης να υπολογιστεί προσθέτοντας 3 αντίγραφα του 4: Ο πολλαπλασιασμός των ρητών αριθμών (κλάσματα) και των πραγματικών αριθμών ορίζεται από συστηματική γενίκευση αυτής της βασικής ιδέας. Ο πολλαπλασιασμός μπορεί επίσης να απεικονιστεί ως καταμέτρηση αντικείμενων τοποθετημένων σε ένα ορθογώνιο (για ακέραιους αριθμούς) είτε υπολογίζοντας το εμβαδόν ενός ορθογωνίου, του οποίου τα μήκη έχουν δοθεί (για τους αριθμούς γενικά). Το εμβαδόν ενός ορθογωνίου δεν εξαρτάται από το ποια πλευρά θα μετρηθεί πρώτη, το οποίο καταδεικνύει ότι οι ομόσημοι αριθμοί που πολλαπλασιάζονται μαζί έχουν θετικό αποτέλεσμα. Σε γενικές γραμμές το αποτέλεσμα του πολλαπλασιασμού δύο μετρήσεων δίνει ένα αποτέλεσμα ενός νέου τύπου, ανάλογα με τις μετρήσεις. Για παράδειγμα: Η αντίστροφη πράξη του πολλαπλασιασμού είναι η διαίρεση. Για παράδειγμα, 4 επί 3, ισούται με 12. Στη συνέχεια, 12 δια 3 ισούται με 4. Ο πολλαπλασιασμός ενός αριθμού με το 3 δίνει ένα γινόμενο, όταν ακολούθως γίνει διαίρεση του γινομένου με το 3, αυτή δίνει και πάλι τον αρχικό αριθμό. Ο πολλαπλασιασμός ορίζεται επίσης για άλλους τύπους αριθμών (όπως μιγαδικούς αριθμούς), και για πιο αφηρημένα κατασκευάσματα όπως οι πίνακες. Για αυτές τις πιο αφηρημένες έννοιες, η σειρά που οι τελεστές πολλαπλασιάζονται σε ορισμένες περιπτώσεις, έχει σημασία. (el)</li> <li style="display:none;">عملية الضرب في الرياضيات، هي عملية رياضية تقابل عملية القسمة، وفي الحساب الابتدائي يمكن تفسير عملية الضرب بأنها عمليات جمع متكررة للعدد ذاته. في أبسط حالتها تكون عملية الضرب عبارة عن مجموع عدد معين من رقم ما، على سبيل المثال 7 × 4 هي 7 + 7 + 7 + 7. يسمى حدا عملية الضرب «المضروب» و«المضروب به» أو عوامل الضرب وتسمي النتيجة حاصل الضرب أو الجداء.وعليه فالضرب هو جمع المضروب مع نفسه ثم تكرار ذلك بعدد المضروب فيه والناتج الذي نحصل عليه من جمع المضروب على نفسه عدد من المرات يساوي المضروب فيه هو نفس الناتج الذي نحصل عليه لو أننا جمعنا المضروب فيه على نفسه عد من المرات. لجأ المصريون القدماء إلى تلك الطريقة بتكرار عملية الجمع لإجراء «عملية الضرب» (الحساب عند قدماء المصريين). (ar)</li> <li style="display:none;">Die Multiplikation (lateinisch multiplicatio, von multiplicare ‚vervielfachen‘, auch Malnehmen genannt) ist eine der vier Grundrechenarten in der Arithmetik. Ihre Umkehroperation ist die Division (das Teilen). Das Rechenzeichen für die Multiplikation ist das Malzeichen „·“ bzw. „×“. (de)</li> <li style="display:none;">En matematiko, multipliko aŭ obligo estas duvalenta operacio. Ĝi povas esti aplikata al diversaj objektoj. La argumentoj de multipliko nomiĝas faktoroj kaj la rezulto estas produto. (eo)</li> <li style="display:none;">Matematikan, biderketa edo biderkaketa bi zenbakiren arteko eragiketa aritmetiko bat da, × ikurrez adierazi ohi dena. Biderketaren emaitza kalkulatzeko bigarren zenbakia lehenengo zenbakiak adierazten duen adina aldiz batu behar da. Adibidez: Biderketak hartzen dituen zenbakiak biderkagaiak edo faktoreak direla esaten da. Biderketaren emaitzari biderkadura deritzo. (eu)</li> <li style="display:none;">La multiplication est l'une des quatre opérations de l'arithmétique élémentaire avec l'addition, la soustraction et la division. Cette opération est souvent notée avec la croix de multiplication « × », mais peut aussi être notée par d'autres symboles (par exemple le point médian « · ») ou par l'absence de symbole. Son résultat s'appelle le produit, les nombres que l'on multiplie sont les facteurs. La multiplication de deux nombres a et b se dit indifféremment en français « a multiplié par b » ou « b fois a ». La multiplication de deux nombres entiers peut être vue comme une addition répétée plusieurs fois. Par exemple, « 3 fois 4 » peut se voir comme la somme de trois nombres 4 ; « 4 fois 3 » peut se voir comme la somme de quatre nombres 3 : 3 fois 4 = 4 multiplié par 3 = 4 × 3 = 4 + 4 + 4 ;4 fois 3 = 3 multiplié par 4 = 3 × 4 = 3 + 3 + 3 + 3 ; avec :La multiplication peut permettre de compter des éléments rangés dans un rectangle ou de calculer l'aire d'un rectangle dont on connaît la longueur et la largeur. Elle permet aussi de déterminer un prix d'achat connaissant le prix unitaire et la quantité achetée. La multiplication se généralise à d'autres ensembles que les nombres classiques (entiers, relatifs, réels). Par exemple, on peut multiplier des complexes entre eux, des fonctions, des matrices et même des vecteurs par des nombres. (fr)</li> <li>Multiplication (often denoted by the cross symbol ×, by the mid-line ⋅, by juxtaposition, or, on computers, by an asterisk *) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product. The multiplication of whole numbers may be thought of as repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the multiplicand, as the quantity of the other one, the multiplier. Both numbers can be referred to as factors. For example, 4 multiplied by 3, often written as and spoken as "3 times 4", can be calculated by adding 3 copies of 4 together: Here, 3 (the multiplier) and 4 (the multiplicand) are the factors, and 12 is the product. One of the main of multiplication is the commutative property, which states in this case that adding 3 copies of 4 gives the same result as adding 4 copies of 3: Thus the designation of multiplier and multiplicand does not affect the result of the multiplication. Systematic generalizations of this basic definition define the multiplication of integers (including negative numbers), rational numbers (fractions), and real numbers. Multiplication can also be visualized as counting objects arranged in a rectangle (for whole numbers) or as finding the area of a rectangle whose sides have some given lengths. The area of a rectangle does not depend on which side is measured first—a consequence of the commutative property. The product of two measurements is a new type of measurement. For example, multiplying the lengths of the two sides of a rectangle gives its area. Such a product is the subject of dimensional analysis. The inverse operation of multiplication is division. For example, since 4 multiplied by 3 equals 12, 12 divided by 3 equals 4. Indeed, multiplication by 3, followed by division by 3, yields the original number. The division of a number other than 0 by itself equals 1. Multiplication is also defined for other types of numbers, such as complex numbers, and for more abstract constructs, like matrices. For some of these more abstract constructs, the order in which the operands are multiplied together matters. A listing of the many different kinds of products used in mathematics is given in Product (mathematics). (en)</li> <li style="display:none;">La multiplicación es una operación binaria y derivada de la suma que se establece en un conjunto numérico. En aritmética, es una de las cuatro operaciones elementales, junto con la suma, la resta y la división, y es la operación inversa de esta última. Esto significa que para toda multiplicación hay una división, por ejemplo para «5 por 2 igual a 10» la división equivalente es «10 dividido entre 2 igual a 5», o «10 dividido entre 5 igual a 2». Existen dos signos para indicar esta operación entre números naturales: el aspa "×" y el punto gordo a media altura ( • ). En el caso de variables representadas por letras (solo letras o mezcla) se usa el punto (no el aspa) pero se puede prescindir de él por ejemplo 3ab (se lee «tres a b») xy + 2y (se lee «equis i más dos i») Multiplicar una cantidad por un número consiste en sumar dicha cantidad tantas veces como indica el número. Así, 4×3 (léase «cuatro multiplicado por tres» o, simplemente, «cuatro por tres») es igual a sumar tres veces el número 4 (4+4+4)(nota) También se puede interpretar como 3 filas de 4 objetos, o 4 filas de 3 (véase el dibujo). 4 y 3 son los factores, y 12, el resultado de la operación, es el producto. La multiplicación está asociada al concepto de área geométrica: es fácil ver que el área de un rectángulo se obtiene multiplicando la longitud de ambos lados, basta con imaginarnos la superficie cubierta con baldosas cuadradas. Podemos multiplicar dos números o más, y da igual en qué orden efectuemos la operación o cómo agrupemos los números; siempre se obtendrá el mismo resultado: 3 • 4 • 5 = 5 • 3 • 4 = 4 • 5 • 3 = 12 • 5 = 15 • 4 = 20 • 3 = 60 El resultado de la multiplicación de dos o más números se llama producto. Los números que se multiplican se llaman factores o coeficientes, e individualmente: multiplicando (número a sumar o número que se está multiplicando) y multiplicador (veces que se suma el multiplicando). Esta diferenciación tiene poco sentido cuando, en el conjunto donde esté definido el producto, se da la propiedad conmutativa de la multiplicación (por ejemplo, en los conjuntos numéricos: 3×7 = 7×3, es decir, el orden de los factores no altera el producto). Sin embargo puede ser útil si se usa para referirse al multiplicador de una expresión algebraica (ej: en o , 3 es el multiplicador o coeficiente, mientras que el monomio es el multiplicando). La potenciación es un caso particular de la multiplicación donde el exponente indica las veces que debe multiplicarse un número por sí mismo. Ejemplo: 2 • 2 • 2 • 2 • 2 • 2 • = 2 6 = 64 Aquí, 6 es el exponente, y 2 la base. En álgebra moderna se suele usar la denominación «cociente» o «multiplicación» con su notación habitual «·» para designar la operación externa en un módulo, para designar también la segunda operación que se define en un anillo (aquella para la que no está definido el elemento inverso del 0), o para designar la operación que dota a un conjunto de estructura de grupo. La operación inversa de la multiplicación es la división. (es)</li> <li style="display:none;">Perkalian (dilambangkan dengan ×, oleh garis tengah ⋅, oleh , atau, pada komputer, dengan asterisk *) adalah salah satu dari empat dasar operasi matematika dari aritmetika, dengan yang lainnya adalah penambahan, pengurangan dan . Hasil dari operasi perkalian disebut darab. Perkalian bilangan bulat dapat dianggap sebagai ; yaitu, perkalian dua bilangan sama dengan menjumlahkan sebanyak mungkin salinan salah satunya, perkalian, sebagai kuantitas yang lain, "pengganda". Kedua angka tersebut dapat disebut sebagai faktor. Misalnya, 4 dikalikan 3, ditulis sebagai dan diucapkan sebagai "3 dikali 4", dapat dihitung dengan menambahkan 3 salinan dari 4 secara bersamaan: Maka, 3 (pengganda) dan 4 (pengganda) adalah faktor, dan 12 adalah produk. Salah satu utama dari perkalian adalah sifat komutatif, yang menyatakan dalam hal ini bahwa menambahkan 3 salinan dari 4 memberikan hasil yang sama dengan menambahkan 4 salinan dari 3: Dengan demikian penunjukan pengali dan pengali tidak mempengaruhi hasil perkalian. Perkalian bilangan bulat (termasuk bilangan negatif), bilangan rasional (pecahan) dan bilangan riil didefinisikan oleh sistematis dari definisi dasar ini. Perkalian juga divisualisasikan sebagai menghitung objek yang disusun dalam persegi panjang (untuk bilangan bulat), atau mencari luas persegi panjang yang sisi-sisinya memiliki panjang tertentu. Luas persegi panjang tidak bergantung pada sisi mana yang diukur terlebih dahulu—konsekuensi dari sifat komutatif. Produk dari dua pengukuran adalah jenis pengukuran baru. Misalnya, mengalikan panjang kedua sisi persegi panjang memberikan luasnya. Darab tersebut adalah subjek analisis dimensi. Operasi invers dari perkalian adalah . Misalnya, karena 4 dikalikan 3 sama dengan 12, 12 dibagi 3 sama dengan 4. Memang, perkalian dengan 3, diikuti dengan pembagian 3, menghasilkan bilangan asli. Pembagian bilangan selain 0 dengan sendirinya sama dengan 1. Perkalian juga didefinisikan untuk jenis bilangan lain, seperti bilangan kompleks, dan konstruksi yang abstrak seperti matriks. Untuk beberapa konstruksi yang abstrak ini, urutan operan dikalikan menjadi penting. Daftar berbagai jenis produk yang digunakan dalam matematika diberikan oleh Darab (matematika). (in)</li> <li style="display:none;">La moltiplicazione è una delle quattro operazioni fondamentali dell'aritmetica. È un modo rapido per rappresentare la somma di numeri uguali. Il risultato di una moltiplicazione è chiamato prodotto, mentre i due numeri moltiplicati sono detti fattori se considerati insieme, e rispettivamente moltiplicando e moltiplicatore se presi individualmente. È spesso indicata dal simbolo "per" a croce ×, oppure dal punto a mezza altezza matematico ⋅, o in ambito informatico dall'asterisco <a href="/wiki/Asterisco" title="Asterisco">*</a>. (it)</li> <li style="display:none;">곱셈(영어: multiplication) 또는 승법(乘法)은 주로 '×', '*'로 표기되는 연산으로, 산술에서 덧셈, 뺄셈, 나눗셈과 함께 사칙연산을 이룬다. 두 자연수의 곱셈은 덧셈의 반복을 나타낸다. 예를 들어 4와 3의 곱(4 × 3, 4 곱하기 3)은 3를 4번 반복해 더한 것, 즉 와 같다(오른쪽 첫째 그림). 곱셈의 요인이 되는 수들을 인수(因數, factor), 그 결과의 값이 되는 수를 곱(product)이라고 한다. 곱셈은 정수, 더 나아가 유리수, 실수, 복소수들에게도 유효하며, 교환법칙, 결합법칙, 덧셈에 대한 분배법칙을 만족한다. 어떤 수에 1을 곱하면 자기 자신 그대로이며, 0을 곱한 결과는 0이다. 곱셈의 역연산은 나눗셈이다. 예를 들어, 3에 4를 곱하면 12이므로, 12를 3으로 나누면 4다. 같은 수를 여러번 곱한 연산을 거듭제곱이라고 한다. 곱셈은 더 일반적인 대상, 이를테면 행렬, 함수 등에게도 정의된다. 더 일반적인 대수 구조에서도 정의 가능하다. 예를 들어 군의 연산은 많은 경우 곱셈으로 불린다. 곱셈에게는 직사각형의 넓이(오른쪽 둘째 그림), 확대와 축소(오른쪽 셋째 그림) 등의 의미도 부여된다. (ko)</li> <li style="display:none;">Het vermenigvuldigen van twee getallen is een rekenkundige bewerking. De bewerking van het vermenigvuldigen van de twee getallen en wordt geschreven als . Het getal wordt vermenigvuldiger genoemd en het getal het vermenigvuldigtal. Het zijn de twee factoren van de vermenigvuldiging. Voor extra duidelijkheid wordt, afhankelijk van de context, soms gesproken van een vermenigvuldigingsfactor. Het resultaat van de vermenigvuldiging heet het product (van de factoren). Als de vermenigvuldiger een positief geheel getal is, komt vermenigvuldigen overeen met herhaald optellen; met andere woorden, een som van termen : In plaats van 18 keer het getal 24 bij elkaar op te tellen: 24 + 24 + 24 + 24 + 24 + 24 + 24 + 24 + 24 + 24 + 24 + 24 + 24 + 24 + 24 + 24 + 24 + 24, met als uitkomst 432, schrijft men: 18 × 24 (18 keer (of maal) 24) en berekent: 18 × 24 = 432 Het resultaat van de vermenigvuldiging, het getal 432, is het product van vermenigvuldiger 18 en vermenigvuldigtal 24. Omdat vermenigvuldigen commutatief is, 18 × 24 = 24 × 18, worden vermenigvuldiger en vermenigvuldigtal beide ook wel met factor aangeduid. Het symbool waarmee een vermenigvuldiging wordt aangeduid, is een kruisje (×) of een wat hoger geplaatst puntje (·), beide uitgesproken als maal of keer. Ook meer dan twee getallen kunnen met elkaar vermenigvuldigd worden. Het product ontstaat door achtereenvolgens herhaaldelijk twee factoren met elkaar te vermenigvuldigen, waarbij het tussenresultaat als nieuwe factor komt in de plaats van de twee. Bijvoorbeeld: Concreet: Een kleine vermenigvuldiger wordt in een zin vaak uitgedrukt als percentage, bijvoorbeeld een inkomstenbelasting van 20% van het inkomen, als het gaat om 0,2 maal het inkomen. (nl)</li> <li style="display:none;">乗法（じょうほう、英: multiplication）は、算術の四則演算と呼ばれるものの一つで、整数では、一方の数 (被乗数、ひじょうすう、英: multiplicand) に対して他方の数 (乗数、じょうすう、英: multiplier) の回数だけ繰り返し加えていく（これを掛けるまたは乗じるという）ことにより定義できる二項演算である。掛け算（かけざん）、乗算（じょうざん）とも呼ばれる。代数学においは、変数の前の乗数（例えば 3y の 3）は係数（けいすう、英: coefficient）と呼ばれる。逆の演算として除法をもつ。乗法の結果を積 (せき、英: product) と呼ぶ。乗法は、有理数、実数、複素数に対しても拡張定義される。また、抽象代数学においては、一般に可換とは限らない二項演算に対して、それを乗法、積などと呼称する（演算が可換である場合はしばしば加法、和などと呼ぶ）。 (ja)</li> <li style="display:none;">Mnożenie – działanie dwuargumentowe będące jednym z czterech podstawowych, obok dodawania, odejmowania i dzielenia, działań arytmetycznych. Stanowi ono uogólnienie wielokrotnego dodawania elementu do siebie. Wynik mnożenia nazywany jest iloczynem, a mnożone elementy to czynniki, przy czym pierwszy czynnik nazywa się czasem mnożną, a drugi – mnożnikiem. Na przykład: gdzie liczby 3 i 4 są czynnikami, a 12 to ich iloczyn. Powyższe oznacza, że trzy grupy po cztery elementy to razem dwanaście elementów. Z każdej z powyższych równolicznych grup można wybrać kolejno po jednym elemencie i w ten sposób stworzyć cztery nowe grupy zawierające po trzy elementy: W ten sposób co w przypadku ogólnym nazywa się formalnie przemiennością. Należy mieć jednak na uwadze, że istnieją działania nazywane mnożeniami, które nie mają tej własności (zob. ). Mnożenia liczb naturalnych o czynnikach od 0 do 10 (czyli do podstawy dziesiętnego systemu liczbowego) uczy się w pierwszych klasach szkoły podstawowej pod postacią tzw. tabliczki mnożenia. Dowolna liczba pomnożona przez zero daje w wyniku zero (tzn. zero jest elementem pochłaniającym mnożenia), podobnie dowolna liczba pomnożona przez jeden daje w wyniku tę liczbę (tzn. jedynka jest elementem neutralnym mnożenia). (pl)</li> <li style="display:none;">Na matemática, a multiplicação é uma forma simples de se adicionar uma quantidade finita de números iguais. O resultado da multiplicação de dois números é chamado produto. Ao lado da adição, da divisão e da subtração, a multiplicação é uma das quatro operações fundamentais da aritmética. Os números sendo multiplicados são chamados de coeficientes ou operandos, e individualmente de multiplicando e multiplicador. (lê-se "x vezes y" ou "y adicionado x vezes") Assim, por exemplo, . Pode também ser uma operação geométrica - a partir de dois segmentos de reta dados determinar um outro cujo comprimento seja igual ao produto dos dois iniciais (veja aqui). (pt)</li> <li style="display:none;">Умноже́ние — одна из основных математических операций над двумя аргументами, которые называются множителями или сомножителями (иногда первый аргумент называют множимым, а второй множителем). Результат умножения называется их произведением. Исторически умножение было впервые определено для натуральных чисел как многократное сложение — чтобы умножить число на число , надо сложить чисел (умножение далее обозначено приподнятой точкой между сомножителями): . Позднее умножение было распространено на целые, рациональные, вещественные, комплексные и другие виды чисел путём систематического обобщения. В настоящее время умножение в математике определяется не только для чисел, оно имеет различный конкретный смысл и соответственно различные определения и свойства для различных математических объектов. Умножение чисел является коммутативной операцией, то есть порядок записи чисел-множителей не влияет на результат их умножения.Например, умножение чисел и может быть записано как , так и (произносится также «пятью три», «трижды пять»), и результатом в любом случае является число . Проверка через сложение: ,. Умножение нечисловых математических, физических и абстрактных величин (например, матриц, векторов, множеств, кватернионов и т. д.) не всегда является коммутативной операцией. При умножении физических величин важную роль играет их размерность. Изучение общих свойств операции умножения входит в задачи общей алгебры, в частности теории групп и колец. (ru)</li> <li style="display:none;">Multiplikation är ett av de grundläggande räknesätten (operationerna) inom aritmetiken. Multiplikationstecknet som Språkrådet rekommenderar till användning av i svensk litteratur är den halvhöga punkten '', men även multiplikationskrysset '' brukar användas. De tal som multipliceras med varandra kallas faktorer, ibland multiplikator respektive multiplikand. Resultatet kallas produkt. Multiplikation kan ses som upprepad addition eller som proportionalitet. (sv)</li> <li style="display:none;">在数学中，乘法（英語：multiplication）是加法的連續運算，同一数的若干次连加，其運算結果稱為積（英語：product）。須注意的是，華人地區有將四則運算的被運算數和運算數統一位置，所以被乘數放前面，乘數放後面。唸作「a 乘以 n」或「n 乘 a」。但在其它語言（如英文）中，有可能乘數是放在前的，寫作，唸作「n times a」。 (zh)</li> <li style="display:none;">Мно́ження — бінарна операція над математичними об'єктами. Операнди називаються множниками, результат — добутком. Позначається хрестиком крапкою астериском В алгебраїчних виразах знак множення зазвичай опускається. Для позначення послідовного множення багатьох елементів використовується символ . Операція множення загалом має властивість асоціативності, але комутативність для неї не обов'язкова. Множники можуть бути математичними об'єктами як однієї природи, так і різної. Добуток теж може бути математичним об'єктом зовсім іншого типу, відмінного від типу множників. 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class="even"><td class="col-2"><a class="uri" href="http://www.w3.org/1999/02/22-rdf-syntax-ns#type">rdf:type</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="rdf:type" resource="http://www.w3.org/2002/07/owl#Thing" href="http://www.w3.org/2002/07/owl#Thing">owl:Thing</a></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#comment">rdfs:comment</a> </td><td class="col-10 text-break"><ul> <li style="display:none;">Násobení je vedle sčítání, odčítání a dělení jedna ze čtyř základních početních operací v aritmetice. Symbol násobení je , × nebo *, vstupní hodnoty se nazývají činitelé, výsledek násobení součin. Opakovaným násobením získáváme umocňování. Například 3 · 4 se čte „tři krát čtyři“ a je násobení činitelů 3 a 4, jejich součin je 12: 3 · 4 = 12 Násobení je stejně jako sčítání komutativní, nezáleží na pořadí činitelů: 3 · 4 = 4 · 3 = 12 (cs)</li> <li style="display:none;">Die Multiplikation (lateinisch multiplicatio, von multiplicare ‚vervielfachen‘, auch Malnehmen genannt) ist eine der vier Grundrechenarten in der Arithmetik. Ihre Umkehroperation ist die Division (das Teilen). Das Rechenzeichen für die Multiplikation ist das Malzeichen „·“ bzw. „×“. (de)</li> <li style="display:none;">En matematiko, multipliko aŭ obligo estas duvalenta operacio. Ĝi povas esti aplikata al diversaj objektoj. La argumentoj de multipliko nomiĝas faktoroj kaj la rezulto estas produto. (eo)</li> <li style="display:none;">Matematikan, biderketa edo biderkaketa bi zenbakiren arteko eragiketa aritmetiko bat da, × ikurrez adierazi ohi dena. Biderketaren emaitza kalkulatzeko bigarren zenbakia lehenengo zenbakiak adierazten duen adina aldiz batu behar da. Adibidez: Biderketak hartzen dituen zenbakiak biderkagaiak edo faktoreak direla esaten da. Biderketaren emaitzari biderkadura deritzo. (eu)</li> <li style="display:none;">La moltiplicazione è una delle quattro operazioni fondamentali dell'aritmetica. È un modo rapido per rappresentare la somma di numeri uguali. Il risultato di una moltiplicazione è chiamato prodotto, mentre i due numeri moltiplicati sono detti fattori se considerati insieme, e rispettivamente moltiplicando e moltiplicatore se presi individualmente. È spesso indicata dal simbolo "per" a croce ×, oppure dal punto a mezza altezza matematico ⋅, o in ambito informatico dall'asterisco <a href="/wiki/Asterisco" title="Asterisco">*</a>. (it)</li> <li style="display:none;">곱셈(영어: multiplication) 또는 승법(乘法)은 주로 '×', '*'로 표기되는 연산으로, 산술에서 덧셈, 뺄셈, 나눗셈과 함께 사칙연산을 이룬다. 두 자연수의 곱셈은 덧셈의 반복을 나타낸다. 예를 들어 4와 3의 곱(4 × 3, 4 곱하기 3)은 3를 4번 반복해 더한 것, 즉 와 같다(오른쪽 첫째 그림). 곱셈의 요인이 되는 수들을 인수(因數, factor), 그 결과의 값이 되는 수를 곱(product)이라고 한다. 곱셈은 정수, 더 나아가 유리수, 실수, 복소수들에게도 유효하며, 교환법칙, 결합법칙, 덧셈에 대한 분배법칙을 만족한다. 어떤 수에 1을 곱하면 자기 자신 그대로이며, 0을 곱한 결과는 0이다. 곱셈의 역연산은 나눗셈이다. 예를 들어, 3에 4를 곱하면 12이므로, 12를 3으로 나누면 4다. 같은 수를 여러번 곱한 연산을 거듭제곱이라고 한다. 곱셈은 더 일반적인 대상, 이를테면 행렬, 함수 등에게도 정의된다. 더 일반적인 대수 구조에서도 정의 가능하다. 예를 들어 군의 연산은 많은 경우 곱셈으로 불린다. 곱셈에게는 직사각형의 넓이(오른쪽 둘째 그림), 확대와 축소(오른쪽 셋째 그림) 등의 의미도 부여된다. (ko)</li> <li style="display:none;">乗法（じょうほう、英: multiplication）は、算術の四則演算と呼ばれるものの一つで、整数では、一方の数 (被乗数、ひじょうすう、英: multiplicand) に対して他方の数 (乗数、じょうすう、英: multiplier) の回数だけ繰り返し加えていく（これを掛けるまたは乗じるという）ことにより定義できる二項演算である。掛け算（かけざん）、乗算（じょうざん）とも呼ばれる。代数学においは、変数の前の乗数（例えば 3y の 3）は係数（けいすう、英: coefficient）と呼ばれる。逆の演算として除法をもつ。乗法の結果を積 (せき、英: product) と呼ぶ。乗法は、有理数、実数、複素数に対しても拡張定義される。また、抽象代数学においては、一般に可換とは限らない二項演算に対して、それを乗法、積などと呼称する（演算が可換である場合はしばしば加法、和などと呼ぶ）。 (ja)</li> <li style="display:none;">Multiplikation är ett av de grundläggande räknesätten (operationerna) inom aritmetiken. Multiplikationstecknet som Språkrådet rekommenderar till användning av i svensk litteratur är den halvhöga punkten '', men även multiplikationskrysset '' brukar användas. De tal som multipliceras med varandra kallas faktorer, ibland multiplikator respektive multiplikand. Resultatet kallas produkt. Multiplikation kan ses som upprepad addition eller som proportionalitet. (sv)</li> <li style="display:none;">在数学中，乘法（英語：multiplication）是加法的連續運算，同一数的若干次连加，其運算結果稱為積（英語：product）。須注意的是，華人地區有將四則運算的被運算數和運算數統一位置，所以被乘數放前面，乘數放後面。唸作「a 乘以 n」或「n 乘 a」。但在其它語言（如英文）中，有可能乘數是放在前的，寫作，唸作「n times a」。 (zh)</li> <li style="display:none;">Мно́ження — бінарна операція над математичними об'єктами. Операнди називаються множниками, результат — добутком. Позначається хрестиком крапкою астериском В алгебраїчних виразах знак множення зазвичай опускається. Для позначення послідовного множення багатьох елементів використовується символ . Операція множення загалом має властивість асоціативності, але комутативність для неї не обов'язкова. Множники можуть бути математичними об'єктами як однієї природи, так і різної. Добуток теж може бути математичним об'єктом зовсім іншого типу, відмінного від типу множників. (uk)</li> <li style="display:none;">عملية الضرب في الرياضيات، هي عملية رياضية تقابل عملية القسمة، وفي الحساب الابتدائي يمكن تفسير عملية الضرب بأنها عمليات جمع متكررة للعدد ذاته. في أبسط حالتها تكون عملية الضرب عبارة عن مجموع عدد معين من رقم ما، على سبيل المثال 7 × 4 هي 7 + 7 + 7 + 7. يسمى حدا عملية الضرب «المضروب» و«المضروب به» أو عوامل الضرب وتسمي النتيجة حاصل الضرب أو الجداء.وعليه فالضرب هو جمع المضروب مع نفسه ثم تكرار ذلك بعدد المضروب فيه والناتج الذي نحصل عليه من جمع المضروب على نفسه عدد من المرات يساوي المضروب فيه هو نفس الناتج الذي نحصل عليه لو أننا جمعنا المضروب فيه على نفسه عد من المرات. (ar)</li> <li style="display:none;">La multiplicació és una operació aritmètica resultat d'un cas particular de la suma. Quan tots els sumands d'una suma són iguals, es pot simplificar. Així, si el nombre m se suma n vegades, es diu que es multiplica el nombre m pel nombre n. Els nombres que es multipliquen en una multiplicació, s'anomenen factors, i el resultat de la multiplicació s'anomena producte. Exemples: 5⋅2 = 5 +5 = 102⋅5 = 2 +2 +2 +2 +2 = 104⋅3 = 4 +4 +4 = 12m⋅6 = m +m +m +m +m +m Igual que la suma, la multiplicació és una operació interna dins els nombres naturals, els enters, els racionals, els reals i els complexos. (ca)</li> <li style="display:none;">Ο πολλαπλασιασμός (συχνά συμβολίζεται με το εγκάρσιο σύμβολο "×") είναι η μαθηματική πράξη της κλιμάκωσης ενός αριθμού από έναν άλλο. Είναι μία από τις τέσσερις βασικές πράξεις στη στοιχειώδη αριθμητική (οι άλλες είναι η πρόσθεση, η αφαίρεση και η διαίρεση). Εδώ το 3 και το 4 είναι οι "παράγοντες" και το 12 είναι το "γινόμενο". Ο πολλαπλασιασμός των ρητών αριθμών (κλάσματα) και των πραγματικών αριθμών ορίζεται από συστηματική γενίκευση αυτής της βασικής ιδέας. (el)</li> <li style="display:none;">La multiplicación es una operación binaria y derivada de la suma que se establece en un conjunto numérico. En aritmética, es una de las cuatro operaciones elementales, junto con la suma, la resta y la división, y es la operación inversa de esta última. Esto significa que para toda multiplicación hay una división, por ejemplo para «5 por 2 igual a 10» la división equivalente es «10 dividido entre 2 igual a 5», o «10 dividido entre 5 igual a 2». 3 • 4 • 5 = 5 • 3 • 4 = 4 • 5 • 3 = 12 • 5 = 15 • 4 = 20 • 3 = 60 o , 3 es el multiplicador o coeficiente, mientras que el monomio es el multiplicando). (es)</li> <li>Multiplication (often denoted by the cross symbol ×, by the mid-line ⋅, by juxtaposition, or, on computers, by an asterisk *) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product. For example, 4 multiplied by 3, often written as and spoken as "3 times 4", can be calculated by adding 3 copies of 4 together: Here, 3 (the multiplier) and 4 (the multiplicand) are the factors, and 12 is the product. (en)</li> <li style="display:none;">La multiplication est l'une des quatre opérations de l'arithmétique élémentaire avec l'addition, la soustraction et la division. Cette opération est souvent notée avec la croix de multiplication « × », mais peut aussi être notée par d'autres symboles (par exemple le point médian « · ») ou par l'absence de symbole. Son résultat s'appelle le produit, les nombres que l'on multiplie sont les facteurs. La multiplication de deux nombres a et b se dit indifféremment en français « a multiplié par b » ou « b fois a ». (fr)</li> <li style="display:none;">Perkalian (dilambangkan dengan ×, oleh garis tengah ⋅, oleh , atau, pada komputer, dengan asterisk *) adalah salah satu dari empat dasar operasi matematika dari aritmetika, dengan yang lainnya adalah penambahan, pengurangan dan . Hasil dari operasi perkalian disebut darab. Perkalian bilangan bulat dapat dianggap sebagai ; yaitu, perkalian dua bilangan sama dengan menjumlahkan sebanyak mungkin salinan salah satunya, perkalian, sebagai kuantitas yang lain, "pengganda". Kedua angka tersebut dapat disebut sebagai faktor. Maka, 3 (pengganda) dan 4 (pengganda) adalah faktor, dan 12 adalah produk. (in)</li> <li style="display:none;">Het vermenigvuldigen van twee getallen is een rekenkundige bewerking. De bewerking van het vermenigvuldigen van de twee getallen en wordt geschreven als . Het getal wordt vermenigvuldiger genoemd en het getal het vermenigvuldigtal. Het zijn de twee factoren van de vermenigvuldiging. Voor extra duidelijkheid wordt, afhankelijk van de context, soms gesproken van een vermenigvuldigingsfactor. Het resultaat van de vermenigvuldiging heet het product (van de factoren). In plaats van 18 keer het getal 24 bij elkaar op te tellen: met als uitkomst 432, schrijft men: 18 × 24 (18 keer (of maal) 24) (nl)</li> <li style="display:none;">Mnożenie – działanie dwuargumentowe będące jednym z czterech podstawowych, obok dodawania, odejmowania i dzielenia, działań arytmetycznych. Stanowi ono uogólnienie wielokrotnego dodawania elementu do siebie. Wynik mnożenia nazywany jest iloczynem, a mnożone elementy to czynniki, przy czym pierwszy czynnik nazywa się czasem mnożną, a drugi – mnożnikiem. Na przykład: W ten sposób co w przypadku ogólnym nazywa się formalnie przemiennością. Należy mieć jednak na uwadze, że istnieją działania nazywane mnożeniami, które nie mają tej własności (zob. ). (pl)</li> <li style="display:none;">Na matemática, a multiplicação é uma forma simples de se adicionar uma quantidade finita de números iguais. O resultado da multiplicação de dois números é chamado produto. Ao lado da adição, da divisão e da subtração, a multiplicação é uma das quatro operações fundamentais da aritmética. Os números sendo multiplicados são chamados de coeficientes ou operandos, e individualmente de multiplicando e multiplicador. (lê-se "x vezes y" ou "y adicionado x vezes") Assim, por exemplo, . (pt)</li> <li style="display:none;">Умноже́ние — одна из основных математических операций над двумя аргументами, которые называются множителями или сомножителями (иногда первый аргумент называют множимым, а второй множителем). Результат умножения называется их произведением. Исторически умножение было впервые определено для натуральных чисел как многократное сложение — чтобы умножить число на число , надо сложить чисел (умножение далее обозначено приподнятой точкой между сомножителями): . Позднее умножение было распространено на целые, рациональные, вещественные, комплексные и другие виды чисел путём систематического обобщения. (ru)</li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#label">rdfs:label</a> </td><td class="col-10 text-break"><ul> <li>Multiplication (en)</li> <li style="display:none;">ضرب (ar)</li> <li style="display:none;">Multiplicació (ca)</li> <li style="display:none;">Násobení (cs)</li> <li style="display:none;">Multiplikation (de)</li> <li style="display:none;">Πολλαπλασιασμός (el)</li> <li style="display:none;">Multipliko (eo)</li> <li style="display:none;">Multiplicación (es)</li> <li style="display:none;">Biderketa (eu)</li> <li style="display:none;">Multiplication (fr)</li> <li style="display:none;">Perkalian (in)</li> <li style="display:none;">Moltiplicazione (it)</li> <li style="display:none;">乗法 (ja)</li> <li style="display:none;">곱셈 (ko)</li> <li style="display:none;">Vermenigvuldigen (nl)</li> <li style="display:none;">Mnożenie (pl)</li> <li style="display:none;">Multiplicação (pt)</li> <li style="display:none;">Умножение (ru)</li> <li style="display:none;">Multiplikation (sv)</li> <li style="display:none;">Множення (uk)</li> <li style="display:none;">乘法 (zh)</li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#seeAlso">rdfs:seeAlso</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="rdfs:seeAlso" resource="http://dbpedia.org/resource/Multiplier_(linguistics)" href="http://dbpedia.org/resource/Multiplier_(linguistics)">dbr:Multiplier_(linguistics)</a></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://www.w3.org/2002/07/owl#sameAs">owl:sameAs</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="owl:sameAs" resource="http://rdf.freebase.com/ns/m.057mq" href="http://rdf.freebase.com/ns/m.057mq">freebase:Multiplication</a></li> <li><a class="uri" rel="owl:sameAs" resource="http://d-nb.info/gnd/4170732-1" 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