multiplication

mul·ti·pli·ca·tion

M0477900 (mŭl′tə-plĭ-kā′shən)n.1. The act or process of multiplying or the condition of being multiplied.2. Propagation of plants and animals; procreation.3. Mathematics a. The operation that, for positive integers, consists of adding a number (the multiplicand) to itself a certain number of times. The operation is extended to other numbers according to the multiplicative properties of positive integers and other algebraic properties.b. Any of certain analogous operations involving mathematical objects other than numbers.

mul′ti·pli·ca′tion·al adj.

multiplication

(ˌmʌltɪplɪˈkeɪʃən) n1. (Mathematics) an arithmetical operation, defined initially in terms of repeated addition, usually written a × b, a.b, or ab, by which the product of two quantities is calculated: to multiply a by positive integral b is to add a to itself b times. Multiplication by fractions can then be defined in the light of the associative and commutative properties; multiplication by 1/n is equivalent to multiplication by 1 followed by division by n: for example 0.3 × 0.7 = 0.3 × = (0.3 × 7)/10 = 2 = 0.212. the act of multiplying or state of being multiplied3. (Biology) the act or process in animals, plants, or people of reproducing or breeding ˌmultipliˈcational adj

mul•ti•pli•ca•tion

(ˌmʌl tə plɪˈkeɪ ʃən)

n. 1. the act or process of multiplying or the state of being multiplied. 2. a mathematical operation, symbolized by axb, a ∙b, a * b, or ab, and signifying, when a and b are positive integers, that a is to be added to itself as many times as there are units in b; the addition of a number to itself as often as is indicated by another number, as in 2x3 or 5x10. 3. any generalization of this operation applicable to numbers other than integers, as fractions or irrational numbers. [1350–1400; Middle English < Latin] mul`ti•pli•ca′tion•al, adj.

mul·ti·pli·ca·tion

(mŭl′tə-plĭ-kā′shən)1. The mathematical operation that consists of adding a number (the multiplicand) to itself a specified number of times. Thus multiplying 6 by 3 means adding 6 to itself three times.2. A mathematical operation performed on a pair of numbers in order to derive a third number called a product. It is sometimes convenient to consider multiplication as repeated addition in which one number indicates how many times the other is to be added together. For example, 3 × 4 = 4 + 4 + 4 = 4 × 3 = 3 + 3 + 3 + 3 = 12.

Thesaurus

Noun	1.	multiplication - the act of producing offspring or multiplying by such productionpropagation, generationfacts of life, procreation, reproduction, breeding - the sexual activity of conceiving and bearing offspringbiogeny, biogenesis - the production of living organisms from other living organisms
	2.	multiplication - a multiplicative increase; "repeated copying leads to a multiplication of errors"; "this multiplication of cells is a natural correlate of growth"doubling - increase by a factor of two; "doubling with a computer took no time at all"increment, growth, increase - a process of becoming larger or longer or more numerous or more important; "the increase in unemployment"; "the growth of population"quadrupling - increase by a factor of fourquintupling - increasing by a factor of fivetripling - increase by a factor of three
	3.	multiplication - 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"timesarithmetic operation - a mathematical operation involving numbers

multiplication

noun1. The act of increasing or rising:aggrandizement, amplification, augment, augmentation, boost, buildup, enlargement, escalation, growth, hike, increase, jump, proliferation, raise, rise, swell, upsurge, upswing, upturn.2. The result or product of building up:accretion, buildup, development, enlargement, proliferation.3. The process by which an organism produces others of its kind:breeding, procreation, proliferation, propagation, reproduction, spawning.Obsolete: increase.

Translations

乘法繁殖

multiply

(ˈmaltiplai) verb1. to add a number to itself a given number of times and find the total. 4 + 4 + 4 or 4 multiplied by 3 or 4  3 = 12.乘2. to (cause to) increase in number, especially by breeding. Rabbits multiply very rapidly.增殖ˌmultipliˈcation (-pli-) noun the act of multiplying numbers. 乘法

multiplication

→ 繁殖zhCN

multiplication

multiplication,

fundamental operation in arithmetic and algebra. Multiplication by a whole number can be interpreted as successive addition. For example, a number N multiplied by 3 is N + N + N. In general, multiplying positive numbers N and M gives the area of the rectangle with sides N and M. The result of a multiplication is known as the product. Numbers that give a product when multiplied together are called factors of that product. The symbol of the operation is × or · and, in algebra, simple juxtaposition (e.g., xy means x×y or x·y). Like addition, multiplication, in arithmetic and elementary algebra, obeys the associative lawassociative law,
in mathematics, law holding that for a given operation combining three quantities, two at a time, the initial pairing is arbitrary; e.g., using the operation of addition, the numbers 2, 3, and 4 may be combined (2+3)+4=5+4=9 or 2+(3+4)=2+7=9.
..... Click the link for more information. , the commutative lawcommutative law,
in mathematics, law holding that for a given binary operation (combining two quantities) the order of the quantities is arbitrary; e.g., in addition, the numbers 2 and 5 can be combined as 2+5=7 or as 5+2=7.
..... Click the link for more information. , and, in combination with addition, the distributive lawdistributive law.
In mathematics, given any two operations, symbolized by * and +, the first operation, *, is distributive over the second, +, if a*(b+c)=(a*b)+(a*c) for all possible choices of a, b, and c.
..... Click the link for more information. . Multiplication in abstract algebra, as between vectors or other mathematical objects, does not always obey these rules. Quantities with unlike units may sometimes be multiplied, resulting in such units as foot-pounds, gram-centimeters, and kilowatt-hours. See also divisiondivision,
fundamental operation in arithmetic; the inverse of multiplication. Division may be indicated by the symbol ÷, as in 15 ÷ 3, or simply by a fraction, 15/3. The number that is being divided, e.g.
..... Click the link for more information. .

Multiplication

a binary operation that associates to objects a, b an object c; a and b are called factors, and c is called their product. Multiplication is indicated by the symbol × or by the symbol. The first symbol was introduced by the English mathematician W. Oughtred in 1631, and the second by the German savant G. von Leibniz in 1698. When multiplying letters rather than numbers, we omit these symbols and write ab instead of a × b or a · b. The concrete sense of a multiplication depends on the nature of the factors and the definition of the multiplication. Multiplication of positive integers is the operation that associates to positive integers a and b the positive integer c = ab = a + a + . . . + a, where a is taken b times. Multiplication of fractions m/n and p/q is defined by the equation

The product of fractions is a fraction whose absolute value is the product of the absolute values of the factors. The product of fractions is positive if both factors have the same sign and is negative otherwise. Multiplication of irrational numbers is defined in terms of multiplication of rational approximations of these numbers. Multiplication of complex numbers α and β given as α = a + bi and β = c + di is defined by means of the equation

αβ = (ac – bd) + (ad + bc)i

If α and β are given in polar form,

α = r₁(cos φ₁) + i sin φ₁)

β = r₂(cos φ₂ + i sin φ₂)

then αβ is defined as

αβ = r₁,r₂ {cos (φ₁ + φ₂) + i sin (φ₁ + φ₂)}

that is, the modulus of the product is the product of the moduli of the factors and the argument of the product is the sum of the arguments of the factors.

Multiplication of numbers has the following properties: (1) ab = ba (commutativity), (2) a(bc) = (ab)c (associativity), and (3) a(b + c) = ab + ac (distributivity of multiplication over addition). We have a · 0 = 0 and a · 1 = a. The techniques for multiplying multivalued expressions rely on these properties.

Further generalization of multiplication relies on the possibility of viewing numbers as operators on vectors in the plane. Thus, to the complex number r(cos φ + i sin φ) we associate the operator of dilation of all vectors by a factor r and their rotation through an angle φ about the origin. Here, to the product of complex numbers there corresponds the product of the operators associated with these numbers, that is, the operator that is the result of successive application of the operators associated with the numbers in question. Such multiplication of operators can be extended to operators that cannot be represented by numbers, for example, to linear operators. In this way, we are led to define multiplication of matrices, of quarternions viewed as dilations and rotations in 3-space, and of kernels of integral operators. In these generalizations some of the properties of multiplication of numbers may not hold. The property that fails to hold most frequently is commutativity.

The study of the general properties of multiplication is part of algebra, in particular, group theory and ring theory.

multiplication

[‚məl·tə·pli′kā·shən] (electronics) An increase in current flow through a semiconductor because of increased carrier activity. (mathematics) Any algebraic operation analogous to multiplication of real numbers. (nucleonics) The ratio of neutron flux in a subcritical reactor to that supplied by a neutron source; it is the factor by which, in effect, the reactor multiplies the source strength.

multiplication

1. an arithmetical operation, defined initially in terms of repeated addition, usually written a × b, a.b, or ab, by which the product of two quantities is calculated: to multiply a by positive integral b is to add a to itself b times. Multiplication by fractions can then be defined in the light of the associative and commutative properties; multiplication by 1/n is equivalent to multiplication by 1 followed by division by n: for example 0.3 × 0.7 = 0.3 × 7/10 = (0.3 × 7)/10 = 2.1/10 = 0.21 2. the act or process in animals, plants, or people of reproducing or breeding

multiplication

mul·ti·pli·ca·tion

multiplication

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mul·ti·pli·ca·tion

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Multiplication

multiplication

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mul·ti·pli·ca·tion

Patient discussion about multiplication

multiplication

Synonyms for multiplication

noun the act of increasing or rising

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noun the result or product of building up

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noun the process by which an organism produces others of its kind

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Synonyms for multiplication

noun the act of producing offspring or multiplying by such production

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noun a multiplicative increase

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noun an arithmetic operation that is the inverse of division

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