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Multiplication

Multiplication Mul`ti*pli*ca"tion, n. [L. multiplicatio: cf. F. multiplication. See Multiply.] 1. The act or process of multiplying, or of increasing in number; the state of being multiplied; as, the multiplication of the human species by natural generation. The increase and multiplication of the world. --Thackeray. 2. (Math.) The process of repeating, or adding to itself, any given number or quantity a certain number of times; commonly, the process of ascertaining by a briefer computation the result of such repeated additions; also, the rule by which the operation is performed; -- the reverse of division. Note: The word multiplication is sometimes used in mathematics, particularly in multiple algebra, to denote any distributive operation expressed by one symbol upon any quantity or any thing expressed by another symbol. Corresponding extensions of meaning are given to the words multiply, multiplier, multiplicand, and product. Thus, since [phi](x + y) = [phi]x + [phi]y (see under Distributive), where [phi](x + y), [phi]x, and [phi]y indicate the results of any distributive operation represented by the symbol [phi] upon x + y, x, and y, severally, then because of many very useful analogies [phi](x + y) is called the product of [phi] and x + y, and the operation indicated by [phi] is called multiplication. Cf. Facient, n., 2. 3. (Bot.) An increase above the normal number of parts, especially of petals; augmentation. 4. The art of increasing gold or silver by magic, -- attributed formerly to the alchemists. [Obs.] --Chaucer. Multiplication table, a table giving the product of a set of numbers multiplied in some regular way; commonly, a table giving the products of the first ten or twelve numbers multiplied successively by 1, 2, 3, etc., up to 10 or 12.

Multiplication Mul`ti*pli*ca"tion, n. [L. multiplicatio: cf. F. multiplication. See Multiply.] 1. The act or process of multiplying, or of increasing in number; the state of being multiplied; as, the multiplication of the human species by natural generation. The increase and multiplication of the world. --Thackeray. 2. (Math.) The process of repeating, or adding to itself, any given number or quantity a certain number of times; commonly, the process of ascertaining by a briefer computation the result of such repeated additions; also, the rule by which the operation is performed; -- the reverse of division. Note: The word multiplication is sometimes used in mathematics, particularly in multiple algebra, to denote any distributive operation expressed by one symbol upon any quantity or any thing expressed by another symbol. Corresponding extensions of meaning are given to the words multiply, multiplier, multiplicand, and product. Thus, since [phi](x + y) = [phi]x + [phi]y (see under Distributive), where [phi](x + y), [phi]x, and [phi]y indicate the results of any distributive operation represented by the symbol [phi] upon x + y, x, and y, severally, then because of many very useful analogies [phi](x + y) is called the product of [phi] and x + y, and the operation indicated by [phi] is called multiplication. Cf. Facient, n., 2. 3. (Bot.) An increase above the normal number of parts, especially of petals; augmentation. 4. The art of increasing gold or silver by magic, -- attributed formerly to the alchemists. [Obs.] --Chaucer. Multiplication table, a table giving the product of a set of numbers multiplied in some regular way; commonly, a table giving the products of the first ten or twelve numbers multiplied successively by 1, 2, 3, etc., up to 10 or 12.

multiplication

Compound Com"pound, a. [OE. compouned, p. p. of compounen. See Compound, v. t.] Composed of two or more elements, ingredients, parts; produced by the union of several ingredients, parts, or things; composite; as, a compound word. Compound substances are made up of two or more simple substances. --I. Watts. Compound addition, subtraction, multiplication, division (Arith.), the addition, subtraction, etc., of compound numbers. Compound crystal (Crystallog.), a twin crystal, or one seeming to be made up of two or more crystals combined according to regular laws of composition. Compound engine (Mech.), a form of steam engine in which the steam that has been used in a high-pressure cylinder is made to do further service in a larger low-pressure cylinder, sometimes in several larger cylinders, successively. Compound ether. (Chem.) See under Ether. Compound flower (Bot.), a flower head resembling a single flower, but really composed of several florets inclosed in a common calyxlike involucre, as the sunflower or dandelion. Compound fraction. (Math.) See Fraction. Compound fracture. See Fracture. Compound householder, a householder who compounds or arranges with his landlord that his rates shall be included in his rents. [Eng.] Compound interest. See Interest. Compound larceny. (Law) See Larceny. Compound leaf (Bot.), a leaf having two or more separate blades or leaflets on a common leafstalk. Compound microscope. See Microscope. Compound motion. See Motion. Compound number (Math.), one constructed according to a varying scale of denomination; as, 3 cwt., 1 qr., 5 lb.; -- called also denominate number. Compound pier (Arch.), a clustered column. Compound quantity (Alg.), a quantity composed of two or more simple quantities or terms, connected by the sign + (plus) or - (minus). Thus, a + b - c, and bb - b, are compound quantities. Compound radical. (Chem.) See Radical. Compound ratio (Math.), the product of two or more ratios; thus ab:cd is a ratio compounded of the simple ratios a:c and b:d. Compound rest (Mech.), the tool carriage of an engine lathe. Compound screw (Mech.), a screw having on the same axis two or more screws with different pitch (a differential screw), or running in different directions (a right and left screw). Compound time (Mus.), that in which two or more simple measures are combined in one; as, 6-8 time is the joining of two measures of 3-8 time. Compound word, a word composed of two or more words; specifically, two or more words joined together by a hyphen.

Compound Com"pound, a. [OE. compouned, p. p. of compounen. See Compound, v. t.] Composed of two or more elements, ingredients, parts; produced by the union of several ingredients, parts, or things; composite; as, a compound word. Compound substances are made up of two or more simple substances. --I. Watts. Compound addition, subtraction, multiplication, division (Arith.), the addition, subtraction, etc., of compound numbers. Compound crystal (Crystallog.), a twin crystal, or one seeming to be made up of two or more crystals combined according to regular laws of composition. Compound engine (Mech.), a form of steam engine in which the steam that has been used in a high-pressure cylinder is made to do further service in a larger low-pressure cylinder, sometimes in several larger cylinders, successively. Compound ether. (Chem.) See under Ether. Compound flower (Bot.), a flower head resembling a single flower, but really composed of several florets inclosed in a common calyxlike involucre, as the sunflower or dandelion. Compound fraction. (Math.) See Fraction. Compound fracture. See Fracture. Compound householder, a householder who compounds or arranges with his landlord that his rates shall be included in his rents. [Eng.] Compound interest. See Interest. Compound larceny. (Law) See Larceny. Compound leaf (Bot.), a leaf having two or more separate blades or leaflets on a common leafstalk. Compound microscope. See Microscope. Compound motion. See Motion. Compound number (Math.), one constructed according to a varying scale of denomination; as, 3 cwt., 1 qr., 5 lb.; -- called also denominate number. Compound pier (Arch.), a clustered column. Compound quantity (Alg.), a quantity composed of two or more simple quantities or terms, connected by the sign + (plus) or - (minus). Thus, a + b - c, and bb - b, are compound quantities. Compound radical. (Chem.) See Radical. Compound ratio (Math.), the product of two or more ratios; thus ab:cd is a ratio compounded of the simple ratios a:c and b:d. Compound rest (Mech.), the tool carriage of an engine lathe. Compound screw (Mech.), a screw having on the same axis two or more screws with different pitch (a differential screw), or running in different directions (a right and left screw). Compound time (Mus.), that in which two or more simple measures are combined in one; as, 6-8 time is the joining of two measures of 3-8 time. Compound word, a word composed of two or more words; specifically, two or more words joined together by a hyphen.

- method of multiplying two n-digit numbers requires n2 digit multiplications. Multiplication algorithms have been designed that reduce the com****tion time...

- method to introduce the idea of multiple-digit multiplications; and, in an age when most multiplication calculations are done using a calculator or a spreadsheet...

- Multiplicative may refer to: Multiplication Multiplicative calculus Multiplicative function Multiplicative group Multiplicative identity Multiplicative...

- _{2}n\rfloor } multiplications, where ⌊ ⌋ {\displaystyle \lfloor \;\rfloor } denotes the floor function. More precisely, the number of multiplications is one...

- needs 10×30×5 + 10×5×60 = 4,500 multiplications, while computing A(BC) needs 30×5×60 + 10×30×60 = 27,000 multiplications. Algorithms have been designed...

- real or complex number field, these two multiplications are the same, and are simply called scalar multiplication. However, for matrices over a more general...

- mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an...

- count of complex multiplications and additions for N=4096 data points. Evaluating the DFT's sums directly involves N2 complex multiplications and N(N−1) complex...

- eight multiplications of pairs of submatrices, followed by an addition step. The divide and conquer algorithm computes the smaller multiplications recursively...

- reduced the number of multiplications. We still need 8 multiplications to calculate the Ci,j matrices, the same number of multiplications we need when using...

- method to introduce the idea of multiple-digit multiplications; and, in an age when most multiplication calculations are done using a calculator or a spreadsheet...

- Multiplicative may refer to: Multiplication Multiplicative calculus Multiplicative function Multiplicative group Multiplicative identity Multiplicative...

- _{2}n\rfloor } multiplications, where ⌊ ⌋ {\displaystyle \lfloor \;\rfloor } denotes the floor function. More precisely, the number of multiplications is one...

- needs 10×30×5 + 10×5×60 = 4,500 multiplications, while computing A(BC) needs 30×5×60 + 10×30×60 = 27,000 multiplications. Algorithms have been designed...

- real or complex number field, these two multiplications are the same, and are simply called scalar multiplication. However, for matrices over a more general...

- mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an...

- count of complex multiplications and additions for N=4096 data points. Evaluating the DFT's sums directly involves N2 complex multiplications and N(N−1) complex...

- eight multiplications of pairs of submatrices, followed by an addition step. The divide and conquer algorithm computes the smaller multiplications recursively...

- reduced the number of multiplications. We still need 8 multiplications to calculate the Ci,j matrices, the same number of multiplications we need when using...

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