Multiplication
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Multiplication
Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division (mathematics), division. The result of a multiplication operation is called a ''Product (mathematics), product''. Multiplication is often denoted by the cross symbol, , by the mid-line dot operator, , by juxtaposition, or, in programming languages, by an asterisk, . 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''. This is to be distinguished from term (arithmetic), ''terms'', which are added. :a\times b = \underbrace_ . Whether the first factor is the multiplier or the multiplicand may be ambiguous or depend upon context. For example, the expression 3 \times 4 , can be phrased as "3 ti ...
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Multiply Scaling
Multiplication 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''. Multiplication is often denoted by the cross symbol, , by the mid-line dot operator, , by juxtaposition, or, in programming languages, by an asterisk, . 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''. This is to be distinguished from ''terms'', which are added. :a\times b = \underbrace_ . Whether the first factor is the multiplier or the multiplicand may be ambiguous or depend upon context. For example, the expression 3 \times 4 , can be phrased as "3 times 4" and evaluated as 4+4+4, where 3 is the multiplier, but ...
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Arithmetic
Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. Arithmetic systems can be distinguished based on the type of numbers they operate on. Integer arithmetic is about calculations with positive and negative integers. Rational number arithmetic involves operations on fractions of integers. Real number arithmetic is about calculations with real numbers, which include both rational and irrational numbers. Another distinction is based on the numeral system employed to perform calculations. Decimal arithmetic is the most common. It uses the basic numerals from 0 to 9 and their combinations to express numbers. Binary arithmetic, by contrast, is used by most computers and represents numbers as combinations of the basic numerals 0 and 1. Computer arithmetic deals with the specificities of the ...
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Multiplication Sign
The multiplication sign (), also known as the times sign or the dimension sign, is a mathematical symbol used to denote the operation of multiplication, which results in a product. The symbol is also used in botany, in botanical hybrid names. The form is properly a four-fold rotationally symmetric saltire. The multiplication sign is similar to a lowercase X (). History The earliest known use of the symbol to indicate multiplication appears in an anonymous appendix to the 1618 edition of John Napier's . This appendix has been attributed to William Oughtred, who used the same symbol in his 1631 algebra text, , stating:Multiplication of species .e. unknownsconnects both proposed magnitudes with the symbol 'in' or : or ordinarily without the symbol if the magnitudes be denoted with one letter. Other works have been identified in which crossed diagonals appear in diagrams involving multiplied numbers, such as Robert Recorde's '' The Ground of Arts'' and Oswald Schr ...
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Product (mathematics)
In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called ''factors''. For example, 21 is the product of 3 and 7 (the result of multiplication), and x\cdot (2+x) is the product of x and (2+x) (indicating that the two factors should be multiplied together). When one factor is an integer, the product is called a '' multiple''. The order in which real or complex numbers are multiplied has no bearing on the product; this is known as the ''commutative law'' of multiplication. When matrices or members of various other associative algebras are multiplied, the product usually depends on the order of the factors. Matrix multiplication, for example, is non-commutative, and so is multiplication in other algebras in general as well. There are many different kinds of products in mathematics: besides being able to multiply just numbers, polynomials or matrices, one can also define products on many di ...
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Addition
Addition (usually signified by the Plus and minus signs#Plus sign, plus symbol, +) is one of the four basic Operation (mathematics), operations of arithmetic, the other three being subtraction, multiplication, and Division (mathematics), division. The addition of two Natural number, whole numbers results in the total or ''summation, sum'' of those values combined. For example, the adjacent image shows two columns of apples, one with three apples and the other with two apples, totaling to five apples. This observation is expressed as , which is read as "three plus two Equality (mathematics), equals five". Besides counting items, addition can also be defined and executed without referring to concrete objects, using abstractions called numbers instead, such as integers, real numbers, and complex numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects such as Euclidean vector, vec ...
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Term (arithmetic)
Addition (usually signified by the plus symbol, +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication, and division. The addition of two whole numbers results in the total or '' sum'' of those values combined. For example, the adjacent image shows two columns of apples, one with three apples and the other with two apples, totaling to five apples. This observation is expressed as , which is read as "three plus two equals five". Besides counting items, addition can also be defined and executed without referring to concrete objects, using abstractions called numbers instead, such as integers, real numbers, and complex numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces, and subgroups. Addition has several important properties. It is commutative, meaning that the order of the numb ...
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Interpunct
An interpunct , also known as an interpoint, middle dot, middot, centered dot or centred dot, is a punctuation mark consisting of a vertically centered dot used for interword separation in Classical Latin. ( Word-separating spaces did not appear until some time between 600 and 800 CE.) It appears in a variety of uses in some modern languages. The multiplication dot or "dot operator" is frequently used in mathematical and scientific notation, and it may differ in appearance from the interpunct. In written language Various dictionaries use the interpunct (in this context, sometimes called a hyphenation point) to indicate where to split a word and insert a hyphen if the word doesn't fit on the line. There is also a separate Unicode character, . English In British typography, the space dot was once used as the formal decimal point. Its use was advocated by laws and can still be found in some UK-based academic journals such as ''The Lancet''. When the pound sterling was de ...
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Algebra
Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication. Elementary algebra is the main form of algebra taught in schools. It examines mathematical statements using variables for unspecified values and seeks to determine for which values the statements are true. To do so, it uses different methods of transforming equations to isolate variables. Linear algebra is a closely related field that investigates linear equations and combinations of them called '' systems of linear equations''. It provides methods to find the values that solve all equations in the system at the same time, and to study the set of these solutions. Abstract algebra studies algebraic structures, which consist of a set of mathemati ...
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Full Stop
The full stop ( Commonwealth English), period (North American English), or full point is a punctuation mark used for several purposes, most often to mark the end of a declarative sentence (as distinguished from a question or exclamation). A full stop is frequently used at the end of word abbreviations—in British usage, primarily truncations like ''Rev.'', but not after contractions like '' Revd''; in American English, it is used in both cases. It may be placed after an initial letter used to abbreviate a word. It is often placed after each individual letter in acronyms and initialisms (e.g., "U.S."). However, the use of full stops after letters in an initialism or acronym is declining, and many of these without punctuation have become accepted norms (e.g., "UK" and "NATO"). When used in a series (typically of three, an ellipsis) the mark is also used to indicate omitted words. In the English-speaking world, a punctuation mark identical to the full stop is used as the d ...
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Decimal Point
FIle:Decimal separators.svg, alt=Four types of separating decimals: a) 1,234.56. b) 1.234,56. c) 1'234,56. d) ١٬٢٣٤٫٥٦., Both a comma and a full stop (or period) are generally accepted decimal separators for international use. The apostrophe and Arabic decimal separator are also used in certain contexts. A decimal separator is a symbol that separates the integer part from the fractional part of a number written in decimal form. Different countries officially designate different symbols for use as the separator. The choice of symbol can also affect the choice of symbol for the #Digit grouping, thousands separator used in digit grouping. Any such symbol can be called a decimal mark, decimal marker, or decimal sign. Symbol-specific names are also used; decimal point and decimal comma refer to a dot (either Baseline dot, baseline or Middle dot, middle) and comma respectively, when it is used as a decimal separator; these are the usual terms used in English, with the aforem ...
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Comma (punctuation)
The comma is a punctuation mark that appears in several variants in different languages. Some typefaces render it as a small line, slightly curved or straight, but inclined from the vertical; others give it the appearance of a miniature filled-in figure placed on the baseline. In many typefaces it is the same shape as an apostrophe or single closing quotation mark . The comma is used in many contexts and languages, mainly to separate parts of a sentence such as clauses, and items in lists mainly when there are three or more items listed. The word ''comma'' comes from the Greek (), which originally meant a cut-off piece, specifically in grammar, a short clause. A comma-shaped mark is used as a diacritic in several writing systems and is considered distinct from the cedilla. In Byzantine and modern copies of Ancient Greek, the " rough" and "smooth breathings" () appear above the letter. In Latvian, Romanian, and Livonian, the comma diacritic appears below the letter ...
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