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Homemultiplication

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# multiplication

Multiplication is a mathematical operation in which two or more numbers are added up to themselves by a factor of other numbers. For example, $2\times 3=2+2+2=3+3=6$. The numbers may be real, imaginary or complex, they may be integers or fractions. Among real numbers, if an odd number of multiplicands are negative, the overall result is negative; if an even number of multiplicands are negative, the overall result is positive. Two examples: $(-3)\times(-5)=15$; $(-2)\times(-3)\times(-5)=(-30)$.

The usual operator is the cross with its four arms of equal length pointing northeast, northwest, southeast and southwest: $\times$. Other options are the central dot $\cdot$ and the tacit multiplication operator. In many computer programming languages the asterisk is often used as it is almost always available on the keyboard (Shift-8 in most American layouts, as well as dedicated key if the keyboard has a numeric keypad), and this is the operator likely to be used in a computer implementation of a reverse Polish notation calculator. In Mathematica, the space can sometimes function as a multiplication operator, but more experienced users warn novices not to rely on this feature.

Just as with addition, multiplication is commutative: $xyz=xzy=yxz$, etc.

The iterative operator is the Greek capital letter pi:

$\prod_{{i=1}}^{n}a_{i},$ |

which is a compact way of writing $a_{1}\times a_{2}\times\ldots\times a_{n}$.

Multiplication of complex numbers is helped by the following identity: $(a+bi)\times(x+yi)=(ax-by)+(ay+bx)i$. To give three examples: $(17+29i)(11+38i)=-915+965i$ (the result has both real and imaginary parts), $(1+2i)(1-2i)=5$ (the result is a real prime) and $(4+7i)(7+4i)=65i$ (the result has only an imaginary part).

## Mathematics Subject Classification

00A06*no label found*11B25

*no label found*00A05

*no label found*

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## Comments

## The terms in multiplication

PrimeFan used in http://planetmath.org/encyclopedia/Multiplication.html the term "multiplicand" to mean any of the numbers which are multiplied among themselves in a product. Is this the general usage in English? In most European languages, they are "factors" of the product; Wolfram (http://mathworld.wolfram.com/Multiplication.html) takes the same view on the thing.

Wolfram says (http://mathworld.wolfram.com/Multiplicand.html) that in the product "a times b", "a" is the "multiplier" and "b" the "multiplicand". But Wikipedia (http://en.wikipedia.org/wiki/Multiplicand) says quite the contrary.

Is there a definite standard which we should take in PM entries,

concerning the terms "factor", "multiplier", "multiplicand"? Perhaps PrimeFan could define these terms in the entry "multiplication".

Jussi

## Re: The terms in multiplication

I thought the term "multiplicand" was analogous to "operand" and that an "operand" is any of the terms an "operator" works on. And because multiplication is commutative, I don't think there is much use for a distinction; whether we have six rows and seven columns or six columns and seven rows we still have 42 cells. Maybe this is another question for Barbara Wallraff.