Multiplication Operation
A Multiplication Operation is an algebraic operation composed of a sequence of one or more multiplication function.
- AKA: ×, Multiplication Function.
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- Counter-Example(s):
- See: Algebraic Function, Elementary Arithmetic, Natural Number, Commutative Property, Integer, Rational Number, Real Number.
References
2015
- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/multiplication Retrieved:2015-1-17.
- Multiplication (often denoted by the cross symbol "×", or by the absence of symbol) is one of the four elementary, mathematical operations of arithmetic; with the others being addition, subtraction and division.
The multiplication of two whole numbers is equivalent to the addition of one of them with itself as many times as the value of the other one; for example, 3 multiplied by 4 (often said as "3 times 4") can be calculated by adding 3 copies of 4 together: :[math]\displaystyle{ 3 \times 4 = 4 + 4 + 4 = 12 }[/math]
Here 3 and 4 are the "factors" and 12 is the "product".
One of the main properties of multiplication is that the result does not depend on the place of the factor that is repeatedly added to itself (commutative property). 3 multiplied by 4 can also be calculated by adding 4 copies of 3 together: :[math]\displaystyle{ 3 \times 4 = 3 + 3 + 3 + 3 = 12 }[/math]
The multiplication of integers (including negative numbers), rational numbers (fractions) and real numbers is defined by a systematic generalization of this basic definition.
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 given lengths. The area of a rectangle does not depend on which side is measured first, which illustrates the commutative property.
In general, multiplying two measurements gives a new type, depending on the measurements. For instance: :[math]\displaystyle{ 2.5 \mbox{ meters} \times 4.5 \mbox{ meters} = 11.25 \mbox{ square meters} }[/math] :[math]\displaystyle{ 11 \mbox{ meters/second} \times 9 \mbox{ seconds} = 99 \mbox{ meters} }[/math]
The inverse operation of the multiplication is the division. For example, since 4 multiplied by 3 equals 12, then 12 divided by 3 equals 4. Multiplication by 3, followed by division by 3, yields the original number (since 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 more abstract constructs, like matrices. For these more abstract constructs, the order that the operands are multiplied sometimes does matter.
- Multiplication (often denoted by the cross symbol "×", or by the absence of symbol) is one of the four elementary, mathematical operations of arithmetic; with the others being addition, subtraction and division.