Difference between revisions of "Common Multiplication"

m (Multiplication moved to Ordinary Multiplication: The word '''multiplication''' has more broader definition and the one defined in this page provides information that only pertains to ordinary arithmetic.)
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In [[mathematics]], '''multiplication''' is an arithmetic [[operation]]. The result of multiplying is the [[product]]. If one of the [[number]]s is a [[whole number]], multiplication is the repeated [[sum]] of that number. For example, <math>4\times3=4+4+4=12</math>. The inverse of multiplication is [[division]].
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In ordinary [[arithmetic]], '''multiplication''' is an arithmetic [[operation]]. The result of multiplying is the [[product]]. If one of the [[number]]s is a [[whole number]], multiplication is the repeated [[sum]] of that number. For example, <math>4\times3=4+4+4=12</math>. The [[inverse]] of multiplication is [[division]].
  
 
To multiply [[fraction]]s, the [[numerator]]s and [[denominator]]s are multiplied: <math>\frac{a}{c}\times\frac{b}{d}=\frac{a\times b}{c\times d}=\frac{ab}{cd}</math>.
 
To multiply [[fraction]]s, the [[numerator]]s and [[denominator]]s are multiplied: <math>\frac{a}{c}\times\frac{b}{d}=\frac{a\times b}{c\times d}=\frac{ab}{cd}</math>.
  
 
== Properties ==
 
== Properties ==
* Commutative property: <math>a\times b=b\times a</math>
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* [[Commutative]] property: <math>a\times b=b\times a</math>
* Associative property: <math>a(b\times c)=(a\times b)c</math>
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* [[Associative]] property: <math>a\times(b\times c)=(a\times b)\times c</math>
* Distributive property: <math>a(b+c)=ab+ac</math>
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* [[Distributive]] property: <math>a\times(b+c)=ab+ac</math>
* Identity property: <math>a\times1=a</math> and <math>a\times0=0</math>
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* [[zero (constant) | Zero]] property: <math>a\times0=0</math>
* Any number, except [[zero (constant) | zero]], multiplied by its reciprocal is equal to 1: <math>x\times\frac{1}{x}=1</math>
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* [[Identity]] property: <math>a\times1=a</math>
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* [[Inverse]] property: For any <math>x\neq0</math>, <math>x\times\frac{1}{x}=1</math>

Revision as of 10:19, 15 November 2007

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In ordinary arithmetic, multiplication is an arithmetic operation. The result of multiplying is the product. If one of the numbers is a whole number, multiplication is the repeated sum of that number. For example, $4\times3=4+4+4=12$. The inverse of multiplication is division.

To multiply fractions, the numerators and denominators are multiplied: $\frac{a}{c}\times\frac{b}{d}=\frac{a\times b}{c\times d}=\frac{ab}{cd}$.

Properties