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Common Multiplication

From AoPSWiki

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

Commutative property: $a\times b=b\times a$
Associative property: $a\times(b\times c)=(a\times b)\times c$
Distributive property: $a\times(b+c)=ab+ac$
Zero property: $a\times0=0$
Identity property: $a\times1=a$
Inverse property: For any $x\neq0$ , $x\times\frac{1}{x}=1$

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