# Common Multiplication

In ordinary arithmetic, multiplication is an arithmetic operation. It is represented by parentheses, the $\cdot$ sign, and the $\times$ sign. 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 $x\neq0$, $x\times\frac{1}{x}=1$

Note that $\frac{1}{x}$ is $x$'s reciprocal. As long as a number is not equal to 0, the product of that number and its reciprocal is 1.

## Multiplication between positive and negative numbers and 0

If you multiply no 0's, any amount of positive numbers, and an odd number of negative numbers, the result is negative. However, if you multiply no 0's, any amount of positive numbers, and an even number of negative numbers, the result is positive. As mentioned, multiplying any number of 0's will result in the product 0.