# Arithmetic/Number Operations/Multiplication

Multiplication is one of the four basic operations of arithmetic. The operation is usually shown by the times symbol (*). This is the act of taking a number and adding it to itself a certain number of times. Think of multiplication as a shorthand way of performing repeated addition. For example, the following equation:

${\displaystyle 5*4=20}$

This means, "Multiplying five by four gives twenty," or put more simply, "five times four equals twenty." In this example, 5 and 4 are the factors, and 20 is the product, the result of the multiplication.

## Properties of Multiplication

### Commutativity

When multiplying two numbers together, it doesn't matter what order the numbers are placed in, since the outcome will be the same. That is to say for any two numbers ${\displaystyle x}$ and ${\displaystyle y}$, ${\displaystyle x*y=y*x}$ For example, the two equations end up with the same result.

${\displaystyle 3*7=21}$
${\displaystyle 7*3=21}$

### Associativity

When multiplying multiple numbers together, the order in which you multiply the numbers doesn't matter, since the outcome will be the same. For any three numbers ${\displaystyle x,y}$ and ${\displaystyle z}$, ${\displaystyle (x*y)*z=x*(y*z)}$ For example, the two equations will end up with the same result.

${\displaystyle (2*3)*4=6*4=24}$
${\displaystyle 2*(3*4)=2*12=24}$

${\displaystyle 4*1=4}$
${\displaystyle 6.24*1=6.24}$
${\displaystyle (5+4i)*1=5+4i}$