View source for 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:
:<math>5 * 4 = 20</math>

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 <math>x</math> and <math>y</math>, <math> x * y = y * x </math>
For example, the two equations end up with the same result.
:<math> 3 * 7 = 21 </math>
:<math> 7 * 3 = 21 </math>

===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 <math>x, y</math> and <math>z</math>, <math>(x * y) * z = x * (y * z)</math>
For example, the two equations will end up with the same result.
:<math>(2 * 3) * 4 = 6 * 4 = 24</math>
:<math>2 * (3 * 4) = 2 * 12 = 24</math>

=== The Multiplicative Identity ===
The number ''1'' is known as the multiplicative identity. This means if you multiply any number with one, you end up with that original number. For example:
:<math>4 * 1 = 4</math>
:<math>6.24 * 1 = 6.24</math>
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[[Category:Book:Arithmetic]]