Distributive Laws/Arithmetic

Theorem
On all the number systems: the operation of multiplication is distributive over addition.
 * natural numbers $\N$
 * integers $\Z$
 * rational numbers $\Q$
 * real numbers $\R$
 * complex numbers $\C$

Proof
This is demonstrated in these pages:


 * Natural Number Multiplication Distributes over Addition
 * Integer Multiplication Distributes over Addition
 * Rational Multiplication Distributes over Addition
 * Real Multiplication Distributes over Addition
 * Complex Multiplication Distributes over Addition

Also known as
This result is known as the Distributive Property.

As such, it typically refers to the various results contributing towards this.

Also see

 * Modulo Multiplication Distributes over Modulo Addition
 * Matrix Multiplication Distributes over Matrix Addition


 * Euclid's proofs:
 * Multiplication of Numbers is Left Distributive over Addition
 * Multiplication of Numbers is Right Distributive over Addition