# Real Numbers Algebra

## The commutative and associative law for addition and more.

### Commutative Law for Addition

Commutative Law for Addition can be expressed as

a + b = b + a (1)

### Associative Law for Addition

Associative Law for Addition can be expressed as

(a + b) + c = a + (b + c) (2)

### Identity Law for Addition

Identity Law for Addition can be expressed as

a + 0 = 0 + a (3)

### Inverse Law of Addition

Inverse Law of Addition can be expressed as

a + (-a) = (-a) + a = 0 (4)

### Associative Law for Multiplication

Associative Law for Multiplication can be expressed as

a · (b·c) = (a·b)·c (5)

### Inverse Law for Multiplication

Inverse Law for Multiplication can be expressed as

a·(1 / a) = (1 / a)·a = 1, a ≠ 0 (6)

### Identity Law for Multiplication

Identity Law for Multiplication can be expressed as

(a)·(1) = (1)·(a) (7)

### Commutative Law for Multiplication

Commutative Law for Multiplication can be expressed as

a·b = b·a (8)

### Distributive Law

Distributive Law can be expressed as

a·(b + c) = a·b + a·c (9)