Real Numbers Algebra

The commutative and associative law for addition and more.

Commutative Law for Addition can be expressed as

a + b = b + a (1)

Associative Law for Addition can be expressed as

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

Identity Law for Addition can be expressed as

a + 0 = 0 + a (3)

Inverse Law of Addition can be expressed as

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

Associative Law for Multiplication can be expressed as

a (b c) = (a b) c (5)

Inverse Law for Multiplication can be expressed as

a (1 / a) = (1 / a) a = 1, a ≠ 0 (6)

Identity Law for Multiplication can be expressed as

(a) (1) = (1) (a) (7)

Commutative Law for Multiplication can be expressed as

a b = b a (8)

Distributive Law can be expressed as

a (b + c) = a b + a c (9)