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)

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