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a + b = b + a

Commutative Property of Addition

a × b = b × a

Commutative Property of Multiplication

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

Associative Property of Addition

a × (b × c) = (a × b) × c

Associative Property of Multiplication

a × (b + c) = a × b + a ×c

Distributive Property of Multiplication over Addition

a + 0 = a

Additive Identity Property

a × 1 = a

Multiplicative Identity Property

a + (-a) = 0

Additive Inverse Property

(a / b) × (b / a) = 1

Multiplicative Inverse Property

a × 0 = 0

Multiplicative Property of Zero

a^b = a^c if b = c

Exponential Property of Equality

If a = b, then a + c = b + c

Addition Property of Equality

If a = b, then a − c = b − c

Subtraction Property of Equality

If a = b, then ac = bc

Multiplication Property of Equality

If a = b, then a/c = b/c

Division Property of Equality

a = a

Reflexive Property of Equality

If a = b, then b = a

Symmetric Property of Equality

If a = b and b = c, then a = c

Transitive Property of Equality

If a = b, then b may be substituted for a in any expression containing a

Substitution Property