Properties of Equality

Let a, b, and c be real numbers.

Addition Property of Equality

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

    i.e. When two quantities are equal, if you add the same number to both quantities, the sums will also be equal. 

Subtraction Property of Equality

If a = b, then a - c = b - c.

    i.e.  When two quantities are equal, if you subtract the same number from both quantities, the differences will also be equal.

Multiplication Property of Equality

If a = b, then ac = bc and ca = ba.

    i.e.  When two quantities are equal, if you multiply them by the same number, the products will also be equal.

Division Property of Equality

If a = b and c does NOT equal 0, then a/c = b/c.

    i.e.  When two quantities are equal, if they are divided by the same non-zero number, the quotients are also equal.

Reflexive Property of Equality

a = a

    i.e.  Any number is equal to itself.

Symmetric Property of Equality

If a = b, then b = a.

Transitive Property of Equality

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

"Structures are the weapons of the mathematician."

Bourbaki