If equals are added to equals, their sums are equal. If unequals are added to equals, their sums are unequal.

• ### Division Axiom

If equals are divided by equals, their quotients is equal. If unequals are divided by equals, their quotients is unequal.

• ### Multiplication Axiom

If equals are multiplied by equals, their products are equal. If unequals are multiplied by equals, their products are unequal.

• ### Partition Axiom

A quantity is equal to the sum of its parts. A quantity is greater than any one of its parts.

• ### Reflexive Property

A quantity is equal to itself.

• ### Substitution Axiom

Equals can be substituted for each other in any equality or inequality.

• ### Subtraction Axiom

If equals are subtracted from equals, their differences are equal. If unequals are subtracted from equals, their differences are unequal.

• ### Transitive Property

If two quantities are equal to a third quantity, they are equal to each other. If a quantity is greater than another quantity, which is greater than a third quantity, then the first quantity is greater than the third quantity.