1. Algebra Properties Definition Numeric Example  Algebraic Example

2. Commutative Property of Addition We can change the order when adding without affecting the sum.

3. Commutative Property of Multiplication We can change the order when multiplying without affecting the product.

4. Associative Property of Addition Numbers can be grouped in any order for addition.

5. Associative Property of Multiplication Numbers can be grouped in any order for multiplication.

6. Identity Property of Addition Adding 0 to any number gives that number.

7. Identity Property of Multiplication Multiplying a number by 1 gives that number.

8. Additive Inverse Property Two rational numbers whose sum is 0.

9. Multiplicative Inverse Property Two rational numbers whose product is 1.

10. Distributive Property Multiplying a number over addition or subtraction.

11. The Inverse of a Sum Property The additive inverse of a sum is the sum of the additive inverses.

12. Multiplicative Property of Zero The product of 0 and any rational number is 0.

13. Multiplicative Property of -1 Negative one times a is the additive inverse of a.

14. The Addition Property of Equality Adding the same number to both sides of an equation results in an equivalent equation.

15. The Subtraction Property of Equality Subtracting the same number to both sides of an equation results in an equivalent equation.

16. The Multiplication Property of Equality Multiplying the same number to both sides of an equation results in an equivalent equation.

17. The Division Property of Equality Dividing the same number to both sides of an equation results in an equivalent equation.

18. Symmetric Property Two equal quantities can be written in any order.

19. Transitive Property