1. Properties A property is something that is true for all situations.

2. Four Properties 1.Distributive 2.Commutative 3.Associative 4.Identity properties of one and zero

3. Distributive Property A(B + C) = AB + BC 4(3 + 5) = 4 x 3 + 4 x 5

4. Commutative Property of addition and multiplication Order doesn’t matter A x B = B x A A + B = B + A

5. Associative Property of multiplication and Addition Associative Property  (a · b) · c = a · (b · c) Example: (6 · 4) · 3 = 6 · (4 · 3) Associative Property  (a + b) + c = a + (b + c) Example: (6 + 4) + 3 = 6 + (4 + 3)

6. Identity Properties If you add 0 to any number, the number stays the same. A + 0 = A or 5 + 0 = 5 If you multiply any number times 1, the number stays the same. A x 1 = A or 5 x 1 = 5

7. (2 + 1) + 4 = 2 + (1 + 4)

8. 3 + 7 = 7 + 3

9. 8 + 0 = 8

10. 6 4 = 4 6

11. 2(5) = 5(2)

12. 3(2 + 5) = 32 + 35

13. 6(78) = (67)8

14. 5 1 = 5

15. (6 – 3)4 = 64 – 34

16. 1(-9) = -9

17. 3 + (-3) = 0

18. -3(6) = 6(-3)

19. -8 + 0 = -8

20. 7 + (-5) = -5 + 7

21. -3(5 4) = (-3 5)4

22. Simplify using properties to justify each step. 10 (2) (14) (5) 9 + 102x + 1

23. -8(4) = 4(-8)