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

4. Six Properties of Addition and Multiplication 1.Distributive 2.Commutative 3.Associative 4.Identity 5.Inverse 6.Multiplicative Property of Zero

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

6. Commutative Property of addition and multiplication Order doesn’t matter A B = B A A + B = B + A CO = Change Order

7. Associative Property of multiplication and Addition Addition  (a + b) + c = a + (b + c) Example: (6 + 4) + 3 = 6 + (4 + 3) Multiplication  (a · b) · c = a · (b · c) Example: (6 · 4) · 3 = 6 · (4 · 3) SO = Same Order

8. 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 1 = A or 5 1 = 5

9. Inverse Properties Addition: a + -a = 0 or 5 + -5=0 Multiplication: a 1 = 1 or 5 1 = 1 a 5

10. Multiplicative Property of Zero Any number times zero will give you the product of 0 (zero) a 0 = 0 4 0 = 0 or 0 4=0

12. (2 + 1) + 4 = 2 +(1 + 4) Associative Property of Addition

13. 3 + 7 = 7 + 3 Commutative Property of Addition

14. 8 + 0 = 8 Identity Property of Addition

15. 6 4 = 4 6 Commutative Property of Multiplication

16. 17 + (-17) = 0 Inverse Property of Addition

17. 2(5) = 5(2) Commutative Property of Multiplication

18. 3(2 + 5) = 32 + 35 Distributive Property

19. 6(78) = (67)8 Associative Property of Multiplication

20. 5 1 = 5 Identity Property of Multiplication

21. (6 – 3)4 = 64 – 34 Distributive Property

22. 1(-9) = -9 Identity Property of Multiplication

23. 3 + (-3) = 0 Inverse Property of Addition

24. 1 + [-9 + 3] = [1 + (-9)] + 3 Associative Property of Addition

25. -3(6) = 6(-3) Commutative Property of Multiplication

26. -8 + 0 = -8 Identity Property of Addition

27. 37 – 34 = 3(7 – 4) Distributive Property

28. 6 + [(3 + (-2)] = (6 + 3) +(- 2) Associative Property of Addition

29. 7 + (-5) = -5 + 7 Commutative Property of Addition

30. (5 + 4)9 = 45 + 36 Distributive Property

31. -3(5 4) = (-3 5)4 Associative Property of Multiplication

32. -8(4) = 4(-8) Commutative Property of Multiplication

33. ab = ba Commutative Property of Multiplication

34. a + 0 = a Identity Property of Addition

35. a(bc) = (ab)c Associative Property of Multiplication

36. a1 = a Identity Property of Multiplication

37. a +b = b + a Commutative Property of Addition

38. a(b + c) = ab + ac Distributive Property

39. a +(b + c) = (a +b)+ c Associative Property of Addition

40. a + (-a) = 0 Inverse Property of Addition