2. Properties of Real Numbers

3. List of Properties of Real Numbers Commutative Associative Distributive Identity Inverse

4. Commutative Properties Definition: Changing the order of the numbers in addition or multiplication will not change the result.

5. Commutative Properties PropertyNumbersAlgebra Addition2 + 3 = 3 + 2a + b = b + a Multiplication4 5 = 5 4ab = ba

6. Associative Properties Definition: Changing the grouping of the numbers in addition or multiplication will not change the result.

7. Associative Properties PropertyNumbersAlgebra Addition 3 + (4 + 5)= (3 + 4)+ 5 a + (b + c)= (a + b)+ c Multiplication (2 3) 4 = 2 (3 4) (ab)c = a(bc)

8. Distributive Property Multiplication distributes over addition.

9. Additive Identity Property Definition: Zero preserves identities under addition. In other words, adding zero to a number does not change its value. Example: a + 0 = a and 0 + a = a

10. Multiplicative Identity Property Definition: The number 1 preserves identities under multiplication. In other words, multiplying a number by 1 does not change the value of the number. Example: a ∙ 1 = a and 1 ∙ a = a

11. Additive Inverse Property Definition: For each real number a there exists a unique real number –a such that their sum is zero. In other words, opposites add to zero. Example: a + (-a) = 0

12. Multiplicative Inverse Property

13. Let’s play “Name that property!”

14. State the property or properties that justify the following. 3 + 2 = 2 + 3 Commutative Property

15. State the property or properties that justify the following. 10(1/10) = 1 Multiplicative Inverse Property

16. State the property or properties that justify the following. 3(x – 10) = 3x – 30 Distributive Property

17. State the property or properties that justify the following. 3 + (4 + 5) = (3 + 4) + 5 Associative Property

18. State the property or properties that justify the following. (5 + 2) + 9 = (2 + 5) + 9 Commutative Property

19. 3 + 7 = 7 + 3 Commutative Property of Addition 2.

20. 8 + 0 = 8 Identity Property of Addition 3.

21. 6 4 = 4 6 Commutative Property of Multiplication 5.

22. 17 + (-17) = 0 Inverse Property of Addition 6.

23. 2(5) = 5(2) Commutative Property of Multiplication 7.

24. (2 + 1) + 4 = 2 + (1 + 4) Associative Property of Addition 1.

25. even + even = even Closure Property 8.

26. 3(2 + 5) = 32 + 35 Distributive Property 9.

27. 6(78) = (67)8 Associative Property of Multiplication 10.

28. 5 1 = 5 Identity Property of Multiplication 11.

30. (6 – 3)4 = 64 – 34 Distributive Property 13.

31. 1(-9) = -9 Identity Property of Multiplication 14.

32. 3 + (-3) = 0 Inverse Property of Addition 15.

33. 1 + [-9 + 3] = [1 + (-9)] + 3 Associative Property of Addition 16.

34. -3(6) = 6(-3) Commutative Property of Multiplication 17.

35. -8 + 0 = -8 Identity Property of Addition 18.

36. 37 – 34 = 3(7 – 4) Distributive Property 19.

37. 6 + [(3 + (-2)] = (6 + 3) + (- 2) Associative Property of Addition 20.

38. 7 + (-5) = -5 + 7 Commutative Property of Addition 21.

39. (5 + 4)9 = 45 + 36 Distributive Property 22.

40. -3(5 4) = (-3 5)4 Associative Property of Multiplication 23.

41. -8(4) = 4(-8) Commutative Property of Multiplication 24.

43. 5 1 / 7 + 0 = 5 1 / 7 Identity Property of Addition 25.

44. 3 / 4 – 6 / 7 = – 6 / 7 + 3 / 4 Commutative Property of Addition 26.

45. 1 2 / 5 1 = 1 2 / 5 Identity Property of Multiplication 27.

46. (fraction)(fraction) = fraction Closure Property 28.

47. -8 2 / 5 + 0 = -8 2 / 5 Identity Property of Addition 29.

48. [(- 2 / 3 )(5)]9 = - 2 / 3 [(5)(9)] Associative Property of Multiplication 30.

50. 6(3 – 2n) = 18 – 12n Distributive Property 31.

51. 2x + 3 = 3 + 2x Commutative Property of Addition 32.

52. ab = ba Commutative Property of Multiplication 33.

53. a + 0 = a Identity Property of Addition 34.

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

55. a1 = a Identity Property of Multiplication 36.

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

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

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

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

60. Properties of Real Numbers Commutative Associative Distributive Identity + × Inverse + ×