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1.6E: Exercises

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Practice Makes Perfect

Use the Commutative and Associative Properties

In the following exercises, simplify.

1. 43m+(12n)+(16m)+(9n)

Answer

27m+(21n)

2. 22p+17q+(35p)+(27q)

3. 38g+112h+78g+512h

Answer

54g+12h

4. 56a+310b+16a+910b

5. 6.8p+9.14q+(4.37p)+(0.88q)

Answer

2.43p+8.26q

6. 9.6m+7.22n+(2.19m)+(0.65n)

7. 24·7·38

Answer

63

8. 36·11·49

9. (56+815)+715

Answer

156

10. (1112+49)+59

11. 17(0.25)(4)

Answer

17

12. 36(0.2)(5)

13. [2.48(12)](0.5)

Answer

14.88

14. [9.731(4)](0.75)

15. 12(56p)

Answer

10p

16. 20(35q)

Use the Properties of Identity, Inverse and Zero

In the following exercises, simplify.

17. 19a+4419a

Answer

44

18. 27c+1627c

19. 12+78+(12)

Answer

78

20. 25+512+(25)

21. 10(0.1d)

Answer

d

22. 100(0.01p)

23. 320·4911·203

Answer

4911

24. 1318·257·1813

25. 0u4.99, where u4.99

Answer

0

26. 0÷(y16), where x16

27. 325a0, where 325a0

Answer

undefined

28. 289b0, where 289b0

29. (34+910m)÷0, where 34+910m0

Answer

undefined

30. (516n37)÷0, where 516n370

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the Distributive Property.

31. 8(4y+9)

Answer

32y+72

32. 9(3w+7)

33. 6(c13)

Answer

6c78

34. 7(y13)

35. 14(3q+12)

Answer

34q+3

36. 15(4m+20)

37. 9(59y13)

Answer

5y3

38. 10(310x25)

39. 12(14+23r)

Answer

3+8r

40. 12(16+34s)

41. 1535(4d+10)

Answer

36d+90

42. 1856(15h+24)

43. r(s18)

Answer

rs18r

44. u(v10)

45. (y+4)p

Answer

yp+4p

46. (a+7)x

47. 7(4p+1)

Answer

28p7

48. 9(9a+4)

49. 3(x6)

Answer

3x+18

50. 4(q7)

51. (3x7)

Answer

3x+7

52. (5p4)

53. 163(y+8)

Answer

3y8

54. 184(x+2)

55. 411(3c2)

Answer

33c+26

56. 96(7n5)

57. 22(a+3)

Answer

a+19

58. 8(r7)

59. (5m3)(m+7)

Answer

4m10

60. (4y1)(y2)

61. 9(8x3)(2)

Answer

72x25

62. 4(6x1)(8)

63. 5(2n+9)+12(n3)

Answer

22n+9

64. 9(5u+8)+2(u6)

65. 14(c1)8(c6)

Answer

6c+34

66. 11(n7)5(n1)

67. 6(7y+8)(30y15)

Answer

12y+63

68. 7(3n+9)(4n13)

Writing Exercises

69. In your own words, state the Associative Property of addition.

Answer

Answers will vary.

70. What is the difference between the additive inverse and the multiplicative inverse of a number

71. Simplify 8(x14) using the Distributive Property and explain each step.

Answer

Answers will vary.

72. Explain how you can multiply 4($5.97) without paper or calculator by thinking of $5.97 as 60.03 and then using the Distributive Property.

Self Check

a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This table has 4 columns, 3 rows and a header row. The header row labels each column I can, confidently, with some help and no, I don’t get it. The first column has the following statements: use the commutative and associative properties, use the properties of identity, inverse and zero, simplify expressions using the Distributive Property. The remaining columns are blank.

b. After reviewing this checklist, what will you do to become confident for all objectives?


This page titled 1.6E: Exercises is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.

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