1.6E: Exercises

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. \(\frac{3}{8}g+\frac{1}{12}h+\frac{7}{8}g+\frac{5}{12}h\)

Answer

\(\frac{5}{4}g+\frac{1}{2}h\)

4. \(\frac{5}{6}a+\frac{3}{10}b+\frac{1}{6}a+\frac{9}{10}b\)

5. \(6.8p+9.14q+(−4.37p)+(−0.88q)\)

Answer

\(2.43p+8.26q\)

6. \(9.6m+7.22n+(−2.19m)+(−0.65n)\)

7. \(−24·7·\frac{3}{8}\)

Answer

\(−63\)

8. \(−36·11·\frac{4}{9}\)

9. \(\left(\frac{5}{6}+\frac{8}{15}\right)+\frac{7}{15}\)

Answer

\(1\frac{5}{6}\)

10. \(\left(\frac{11}{12}+\frac{4}{9}\right)+\frac{5}{9}\)

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. \(12\left(\frac{5}{6}p\right)\)

Answer

\(10p\)

16. \(20\left(\frac{3}{5}q\right)\)

Use the Properties of Identity, Inverse and Zero

In the following exercises, simplify.

17. \(19a+44−19a\)

Answer

\(44\)

18. \(27c+16−27c\)

19. \(\frac{1}{2}+\frac{7}{8}+\left(−\frac{1}{2}\right)\)

Answer

\(\frac{7}{8}\)

20. \(\frac{2}{5}+\frac{5}{12}+\left(−\frac{2}{5}\right)\)

21. \(10(0.1d)\)

Answer

\(d\)

22. \(100(0.01p)\)

23. \(\frac{3}{20}·\frac{49}{11}·\frac{20}{3}\)

Answer

\(\frac{49}{11}\)

24. \(\frac{13}{18}·\frac{25}{7}·\frac{18}{13}\)

25. \(\frac{0}{u−4.99}\), where \(u\neq 4.99\)

Answer

\(0\)

26. \(0÷(y−\frac{1}{6})\), where \(x \neq 16\)

27. \(\frac{32−5a}{0}\), where \(32−5a\neq 0\)

Answer

undefined

28. \(\frac{28−9b}{0}\), where \(28−9b\neq 0\)

29. \(\left(\frac{3}{4}+\frac{9}{10}m\right)÷0\), where \(\frac{3}{4}+\frac{9}{10}m\neq 0\)

Answer

undefined

30. \(\left(\frac{5}{16}n−\frac{3}{7}\right)÷0\), where \(\frac{5}{16}n−\frac{3}{7}\neq 0\)

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. \(6(c−13)\)

Answer

\(6c−78\)

34. \(7(y−13)\)

35. \(\frac{1}{4}(3q+12)\)

Answer

\(\frac{3}{4}q+3\)

36. \(\frac{1}{5}(4m+20)\)

37. \(9(\frac{5}{9}y−\frac{1}{3})\)

Answer

\(5y−3\)

38. \(10(\frac{3}{10}x−\frac{2}{5})\)

39. \(12(\frac{1}{4}+\frac{2}{3}r)\)

Answer

\(3+8r\)

40. \(12(\frac{1}{6}+\frac{3}{4}s)\)

41. \(15⋅\frac{3}{5}(4d+10)\)

Answer

\(36d+90\)

42. \(18⋅\frac{5}{6}(15h+24)\)

43. \(r(s−18)\)

Answer

\(rs−18r\)

44. \(u(v−10)\)

45. \((y+4)p\)

Answer

\(yp+4p\)

46. \((a+7)x\)

47. \(−7(4p+1)\)

Answer

\(−28p−7\)

48. \(−9(9a+4)\)

49. \(−3(x−6)\)

Answer

\(−3x+18\)

50. \(−4(q−7)\)

51. \(−(3x−7)\)

Answer

\(−3x+7\)

52. \(−(5p−4)\)

53. \(16−3(y+8)\)

Answer

\(−3y−8\)

54. \(18−4(x+2)\)

55. \(4−11(3c−2)\)

Answer

\(−33c+26\)

56. \(9−6(7n−5)\)

57. \(22−(a+3)\)

Answer

\(−a+19\)

58. \(8−(r−7)\)

59. \((5m−3)−(m+7)\)

Answer

\(4m−10\)

60. \((4y−1)−(y−2)\)

61. \(9(8x−3)−(−2)\)

Answer

\(72x−25\)

62. \(4(6x−1)−(−8)\)

63. \(5(2n+9)+12(n−3)\)

Answer

\(22n+9\)

64. \(9(5u+8)+2(u−6)\)

65. \(14(c−1)−8(c−6)\)

Answer

\(6c+34\)

66. \(11(n−7)−5(n−1)\)

67. \(6(7y+8)−(30y−15)\)

Answer

\(12y+63\)

68. \(7(3n+9)−(4n−13)\)

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 \(8(x−\frac{1}{4})\) 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 \(6−0.03\) 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.

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