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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. $$43m+(−12n)+(−16m)+(−9n)$$

$$27m+(−21n)$$

2. $$−22p+17q+(−35p)+(−27q)$$

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

$$\frac{5}{4}g+\frac{1}{2}h$$

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

5. $$6.8p+9.14q+(−4.37p)+(−0.88q)$$

$$2.43p+8.26q$$

6. $$9.6m+7.22n+(−2.19m)+(−0.65n)$$

7. $$−24·7·\frac{3}{8}$$

$$−63$$

8. $$−36·11·\frac{4}{9}$$

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

$$1\frac{5}{6}$$

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

11. $$17(0.25)(4)$$

$$17$$

12. $$36(0.2)(5)$$

13. $$[2.48(12)](0.5)$$

$$14.88$$

14. $$[9.731(4)](0.75)$$

15. $$12\left(\frac{5}{6}p\right)$$

$$10p$$

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

Use the Properties of Identity, Inverse and Zero

In the following exercises, simplify.

17. $$19a+44−19a$$

$$44$$

18. $$27c+16−27c$$

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

$$\frac{7}{8}$$

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

21. $$10(0.1d)$$

$$d$$

22. $$100(0.01p)$$

23. $$\frac{3}{20}·\frac{49}{11}·\frac{20}{3}$$

$$\frac{49}{11}$$

24. $$\frac{13}{18}·\frac{25}{7}·\frac{18}{13}$$

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

$$0$$

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

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

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

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

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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. $$8(4y+9)$$

$$32y+72$$

32. $$9(3w+7)$$

33. $$6(c−13)$$

$$6c−78$$

34. $$7(y−13)$$

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

$$\frac{3}{4}q+3$$

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

37. $$9(\frac{5}{9}y−\frac{1}{3})$$

$$5y−3$$

38. $$10(\frac{3}{10}x−\frac{2}{5})$$

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

$$3+8r$$

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

41. $$15⋅\frac{3}{5}(4d+10)$$

$$36d+90$$

42. $$18⋅\frac{5}{6}(15h+24)$$

43. $$r(s−18)$$

$$rs−18r$$

44. $$u(v−10)$$

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

$$yp+4p$$

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

47. $$−7(4p+1)$$

$$−28p−7$$

48. $$−9(9a+4)$$

49. $$−3(x−6)$$

$$−3x+18$$

50. $$−4(q−7)$$

51. $$−(3x−7)$$

$$−3x+7$$

52. $$−(5p−4)$$

53. $$16−3(y+8)$$

$$−3y−8$$

54. $$18−4(x+2)$$

55. $$4−11(3c−2)$$

$$−33c+26$$

56. $$9−6(7n−5)$$

57. $$22−(a+3)$$

$$−a+19$$

58. $$8−(r−7)$$

59. $$(5m−3)−(m+7)$$

$$4m−10$$

60. $$(4y−1)−(y−2)$$

61. $$9(8x−3)−(−2)$$

$$72x−25$$

62. $$4(6x−1)−(−8)$$

63. $$5(2n+9)+12(n−3)$$

$$22n+9$$

64. $$9(5u+8)+2(u−6)$$

65. $$14(c−1)−8(c−6)$$

$$6c+34$$

66. $$11(n−7)−5(n−1)$$

67. $$6(7y+8)−(30y−15)$$

$$12y+63$$

68. $$7(3n+9)−(4n−13)$$

#### Writing Exercises

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.

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.