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1.6E: Ejercicios

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La práctica hace a la perfección

Utilizar las propiedades conmutativas y asociativas

En los siguientes ejercicios, simplifique.

1. $$43m+(−12n)+(−16m)+(−9n)$$

Contestar

$$27m+(−21n)$$

2. $$−22p+17q+(−35p)+(−27q)$$

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

Contestar

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

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

5. $$6.8p+9.14q+(−4.37p)+(−0.88q)$$

Contestar

$$2.43p+8.26q$$

6. $$9.6m+7.22n+(−2.19m)+(−0.65n)$$

7. $$−24·7·\frac{3}{8}$$

Contestar

$$−63$$

8. $$−36·11·\frac{4}{9}$$

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

Contestar

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

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

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

Contestar

$$17$$

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

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

Contestar

$$14.88$$

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

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

Contestar

$$10p$$

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

Utilice las Propiedades de Identidad, Inversa y Cero

En los siguientes ejercicios, simplifique.

17. $$19a+44−19a$$

Contestar

$$44$$

18. $$27c+16−27c$$

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

Contestar

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

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

21. $$10(0.1d)$$

Contestar

$$d$$

22. $$100(0.01p)$$

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

Contestar

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

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

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

Contestar

$$0$$

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

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

Contestar

undefined

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

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

Contestar

undefined

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

Simplificar expresiones usando la propiedad distributiva

En los siguientes ejercicios, simplifique el uso de la Propiedad Distributiva.

31. $$8(4y+9)$$

Contestar

$$32y+72$$

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

33. $$6(c−13)$$

Contestar

$$6c−78$$

34. $$7(y−13)$$

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

Contestar

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

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

37. $$9(\frac{5}{9}y−\frac{1}{3})$$

Contestar

$$5y−3$$

38. $$10(\frac{3}{10}x−\frac{2}{5})$$

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

Contestar

$$3+8r$$

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

41. $$15⋅\frac{3}{5}(4d+10)$$

Contestar

$$36d+90$$

42. $$18⋅\frac{5}{6}(15h+24)$$

43. $$r(s−18)$$

Contestar

$$rs−18r$$

44. $$u(v−10)$$

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

Contestar

$$yp+4p$$

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

47. $$−7(4p+1)$$

Contestar

$$−28p−7$$

48. $$−9(9a+4)$$

49. $$−3(x−6)$$

Contestar

$$−3x+18$$

50. $$−4(q−7)$$

51. $$−(3x−7)$$

Contestar

$$−3x+7$$

52. $$−(5p−4)$$

53. $$16−3(y+8)$$

Contestar

$$−3y−8$$

54. $$18−4(x+2)$$

55. $$4−11(3c−2)$$

Contestar

$$−33c+26$$

56. $$9−6(7n−5)$$

57. $$22−(a+3)$$

Contestar

$$−a+19$$

58. $$8−(r−7)$$

59. $$(5m−3)−(m+7)$$

Contestar

$$4m−10$$

60. $$(4y−1)−(y−2)$$

61. $$9(8x−3)−(−2)$$

Contestar

$$72x−25$$

62. $$4(6x−1)−(−8)$$

63. $$5(2n+9)+12(n−3)$$

Contestar

$$22n+9$$

64. $$9(5u+8)+2(u−6)$$

65. $$14(c−1)−8(c−6)$$

Contestar

$$6c+34$$

66. $$11(n−7)−5(n−1)$$

67. $$6(7y+8)−(30y−15)$$

Contestar

$$12y+63$$

68. $$7(3n+9)−(4n−13)$$

Ejercicios de escritura

69. En sus propias palabras, manifieste la Propiedad Asociativa de la adición.

Contestar

Las respuestas variarán.

70. ¿Cuál es la diferencia entre el inverso aditivo y el inverso multiplicativo de un número

71. Simplifique el $$8(x−\frac{1}{4})$$ uso de la Propiedad Distributiva y explique cada paso.

Contestar

Las respuestas variarán.

72. Explica cómo puedes multiplicar $$4(5.97)$$ sin papel o calculadora pensando en $$5.97$$ as $$6−0.03$$ y luego usando la Propiedad Distributiva.

Autocomprobación

a. Después de completar los ejercicios, utilice esta lista de verificación para evaluar su dominio de los objetivos de esta sección.

b. Después de revisar esta lista de verificación, ¿qué hará para tener confianza en todos los objetivos?

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