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# 1.4E: Ejercicios

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## La práctica hace a la perfección

Simplificar fracciones

En los siguientes ejercicios, simplifique.

1. $$−\dfrac{108}{63}$$

Contestar

$$−\dfrac{12}{7}$$

2. $$−\dfrac{104}{48}$$

3. $$\dfrac{120}{252}$$

Contestar

$$\dfrac{10}{21}$$

4. $$\dfrac{182}{294}$$

5. $$\dfrac{14x^2}{21y}$$

Contestar

$$\dfrac{2x^2}{3y}$$

6. $$\dfrac{24a}{32b^2}$$

7. $$−\dfrac{210a^2}{110b^2}$$

Contestar

$$−\dfrac{21a^2}{11b^2}$$

8. $$−\dfrac{30x^2}{105y^2}$$

Multiplicar y dividir fracciones

En los siguientes ejercicios, realice la operación indicada.

9. $$−\dfrac{3}{4}\left(−\dfrac{4}{9}\right)$$

Contestar

$$\dfrac{1}{3}$$

10. $$−\dfrac{3}{8}⋅\dfrac{4}{15}$$

11. $$\left(−\dfrac{14}{15}\right)\left(\dfrac{9}{20}\right)$$

Contestar

$$−\dfrac{21}{50}$$

12. $$\left(−\dfrac{9}{10}\right)\left(\dfrac{25}{33}\right)$$

13. $$\left(−\dfrac{63}{84}\right)\left(−\dfrac{44}{90}\right)$$

Contestar

$$\dfrac{11}{30}$$

14. $$\left(−\dfrac{33}{60}\right)\left(−\dfrac{40}{88}\right)$$

15. $$\dfrac{3}{7}⋅21n$$

Contestar

$$9n$$

16. $$\dfrac{5}{6}⋅30m$$

17. $$\dfrac{3}{4}÷\dfrac{x}{11}$$

Contestar

$$\dfrac{33}{4x}$$

18. $$\dfrac{2}{5}÷\dfrac{y}{9}$$

19. $$\dfrac{5}{18}÷\left(−\dfrac{15}{24}\right)$$

Contestar

$$−\dfrac{4}{9}$$

20. $$\dfrac{7}{18}÷\left(−\dfrac{14}{27}\right)$$

21. $$\dfrac{8u}{15}÷\dfrac{12v}{25}$$

Contestar

$$\dfrac{10u}{9v}$$

22. $$\dfrac{12r}{25}÷\dfrac{18s}{35}$$

23. $$\dfrac{3}{4}÷(−12)$$

Contestar

$$−\dfrac{1}{16}$$

24. $$−15÷\left(−\dfrac{5}{3}\right)$$

En los siguientes ejercicios, simplifique.

25. $$−\dfrac{\dfrac{8}{21} }{\dfrac{12}{35}}$$

Contestar

$$−\dfrac{10}{9}$$

26. $$− \dfrac{\dfrac{9}{16} }{\dfrac{33}{40}}$$

27. $$−\dfrac{\dfrac{4}{5}}{2}$$

Contestar

$$−\dfrac{2}{5}$$

28. $$\dfrac{\dfrac{5}{3}}{10}$$

29. $$\dfrac{\dfrac{m}{3}}{\dfrac{n}{2}}$$

Contestar

$$\dfrac{2m}{3n}$$

30. $$\dfrac{−\dfrac{3}{8}}{−\dfrac{y}{12}}$$

Sumar y restar fracciones

En los siguientes ejercicios, suma o resta.

31. $$\dfrac{7}{12}+\dfrac{5}{8}$$

Contestar

$$\dfrac{29}{24}$$

32. $$\dfrac{5}{12}+\dfrac{3}{8}$$

33. $$\dfrac{7}{12}−\dfrac{9}{16}$$

Contestar

$$\dfrac{1}{48}$$

34. $$\dfrac{7}{16}−\dfrac{5}{12}$$

35. $$−\dfrac{13}{30}+\dfrac{25}{42}$$

Contestar

$$\dfrac{17}{105}$$

36. $$−\dfrac{23}{30}+\dfrac{5}{48}$$

37. $$−\dfrac{39}{56}−\dfrac{22}{35}$$

Contestar

$$−\dfrac{53}{40}$$

38. $$−\dfrac{33}{49}−\dfrac{18}{35}$$

39. $$−\dfrac{2}{3}−\left(−\dfrac{3}{4}\right)$$

Contestar

$$\dfrac{1}{12}$$

40. $$−\dfrac{3}{4}−\left(−\dfrac{4}{5}\right)$$

41. $$\dfrac{x}{3}+\dfrac{1}{4}$$

Contestar

$$\dfrac{4x+3}{12}$$

42. $$\dfrac{x}{5}−\dfrac{1}{4}$$

43. ⓐ $$\dfrac{2}{3}+\dfrac{1}{6}$$

$$\dfrac{2}{3}÷\dfrac{1}{6}$$

Contestar

$$\dfrac{5}{6}$$$$4$$

44. ⓐ $$−\dfrac{2}{5}−\dfrac{1}{8}$$

$$−\dfrac{2}{5}·\dfrac{1}{8}$$

45. ⓐ $$\dfrac{5n}{6}÷\dfrac{8}{15}$$

$$\dfrac{5n}{6}−\dfrac{8}{15}$$

Contestar

$$\dfrac{25n}{16}$$$$\dfrac{25n−16}{30}$$

46. ⓐ $$\dfrac{3a}{8}÷\dfrac{7}{12}$$

$$\dfrac{3a}{8}−\dfrac{7}{12}$$

47. ⓐ $$−\dfrac{4x}{9}−\dfrac{5}{6}$$

$$−\dfrac{4k}{9}⋅\dfrac{5}{6}$$

Contestar

$$\dfrac{−8x−15}{18}$$$$−\dfrac{10k}{27}$$

48. ⓐ $$−\dfrac{3y}{8}−\dfrac{4}{3}$$

$$−\dfrac{3y}{8}⋅\dfrac{4}{3}$$

49. ⓐ $$−\dfrac{5a}{3}+\left(−\dfrac{10}{6}\right)$$

$$−\dfrac{5a}{3}÷\left(−\dfrac{10}{6}\right)$$

Contestar

$$\dfrac{−5(a+1)}{3}$$$$a$$

50. ⓐ $$\dfrac{2b}{5}+\dfrac{8}{15}$$

$$\dfrac{2b}{5}÷\dfrac{8}{15}$$

Usar el orden de las operaciones para simplificar fracciones

En los siguientes ejercicios, simplifique.

51. $$\dfrac{5⋅6−3⋅4}{4⋅5−2⋅3}$$

Contestar

$$\dfrac{9}{7}$$

52. $$\dfrac{8⋅9−7⋅6}{5⋅6−9⋅2}$$

53. $$\dfrac{5^2−3^2}{3−5}$$

Contestar

$$−8$$

54. $$\dfrac{6^2−4^2}{4−6}$$

55. $$\dfrac{7⋅4−2(8−5)}{9⋅3−3⋅5}$$

Contestar

$$\dfrac{11}{6}$$

56. $$\dfrac{9⋅7−3(12−8)}{8⋅7−6⋅6}$$

57. $$\dfrac{9(8−2)−3(15−7)}{6(7−1)−3(17−9)}$$

Contestar

$$\dfrac{5}{2}$$

58. $$\dfrac{8(9−2)−4(14−9)}{7(8−3)−3(16−9)}$$

59. $$\dfrac{2^3+4^2}{\left(\dfrac{2}{3}\right)^2}$$

Contestar

$$54$$

60. $$\dfrac{3^3−3^2}{\left(\dfrac{3}{4}\right)^2}$$

61. $$\dfrac{\left(\dfrac{3}{5}\right)^2}{\left(\dfrac{3}{7}\right)^2}$$

Contestar

$$\dfrac{49}{25}$$

62. $$\dfrac{\left(\dfrac{3}{4}\right)^2}{\left(\dfrac{5}{8}\right)^2}$$

63. $$\dfrac{2}{\dfrac{1}{3}+\dfrac{1}{5}}$$

Contestar

$$\dfrac{15}{4}$$

64. $$\dfrac{5}{\dfrac{1}{4}+\dfrac{1}{3}}$$

65. $$\dfrac{\dfrac{7}{8}−\dfrac{2}{3}}{\dfrac{1}{2}+\dfrac{3}{8}}$$

Contestar

$$\dfrac{5}{21}$$

66. $$\dfrac{\dfrac{3}{4}−\dfrac{3}{5}}{\dfrac{1}{4}+\dfrac{2}{5}}$$

Práctica Mixta

En los siguientes ejercicios, simplifique.

67. $$−\dfrac{3}{8}÷\left(−\dfrac{3}{10}\right)$$

Contestar

$$\dfrac{5}{4}$$

68. $$−\dfrac{3}{12}÷\left(−\dfrac{5}{9}\right)$$

69. $$−\dfrac{3}{8}+\dfrac{5}{12}$$

Contestar

$$\dfrac{1}{24}$$

70. $$−\dfrac{1}{8}+\dfrac{7}{12}$$

71. $$−\dfrac{7}{15}−\dfrac{y}{4}$$

Contestar

$$\dfrac{−28−15y}{60}$$

72. $$−\dfrac{3}{8}−\dfrac{x}{11}$$

73. $$\dfrac{11}{12a}⋅\dfrac{9a}{16}$$

Contestar

$$\dfrac{33}{64}$$

74. $$\dfrac{10y}{13}⋅\dfrac{8}{15y}$$

75. $$\dfrac{1}{2}+\dfrac{2}{3}⋅\dfrac{5}{12}$$

Contestar

$$\dfrac{7}{9}$$

76. $$\dfrac{1}{3}+\dfrac{2}{5}⋅\dfrac{3}{4}$$

77. $$1−\dfrac{3}{5}÷\dfrac{1}{10}$$

Contestar

$$−5$$

78. $$1−\dfrac{5}{6}÷\dfrac{1}{12}$$

79. $$\dfrac{3}{8}−\dfrac{1}{6}+\dfrac{3}{4}$$

Contestar

$$\dfrac{23}{24}$$

80. $$\dfrac{2}{5}+\dfrac{5}{8}−\dfrac{3}{4}$$

81. $$12\left(\dfrac{9}{20}−\dfrac{4}{15}\right)$$

Contestar

$$\dfrac{11}{5}$$

82. $$8\left(\dfrac{15}{16}−\dfrac{5}{6}\right)$$

83. $$\dfrac{\dfrac{5}{8}+\dfrac{1}{6}}{\dfrac{19}{24}}$$

Contestar

$$1$$

84. $$\dfrac{\dfrac{1}{6}+\dfrac{3}{10}}{\dfrac{14}{30}}$$

​​​​​​​

85. $$\left(\dfrac{5}{9}+\dfrac{1}{6}\right)÷\left(\dfrac{2}{3}−\dfrac{1}{2}\right)$$

Contestar

$$\dfrac{13}{3}$$

86. $$\left(\dfrac{3}{4}+\dfrac{1}{6}\right)÷\left(\dfrac{5}{8}−\dfrac{1}{3}\right)$$

Evaluar expresiones variables con fracciones

En los siguientes ejercicios, evalúe.

87. $$\dfrac{7}{10}−w$$ cuando ⓐ $$w=\dfrac{1}{2}$$$$w=−\dfrac{1}{2}$$

Contestar

$$\dfrac{1}{5}$$$$\dfrac{6}{5}$$

88. $$512−w$$ cuando ⓐ $$w=\dfrac{1}{4}$$$$w=−\dfrac{1}{4}$$

​​​​​​​​​​​​​​

89. $$2x^2y^3$$ cuándo $$x=−\dfrac{2}{3}$$ y $$y=−\dfrac{1}{2}$$

Contestar

$$−\dfrac{1}{9}$$

90. $$8u^2v^3$$ cuándo $$u=−\dfrac{3}{4}$$ y $$v=−\dfrac{1}{2}$$

​​​​​​​​​​​​​​

91. $$\dfrac{a+b}{a−b}$$ cuándo $$a=−3$$ y $$b=8$$

Contestar

$$−\dfrac{5}{11}$$

92. $$\dfrac{r−s}{r+s}$$ cuándo $$r=10$$ y $$s=−5$$

## Ejercicios de escritura

93. ¿Por qué necesitas un denominador común para sumar o restar fracciones? Explicar.

Contestar

Las respuestas variarán.

94. ¿Cómo encuentras el LCD de 2 fracciones?

95. Explica cómo encuentras el recíproco de una fracción.

Contestar

Las respuestas variarán.

96. Explica cómo encuentras el recíproco de un número negativo.

## Autocomprobación

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

ⓑ ¿Qué te dice esta lista de verificación sobre tu dominio de esta sección? ¿Qué pasos tomarás para mejorar?

This page titled 1.4E: Ejercicios 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; a detailed edit history is available upon request.