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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?


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