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9.9: Combinaciones de Operaciones con Decimales y Fracciones

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    Objetivos de aprendizaje

    • ser capaz de combinar operaciones con decimales

    Habiendo considerado operaciones con decimales y fracciones, ahora consideramos operaciones que involucran tanto decimales como fracciones.

    Conjunto de Muestras A

    Realizar las siguientes operaciones.

    \(0.38 \cdot \dfrac{1}{4}\). Convierte ambos números a decimales o ambos números a fracciones. Convertiremos a decimales.

    Solución

    \(\begin{array} {r} {.25} \\ {4 \overline{)1.00}} \\ {\underline{\ \ 8\ \ }} \\ {20} \\ {\underline{20}} \\ {0} \end{array}\)

    Para convertir\(\dfrac{1}{4}\) a decimal, divida 1 por 4.

    Ahora multiplicar 0.38 y .25.

    \(\begin{array} {r} {^1\ \ \ } \\ {^4 \ \ \ } \\ {.38} \\ {\underline{\times .25}} \\ {190} \\ {\underline{76\ \ }} \\ {.0950} \end{array}\)

    Así,\(0.38 \cdot \dfrac{1}{4} = 0.095\).

    En los problemas que siguen, las conversiones de fracción a decimal, o decimal a fracción, y algunas de las sumas, restas, multiplicaciones y divisiones se te dejarán a ti.

    Conjunto de Muestras A

    \(1.85 + \dfrac{3}{8} \cdot 4.1\). Convertir\(\dfrac{3}{8}\) a decimal.

    Solución

    \(1.85 + 0.375 \cdot 4.1\)Multiplica antes de sumar.

    \(1.85 + 1.5375\)Ahora agrega.

    3.3875

    Conjunto de Muestras A

    \(\dfrac{5}{13} (\dfrac{4}{5} - 0.28)\)Convierte 0.28 en una fracción.

    Solución

    \(\begin{array} {rcl} {\dfrac{5}{13} (\dfrac{4}{5} - \dfrac{28}{100}} & = & {\dfrac{5}{13} (\dfrac{4}{5} - \dfrac{7}{25})} \\ {} & = & {\dfrac{5}{13} (\dfrac{20}{25} - \dfrac{7}{25})} \\ {} & = & {\dfrac{\begin{array} {c} {^1} \\ {\cancel{5}} \end{array}}{\begin{array} {c} {\cancel{13}} \\ {^1} \end{array}} \cdot \dfrac{\begin{array} {c} {^1} \\ {\cancel{13}} \end{array}}{\begin{array} {c} {\cancel{25}} \\ {^5} \end{array}}} \\ {} & = & {\dfrac{1}{5}} \end{array}\)

    Conjunto de Muestras A

    \(\begin{array} {rcll} {\dfrac{0.125}{1\dfrac{1}{3}} + \dfrac{1}{16} - 0.1211} & = & {\dfrac{\dfrac{125}{1000}}{\dfrac{4}{3}} + \dfrac{1}{16} - 0.1211} & {} \\ {} & = & {\dfrac{\dfrac{1}{8}}{\dfrac{4}{3}} + \dfrac{1}{16} - 0.1211} & {} \\ {} & = & {\dfrac{1}{8} \cdot \dfrac{3}{4} + \dfrac{1}{16} - 0.1211} & {} \\ {} & = & {\dfrac{3}{32} + \dfrac{1}{16} - 0.1211} & {} \\ {} & = & {\dfrac{3}{32} + \dfrac{1}{16} - 0.1211 = \dfrac{5}{32} - 0.1211} & {} \\ {} & = & {0.15625 - 0.1211} & {} \\ {} & = & {0.03515} & {\text{ Convert this to fraction form}} \\ {} & = & {\dfrac{3515}{100,000}} & {} \\ {} & = & {\dfrac{703}{20,000}} & {} \end{array}\)

    Conjunto de práctica A

    Realizar las siguientes operaciones.

    \(\dfrac{3}{5} + 1.6\)

    Contestar

    2.2 o\(2 \dfrac{1}{5}\)

    Conjunto de práctica A

    \(8.91 + \dfrac{1}{5} \cdot 1.6\)

    Contestar

    9.23

    Conjunto de práctica A

    \(1 \dfrac{9}{16} (6.12 + \dfrac{7}{25})\)

    Contestar

    10

    Conjunto de práctica A

    \(\dfrac{0.156}{1 \dfrac{11}{15}} - 0.05\)

    Contestar

    \(\dfrac{1}{25}\)o 0.04

    Ejercicios

    Ejercicio\(\PageIndex{1}\)

    \(\dfrac{3}{10} + 0.7\)

    Contestar

    1

    Ejercicio\(\PageIndex{2}\)

    \(\dfrac{1}{5} + 0.1\)

    Ejercicio\(\PageIndex{3}\)

    \(\dfrac{5}{8} - 0.513\)

    Contestar

    0.112

    Ejercicio\(\PageIndex{4}\)

    \(0.418 - \dfrac{67}{200}\)

    Ejercicio\(\PageIndex{5}\)

    \(0.22 \cdot \dfrac{1}{4}\)

    Contestar

    0.055

    Ejercicio\(\PageIndex{6}\)

    \(\dfrac{3}{5} \cdot 8.4\)

    Ejercicio\(\PageIndex{7}\)

    \(\dfrac{1}{25} \cdot 3.19\)

    Contestar

    0.1276

    Ejercicio\(\PageIndex{8}\)

    \(\dfrac{3}{20} \div 0.05\)

    Ejercicio\(\PageIndex{9}\)

    \(\dfrac{7}{40} \div 0.25\)

    Contestar

    0.7

    Ejercicio\(\PageIndex{10}\)

    \(1 \dfrac{1}{15} \div 0.9 \cdot 0.12\)

    Ejercicio\(\PageIndex{11}\)

    \(9.26 + \dfrac{1}{4} \cdot 0.81\)

    Contestar

    9.4625

    Ejercicio\(\PageIndex{12}\)

    \(0.588 + \dfrac{1}{40} \cdot 0.24\)

    Ejercicio\(\PageIndex{13}\)

    \(\dfrac{1}{20} + 3.62 \cdot \dfrac{3}{8}\)

    Contestar

    1.4075

    Ejercicio\(\PageIndex{14}\)

    \(7 + 0.15 \div \dfrac{3}{30}\)

    Ejercicio\(\PageIndex{15}\)

    \(\dfrac{15}{16} \cdot (\dfrac{7}{10} - 0.5)\)

    Contestar

    0.1875

    Ejercicio\(\PageIndex{16}\)

    \(0.2 \cdot (\dfrac{7}{20} + 1.1143)\)

    Ejercicio\(\PageIndex{17}\)

    \(\dfrac{3}{4} \cdot (0.875 + \dfrac{1}{8})\)

    Contestar

    0.75

    Ejercicio\(\PageIndex{18}\)

    \(5.198 - 0.26 \cdot (\dfrac{14}{250} + 0.119)\)

    Ejercicio\(\PageIndex{19}\)

    \(0.5 \dfrac{1}{4} + (0.3)^2\)

    Contestar

    0.615

    Ejercicio\(\PageIndex{20}\)

    \((1.4)^2 - 1.6 \dfrac{1}{2}\)

    Ejercicio\(\PageIndex{21}\)

    \((\dfrac{3}{8})^2 - 0.000625 + (1.1)^2\)

    Contestar

    1.35

    Ejercicio\(\PageIndex{22}\)

    \((0.6)^2 \cdot (\dfrac{1}{20} - \dfrac{1}{25})\)

    Ejercicio\(\PageIndex{23}\)

    \((\dfrac{1}{2})^2 - 0.125\)

    Contestar

    0.125

    Ejercicio\(\PageIndex{24}\)

    \(\dfrac{0.75}{4 \dfrac{1}{2}} + \dfrac{5}{12}\)

    Ejercicio\(\PageIndex{25}\)

    \((\dfrac{0.375}{2 \dfrac{1}{16}} - \dfrac{1}{33})\)

    Contestar

    \(0.\overline{15}\)

    Ejercicio\(\PageIndex{26}\)

    \(8 \dfrac{1}{3} \cdot (\dfrac{1 \dfrac{1}{4}}{2.25} + \dfrac{9}{25})\)

    Ejercicio\(\PageIndex{27}\)

    \(\dfrac{\dfrac{0.32}{\dfrac{12}{35}}}{0.35}\)

    Contestar

    \(2.\overline{6}\)

    Ejercicio\(\PageIndex{28}\)

    \(\dfrac{(\sqrt{\dfrac{49}{64}} - 5)0.125}{1.375}\)

    Ejercicios para la revisión

    Ejercicio\(\PageIndex{29}\)

    ¿Es 21.480 divisible por 3?

    Contestar

    si

    Ejercicio\(\PageIndex{30}\)

    Ampliar\(14^4\). No encuentre el valor real.

    Ejercicio\(\PageIndex{31}\)

    Encuentra la factorización prima de 15.400.

    Contestar

    \(2^3 \cdot 5^2 \cdot 7 \cdot 11\)

    Ejercicio\(\PageIndex{32}\)

    Convierte 8.016 en una fracción.

    Ejercicio\(\PageIndex{33}\)

    Encuentra el cociente.

    Contestar

    \(0.\overline{592}\)

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