6.9: Combinaciones de Operaciones con Decimales y Fracciones
- Page ID
- 116434
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)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
-
\(0.\overline{592}\)