viernes, marzo 17, 2006

GUIA DE MATEMATICAS, Multiplicación de Fracciones

  • Lee la siguiente información y luego trabaja en la guia que se ha entregado.

Multipliquemos:

Ya vimos la adición y sustracción con fracciones. En tercer lugar revisaremos la multiplicación.
En esta operación, lo primero convieneque hacer es simplificar las fracciones todo lo que se pueda, en forma vertical o cruzada. Luego, se multiplican los numeradores y los denominadores obteniéndose el producto.Este será siempre una fracción irreductible, debido a que ya simplificamos.

Si algún factor es número mixto o entero, lo reducimos a fracción impropia y luego multiplicamos:
simplificamos y reducimos a número mixto.

Propiedades

Tal como la multiplicación con números cardinales, la multiplicación de fracciones también tiene las siguientes propiedades:

Tiene clausura.
Es conmutativa.
Es asociativa.
Tiene como elemento neutro a cualquier fracción equivalente al entero 1, y como elemento absorbente a toda fracción igual al entero 0.

Es distributiva con respecto a la adición de fracciones.A diferencia de la multiplicación de números cardinales, en la de fracciones aparece una nueva propiedad: El elemento inverso o inverso multiplicativo: consiste en multiplicar una fracción por otra, de manera que se obtenga el elemento neutro, que es el entero 1.Por ejemplo, el inverso multiplicativo de:

9/5 = 5/9 resultado será 1

Aplicaciones
El trabajo con fracciones es muy importante para la vida diaria. En este contexto podemos distinguir dos aplicaciones muy importantes de la multiplicación de fracciones.

a)La multiplicación de fracciones nos permite el cálculo de la fracción de un número o de la fracción de otra fracción. Para eso sólo tenemos que multiplicar los datos.
Estudiemos dos casos:
1) si calculamos los 5/8 de 24 personas, multiplicamos 5 x 24 y el resultado se divide por 24

5 x 24 = 120 120 : 8 = 15

Resultado: 15 personas.


2) si queremos calcular los 7/10 de 20/21 simplificamos por 7

7 : 7 = 1 y 21 : 7 = 3 10 : 10 = 1 y 20 : 10 = 2 luego se multiplica 1/1 x 2/3 = 2/3

Resultado 2/3


b) La multiplicación de fracciones nos permite calcular porcentajes.
Los porcentajes son fracciones con denominador 100. Entonces, si- por ejemplo- decimos que el 60 % (por ciento) de los alumnos tiene hermanos chicos, significa que cada 100 alumnos, 60 cumplen con estacondición.Escrito como fracción esto quedaría: 60/100
En la situación de -como segundo ejemplo- tener que calcular el 30 % de los 600 empleados de una fábrica, bastará con aplicar la multiplicación de:

30 x 600 y el resultado se divide por 100

30 x 600 = 18000 18000 : 100 = 180

Resultado 180 empleados.

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