Macedonia de fracciones

El desafío de la sandía

Sandía entera y un trozo En este mes has comprado dos veces sandía, pero los trozos eran diferentes.

Hace dos semanas, la sandía estaba cortada en 4 trozos. Has cogido un trozo, que es \(\frac{1}{4}\) de la sandía.
Ayer estaba cortada en 2 trozos. Has cogido un trozo, que es \(\frac{1}{2}\) de la sandía.

Si quieres saber los trozos que tomaste este mes, ¿Cuánta sandía compraste en total?

Problema

¡Los trozos son de tamaños distintos!

No puedes sumar \(\frac{1}{4}\) y \(\frac{1}{2}\) directamente.

Primero, tienes que convertir los trozos a un tamaño común.

Solución

¡Fracciones equivalentes!

Recuerda las fracciones equivalentes: son fracciones que parecen diferentes, pero que representan la misma cantidad.

Piensa en la mitad de la sandía \(\frac{1}{2}\). Si la cortas otra vez a la mitad, tendrías 2 trozos. Esos dos trozos son \(\frac{2}{4}\) de sandía.

Una porción es \(\frac{1}{4}\).
La otra porción es \(\frac{2}{4}\).

Ahora ya puedes sumarlos: \(\large \displaystyle\frac{1}{4}+\frac{2}{4}=\frac{1+2}{4}=\frac{3}{4}\)

Entonces, este mes has comprado \(\frac{3}{4}\) de sandía.

Frutas y verduras

Contesta a las preguntas utilizando fracciones equivalentes y realizando las operaciones.

undefined

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E2%F7%D5%F3%FF%F7%B0%A8%B0%C1%F7%FE%F7%F1%F1%FB%FD%FC%F3%B0%EF%EF

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Problemas de tienda

Frutería

Escaparate de frutería con diferentes frutas en el expositor En la frutería tiene en una estantería diferentes tipos de frutas gallegas repartidas en cajas:

\(\frac{1}{4}\) de las cajas son naranjas.
\(\frac{3}{8}\) de las cajas son kiwis.
\(\frac{1}{8}\) de las cajas son manzanas.

Si el resto son mirabeles, ¿Qué fracción será la de esta fruta?

Panadería

En el puesto de la panadería solo quedaban las siguientes fracciones de pan:

\(\frac{1}{2}\) de una barra de trigo.
\(\frac{1}{4}\) de una barra de maíz.
\(\frac{1}{8}\) de una barra de centeno.

Si sumas todas las fracciones. ¿Qué cantidad obtienes?

Pastelería

En la pastelería del mercado han recibido 30 tartas en total:

Escaparate de una pastelería

\(\frac{2}{5}\) tartas de melocotón.
\(\frac{1}{5}\) tartas de coco.
\(\frac{4}{15}\) tartas de queso.
El resto son tartas de zanahoria.

¿Qué parte son tartas de zanahoria?

Trabajo en equipo: Elige y selecciona fracciones

Elegid y seleccionad

Para que vuestras fracciones se puedan sumar, todas deben tener el mismo denominador. Probad con distintos denominadores, eso os ayudará a hacer la mejor elección.
Debéis elegir, al menos, cinco fracciones que tengan como denominador el número seleccionado, y que al sumarlas den el número entero 1.
Las fracciones que elijáis deben seguir estas reglas:

Una fracción muy grande para el título.
Una fracción muy pequeña para la lista de asistentes.
Fracciones de tamaño intermedio para el resto de la información.

Verificad

Cuando hayáis elegido las fracciones, sumad las fracciones.

El resultado debe ser 1.

Por ejemplo, si escogéis \(\frac{3}{8}, \frac{2}{8}, \frac{1}{8}, \frac{1}{8}, \frac{1}{8}\), la suma es 1.

Anotad

Anotad las fracciones que habéis elegido y por qué.

Es una información imprescindible.

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