3.6. Dividiendo los puestos

A vueltas con la división

Los puestos del mercado

Puesto de mercado vacío

En el ayuntamiento van a organizar un mercado y han reservado \( \dfrac{3}{4}\) de un gran terreno para montar los puestos.

Si cada puesto ocupa \( \dfrac{1}{8}\) del terreno total, ¿cuántos puestos se pueden colocar en ese espacio?

Para averiguarlo, necesitas repartir el espacio disponible entre lo que ocupa cada puesto, es decir, calcular cuántas veces cabe \( \dfrac{1}{8}\) dentro de \( \dfrac{3}{4}\).

Solución paso a paso

Para saber cuántos puestos caben, debes hacer la división: \( \dfrac{3}{4} : \dfrac{1}{8}\).

Para resolverlo sigue estos pasos:

Dejas la primera fracción como está: \( \dfrac{3}{4}\).
Le das la vuelta a la segunda fracción: la fracción \( \dfrac{1}{8}\) se convierte en \( \dfrac{8}{1}\).
Cambias la división por una multiplicación: multiplicas en línea recta numerador por numerador y denominador por denominador: \( \dfrac{3}{4} \times \dfrac{8}{1} = \dfrac{24}{4}\).
Calculas el resultado final: divides el numerador entre el denominador: \(\dfrac{24}{4} = 6\).

¡En el mercado se pueden instalar 6 puestos en total!

¿Cómo se dividen las fracciones?

Dividir fracciones es como hacer una multiplicación "dando la vuelta" a la segunda fracción.

Para dividir dos fracciones cualesquiera, solo tienes que seguir esta regla básica:

Escribes la fracción inversa de la segunda fracción (intercambias la posición del número de arriba y el de abajo).
Multiplicas la primera fracción por esa nueva fracción inversa.

\(\large\displaystyle \dfrac{2}{3} : \dfrac{5}{7}=\dfrac{2}{3} \times \dfrac{7}{5}=\dfrac{14}{15}\)

Apoyo visual

Paso 1: Planteamiento

\(\dfrac{3}{4} : \dfrac{5}{7}\)

Paso 2: Invertir

\(\dfrac{5}{7} \rightarrow \mathbf{\dfrac{7}{5}}\)

Paso 3: Multiplicar

\(\dfrac{3 \times 7}{4 \times 5}\)

Paso 4: Resultado

\(\mathbf{\dfrac{21}{20}}\)

¿Cuál es la correcta?

Selecciona la respuesta correcta.

undefined

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Su navegador no es compatible con esta herramienta.

Preparando la ropa

Tienda de ropa

Marisa tiene un puesto en el mercado en el que vende ropa. Su puesto está dividido en 4 zonas iguales:

Escaparate de una tienda de ropa con diferentes prendas

En la primera vende camisas de manga larga.
En la segunda zona vende camisas de manga corta.
En la tercera zona vende pantalones de chándal.
Y en la cuarta zona vende zapatillas deportivas.

¿Qué fracción representa cada una de las zonas del puesto de Marisa?
Marisa quiere redistribuir la tienda y dividir la zona de camisas en 4 zonas diferentes según sus colores y no según el largo de sus mangas. ¿Qué fracción representaría cada una de estas nuevas zonas?
Explícalo y comparte la explicación con el grupo clase.

Zapatería

En la zapatería de Juan se venden cinco tipos de zapatos, clasificados por el número de pie: talla 38, 39, 40, 41 y 42.

Cada tipo de zapato representa una fracción de un quinto del espacio de su estantería.

Juan decide ampliar su colección de calzado, añadiendo siete nuevas tallas: 43, 44, 45, 46, 47, 48 y 49.

Las secciones de cada talla van a tener la misma dimensión.

¿Qué fracción de la estantería representa ahora cada una de las nuevas tallas incorporadas?
¿Qué fracción representa la suma de todas ellas?

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