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3.5. Súmate la diversión

Súmate a la fiesta

En vuestra fiesta no pueden faltar los zumos de frutas pero, revisa los cortes, si no son iguales no los podrás sumar.

Partes iguales

Estas rodajas son cortes iguales, del mismo tamaño, se pueden sumar.

Rodaja de limón Rodaja de naranja

Para sumar  fracciones también es necesario que los denominadores sean iguales.

Luego sumas los numeradores, ¡ya está!

Ejemplo: \(\dfrac{1}{8}+\dfrac{2}{8}= \dfrac{3}{8}\)

¿A que es fácil?

Partes distintas

Ahora has cortado trozos diferentes. ¡Uhm...! ¡No los puedes sumar!

Gajo de naranjaMedio limónEntonces debes hacer fracciones equivalentes a cada una de ellas, buscando, además, que tengan el mismo denominador, como en el apartado 3.2.

Tendrás que multiplicar cada fracción por un número. 

¿Cómo saber cuál es el número?

Sigue leyendo...

Inspírate bajo el árbol

La solución está en la factorización, ¿recuerdas el árbol de factores? Úsalo.

NaranjoLimoneroBuscar un denominador común es parecido a buscar un factor común.

  1. Puedes lograrlo multiplicando los denominadores entre sí.
  2. También puedes hallar el m.c.m. de los denominadores.

Recuerda que para eso, debes factorizarlos.

Ejemplo 1

Por ejemplo: \(\dfrac{1}{4} + \dfrac{5}{6} = ?\) El denominador común es 4 x 6 = 24.

Para conseguirlo, multiplica el numerador y denominador de la primera fracción por 6 y el de la segunda por 4.

\(\dfrac{1 \times 6}{4 \times 6}+\dfrac{5 \times 4}{6 \times 4}\) = \(\dfrac{6}{24} + \dfrac{20}{24}\)

Y ya se pueden sumar; \(\dfrac{6}{24} + \dfrac{20}{24} = \dfrac{6 + 20}{24}=\dfrac{26}{24}=\dfrac{13}{12}\)

Ejemplo 2

Si prefieres utilizar el m.c.m. (4, 6) = 12

Observa que si pones un 12 en el denominador, habrás multiplicado por 3, en la primera fracción, y por 2 en la segunda.

\(\dfrac{1 \times 3}{4 \times 3}+\dfrac{5 \times 2}{6 \times 2}\) = \(\dfrac{3}{12} + \dfrac{10}{12}\)

Y ya se pueden sumar; \(\dfrac{3}{12} + \dfrac{10}{12} = \dfrac{3 + 10}{12}=\dfrac{13}{12}\)

Suma y resta para la fiesta

Haz las siguientes sumas. escribe el resultado en la forma a/b, y utiliza el mcm para reducir a común denominador.

\(\dfrac{2}{5}+\dfrac{1}{8}\) =  \(\dfrac{9}{4}-\dfrac{1}{8}\) = 
\(\dfrac{3}{10}+\dfrac{2}{7}\) =  \(\dfrac{5}{6}-\dfrac{1}{12}\) = 
\(\dfrac{7}{4}+\dfrac{1}{10}\) =   \(\dfrac{2}{5}-\dfrac{1}{8}\) = 
\(\dfrac{10}{6}+\dfrac{3}{2}\) =   \(\dfrac{7}{4}-\dfrac{1}{10}\) = 
\(\dfrac{9}{4}+\dfrac{1}{8}\) =   \(\dfrac{3}{10}-\dfrac{2}{7}\) =
\(\dfrac{1}{12}+\dfrac{5}{6}\) =   \(\dfrac{10}{6}-\dfrac{3}{2}\) =

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01234
Su navegador no es compatible con esta herramienta.

Identifica y suma trozos de tartas para tu fiesta

Suma la fracción de la izquierda con la de la derecha y escribe debajo su valor en forma a/b.

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Suma estas fracciones e indica debajo su expresión en la forma a/b
Fracción Fracción Suma
Fracción 1 Fracción 7 (cREAgal) Pon el resultado simplificado
@@1/8@@ @@2/10@@ @@13/40@@
Fracción 2 (cREAgal) Fracción 5 (cREAgal) Pon el resultado simplificado
@@7/8@@ @@2/3@@ @@37/24@@
Fracción 3 (cREAgal) Fracción 8 (cREAgal) Pon el resultado simplificado
@@5/9@@ @@5/10@@ @@19/18@@
Fracción 4 (cREAgal) Fracción 4 (cREAgal) Pon el resultado simplificado
@@3/9@@ @@1/3@@ @@2/3@@

¡Anímate a hacer una tarta como estas!

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Creado con eXeLearning (Ventana nueva)