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3.5. La devolución

La resta como suma del opuesto

Persona vendiendo productosNecesitas comprar material para el puesto de venta. 

Tienes 30 € para gastar, pero sólo gastas 20 €, (-20 €), entonces te quedan en tu cuenta 10 €. 

Luego, decides anular ese gasto devolviendo el material, porque no lo necesitas. 

Por tanto, restas ese gasto de tu cuenta. 

  • Gasto inicial: -20 €.
  • Devolución: 10 € - (-20 €).

La resta de un número negativo es igual a sumar su opuesto: 

10 € - (-20 €) = 10 € + (+20 €) = 10 € + 20 € = 30 €.

Una resta transformada en suma

Situación inicial Resta Suma del opuesto Explicación
Vendí un dulce por 10 € y gasto 40 € 10 - 40  10 + (-40) = -(40 - 10) = -30 € Tienen diferente signo, entonces restas los números y pones el signo del mayor valor absoluto.
Gasté 20 € y gastó 5 € -20 - 5 -20 + (-5) = -(20 + 5) = -25 € Tienen el mismo signo, entonces se suman y se deja el mismo signo.
Gasté 7 € pero me devuelven 3 € por una oferta -7 - (-3) -7 + 3 = -(7 - 3) = -4 Tienen diferente signo, entonces restas los números y pones el signo del mayor valor absoluto.
Tengo 10 € y me devuelven 4 € que me cobraron de más 10 - (-4) 10 + 4 = 14 Suma de números naturales.

Regla práctica

En los números enteros, la resta se puede convertir en una suma si utilizas el número opuesto.

Esto consigue que sólo tengas que aplicar las reglas de la suma de enteros (signos iguales se suman, signos diferentes se restan).

La equivalencia es:

Restar un número es lo mismo que sumar su opuesto

Cada vez que encuentres el signo de resta (−) inmediatamente después de otro número, cambia la operación a una suma (+) y el signo del número siguiente a su opuesto.

(Número 1) − (Número 2) → (Número 1) + (Opuesto de número 2)

Practica la resta de enteros

https://www.geogebra.org/m/xcexbbzz (Ventana nueva)

Proxecto%20cREAgal,https%3A//www.geogebra.org/m/xcexbbzz,Practica%20la%20resta%20de%20enteros,0,Autor%EDa
Actividad%20no%20completada,Actividad%20superada.%20Puntuaci%F3n%3A%20%25s,Actividad%20no%20superada.%20Puntuaci%F3n%3A%20%25s,Guardar%20la%20puntuaci%F3n

Autoría: Rafael Losada Liste

¿Cuál es la correcta?

Escoge las respuestas correctas y presiona el botón "Comprobar".

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Resuelve el desafío

Para abrir un candado se necesita un código.

1

Candado con asteriscos en el medio

Este código numérico es el valor absoluto de la suma de los resultados de los siguientes cuatro problemas. 

¿Serás capaz de realizarlos correctamente?

SubmarinoUn submarino viaja a 36 metros bajo el nivel del mar.

Para no ser localizado, decide descender 12 metros más, y posteriormente asciende 5 metros.

¿En que posición se encuentra ahora mismo?

Monedas de euros y céntimos.A principios de mes teníamos en la cuenta bancaria 1.316 €.

Durante el mes nos han cobrado la factura de la luz (43 €), internet (52 €), la hipoteca (512 €) y nos han pagado 298 € por un trabajo realizado.

¿Cuánto dinero tenemos ahora?

AscensorAmalia vive en el 4ºA.

Entra en el ascensor y toquetea todos los números.

La puerta se cierra y empieza su viaje.

Sube 2 pisos, baja 7 pisos, sube 3 pisos y baja 4 pisos.

¿En qué planta se encuentra?

GaviotaUna gaviota vuela a 18 metros sobre el nivel del mar.

Visualiza un banco de peces y decide descender 12 metros, para posteriormente volver a descender 8 metros para alcanzar su comida.

¿A qué profundidad se encuentran los peces?

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Su navegador no es compatible con esta herramienta.

Creado con eXeLearning (Ventana nueva)