3.1. La balanza del viaje

Glosario

Operar

Pictograma de Arasaac: clase de matemáticas

Definición:: Realizar cálculos a través operaciones matemáticas.
Ejemplo:: Obtuvo el resultado operando con números enteros.

¡Así funcionan!

Balanza Para empezar a conseguir dinero para tu viaje utilizas tus ahorros.

Con 50 € compras dulces, es decir, es dinero que sale:

Gasto: −50 € (negativo)

Luego, vendes todos los dulces y consigues 80 €, entonces, este dinero entra:

Ingreso: +80 € (positivo)

Número entero

El conjunto de los números enteros está formado por los números naturales (incluido el 0), y sus opuestos (con valor negativo).

Positivos (+)

Representan el dinero que entra o los ingresos.
Indican que tu dinero está aumentando (ganancia).
Ejemplo: si vendes un dulce por 2 €, registras +2 o 2.
Los números positivos pueden llevar o no el signo +.

Negativos (-)

Representan el dinero que sale o los gastos.
Indican que tu dinero está disminuyendo (perdida).
Ejemplo: si compras una caja de dulces por 15 €, registras –15.

El cero (0)

Representa la ausencia de dinero.
Indica que, en ese momento, los ingresos y gastos son iguales: no has perdido ni ganado dinero.

Mas ejemplos...

Pictograma de Arasaac: negativo Hasta ahora, has usado siempre los números naturales, los cuales son siempre números positivos.

Pero... ¿Para qué sirven los números negativos?

En realidad, en la vida diaria es muy habitual encontrar números negativos.

¿Has cogido alguna vez un ascensor que bajase al piso -2?
¿Sabías que el congelador de tu cocina suele estar a -18º C?
¿Escuchaste alguna vez que una cuenta bancaria está en números rojos?

Seguro que sí.

Así que no te parecerá extraño escuchar frases como:

Hace una temperatura de 3 grados bajo cero (-3 ºC).
La profesora vive en un cuarto piso (+4).
Cabeza de Manzaneda está a 1.781 metros sobre el nivel del mar (+1.781 m)
El buzo se encuentra a diez metros de profundidad (-10 m).

Porque recuerda, los números enteros son los positivos, los negativos y el cero.

Recta numérica

Para comprenderlo mejor, observa la siguiente recta numérica:

Si te fijas:

El número 0 se coloca en el centro
Todos los números positivos se sitúan a la derecha del 0
Todos los números negativos se sitúan a la izquierda del 0

¡Ahora ya estáis preparadas y preparados para empezar a utilizar los números enteros!

Por último, y como curiosidad, quizás quieras saber que en matemáticas para nombrar al conjunto de todos los números enteros se utiliza la letra Z, del siguiente modo:

Z = {..., -3, -2, -1, 0, +1, +2, +3,...}

Registra las cuentas del viaje

Lee cada situación y escribe el número entero que representa.

Recuerda: los números positivos, generalmente, no llevan el signo y los números negativos tienen el signo "-" delante.

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Situación	Número entero
Comprasteis caramelos por 60 € para vender.	@@-60@@
Un grupo vendió dulces y consiguió 25 €.	@@25@@
Tuvisteis que comprar globos por 10 € más.	@@-10@@
En el recreo más concurrido, se consiguieron 42 €.	@@42@@
Una vendedora os devuelve 5 € que habíais pagado de más.	@@5@@
Pagáis 3 € por el material para hacer un cartel de publicidad.	@@-3@@
Recaudáis 18 € en la última venta.	@@18@@

Su navegador no es compatible con esta herramienta.

Del gasto a la ganancia

Ordena las siguientes cantidades de dinero de menor a mayor.

-8 €
-5 €
-2 €
-1 €
0 €
+3 €
+6 €
+9 €
+10 €
+12 €

Practica en la recta numérica

Indica el valor de los siguientes números enteros:

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Recta numérica con valores marcados mediante letras

A: @@-7@@	B: @@-5@@	C: @@-1@@
D: @@2@@	E: @@4@@	F: @@8@@

Ahora, dibuja una recta numérica y sitúa en ella los siguientes números enteros:

(-4), (+1), (-2), (-6), (+7) y (+3)

Su navegador no es compatible con esta herramienta.

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