II.2. Rechengesetze und Rechenvorteile: Unterschied zwischen den Versionen

Aus RMG-Wiki
Wechseln zu: Navigation, Suche
Zeile 11: Zeile 11:
  
 
<br />
 
<br />
<ggb_applet width="502" height="512"  version="3.2" ggbBase64="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" framePossible = "false" showResetIcon = "false" showAnimationButton = "true" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" allowRescaling = "true" useLocalJar = "true" />
+
<ggb_applet width="497" height="505"  version="3.2" ggbBase64="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" framePossible = "false" showResetIcon = "false" showAnimationButton = "true" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" allowRescaling = "true" useLocalJar = "true" />
 
<br />
 
<br />
 
<br />
 
<br />

Version vom 6. Oktober 2011, 15:09 Uhr

 

II. Addition und Subtraktion natürlicher Zahlen:

1. Addieren und Subtrahieren - 2. Rechengesetze und Rechenvorteile - 3. Terme


Erklärung





Zum besseren Verständnis kannst du auch noch einmal selbst das Kommutativgesetz erproben. Ziehe die Schieberegler!
Man sieht: a + b = b + a



Und hier kannst du das Assoziativgesetz besser verstehen. Ziehe die Schieberegler!
Man sieht: (a + b) + c = a + (b + c)

     (a + b) + c = a + b + c



  Aufgaben

  AUFGABEN:

1. Forme den Text in eine Rechnung um, rechne es dann aus und gib das Ergebnis ein.

Beispiel
Die Summe der Zahlen 228 und 454 wird addiert zur Zahl 368
(228+454)+368=1050
Addiere zu der Differenz aus 450 und 302 die Zahl 169.
=
Addiere die Summe der Zahlen 155 und 71 zur Zahl 24.
=

2. Achte auf die richtige Reihenfolge!

(13 + 17) + 25 =
+ =
45 + (27 - 8) =
+ =
32 - (13 + 8) =
- =
68 - (36 - 22) =
- =
82 - (15 + 34) =
- =

Punkte: 0 / 0



II. Addition und Subtraktion natürlicher Zahlen:

1. Addieren und Subtrahieren - 2. Rechengesetze und Rechenvorteile - 3. Terme