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

Aus RMG-Wiki
Wechseln zu: Navigation, Suche
K
Zeile 17: Zeile 17:
 
'''Man sieht: a + b = b + a'''
 
'''Man sieht: a + b = b + a'''
 
<br /><br />
 
<br /><br />
−
<ggb_applet width="592" height="265"  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="596" height="258"  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 />
+
 
'''Und hier kannst du das Assoziativgesetz besser verstehen. Ziehe die Schieberegler!'''<br />
 
'''Und hier kannst du das Assoziativgesetz besser verstehen. Ziehe die Schieberegler!'''<br />
 
'''Man sieht: (a + b) + c = a + (b + c)'''<br />
 
'''Man sieht: (a + b) + c = a + (b + c)'''<br />
 
::&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;'''(a + b) + c = a + b + c'''
 
::&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;'''(a + b) + c = a + b + c'''
 
<br />
 
<br />
−
<ggb_applet width="662" height="331"  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="660" height="341"  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"/>
  
 
</div>
 
</div>

Version vom 1. Dezember 2011, 16:09 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
 
a. Addiere zu der Differenz aus 450 und 302 die Zahl 169.
=
b. 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
Von „http://rmg.zum.de/index.php?title=P-Seminar/Mathematik_2010-12/II.2._Rechengesetze_und_Rechenvorteile&oldid=44950“