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((8 1/7+6 1/8)+7 1/9)+6 1/2+7/8+(3 5/8-5/9)

 27.06.2015

Beste Antwort 

 #4
avatar+14537 
+3

Und so dürfte es am einfachsten gehen:

$${\mathtt{8}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{7}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{8}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{7}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{9}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{7}}}{{\mathtt{8}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{5}}}{{\mathtt{8}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{5}}}{{\mathtt{9}}}}$$  =

$${\mathtt{30}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{7}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{13}}}{{\mathtt{8}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{4}}}{{\mathtt{9}}}}$$           (  $${\frac{{\mathtt{1}}}{{\mathtt{2}}}} = {\frac{{\mathtt{4}}}{{\mathtt{8}}}}$$     ;   $${\frac{{\mathtt{13}}}{{\mathtt{8}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{4}}}{{\mathtt{8}}}} = {\frac{{\mathtt{17}}}{{\mathtt{8}}}}$$ )

 

$${\mathtt{30}}{\mathtt{\,\small\textbf+\,}}{\frac{\left({\mathtt{72}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1\,071}}{\mathtt{\,-\,}}{\mathtt{224}}\right)}{{\mathtt{504}}}}$$    =  

 

$${\mathtt{30}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{919}}}{{\mathtt{504}}}} = {\mathtt{31.823\: \!412\: \!698\: \!412\: \!698\: \!4}}$$

 

$$31\frac{415}{504}$$

 

Gruß radix !

 28.06.2015
 #1
avatar+14537 
+3

$${\mathtt{8}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{7}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{8}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{7}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{9}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{7}}}{{\mathtt{8}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{5}}}{{\mathtt{8}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{5}}}{{\mathtt{9}}}} = {\mathtt{31.823\: \!412\: \!698\: \!412\: \!698\: \!4}}$$

 

$${\frac{{\mathtt{1}}}{{\mathtt{7}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{8}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{9}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{7}}}{{\mathtt{8}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{5}}}{{\mathtt{8}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{5}}}{{\mathtt{9}}}}$$          Hauptnenner = 504  

 

  =>   $${\frac{{\mathtt{919}}}{{\mathtt{504}}}} = {\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{415}}}{{\mathtt{504}}}}$$

 

$${\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{415}}}{{\mathtt{504}}}} = {\frac{{\mathtt{919}}}{{\mathtt{504}}}} = {\mathtt{1.823\: \!412\: \!698\: \!412\: \!698\: \!4}}$$

 

$${\mathtt{8}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}{\mathtt{\,\small\textbf+\,}}{\mathtt{7}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}} = {\mathtt{30}}$$              ; 

 

  $${\mathtt{30}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{415}}}{{\mathtt{504}}}} = {\mathtt{31.823\: \!412\: \!698\: \!412\: \!698\: \!4}}$$   

 

   Ergebnis:     $$31\frac{415}{504}$$

 

Gruß radix !

 27.06.2015
 #2
avatar+14537 
+3

Das geht mit dem Hauptnenner  (7  * 8 * 9 = 504 ) relativ einfach :


Siehe unten! 


Gruß radix !

 27.06.2015
 #3
avatar+14537 
+3

Berechnen der Brüche:


Gruß radix !

 27.06.2015
 #4
avatar+14537 
+3
Beste Antwort

Und so dürfte es am einfachsten gehen:

$${\mathtt{8}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{7}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{8}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{7}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{9}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{7}}}{{\mathtt{8}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{5}}}{{\mathtt{8}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{5}}}{{\mathtt{9}}}}$$  =

$${\mathtt{30}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{7}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{13}}}{{\mathtt{8}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{4}}}{{\mathtt{9}}}}$$           (  $${\frac{{\mathtt{1}}}{{\mathtt{2}}}} = {\frac{{\mathtt{4}}}{{\mathtt{8}}}}$$     ;   $${\frac{{\mathtt{13}}}{{\mathtt{8}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{4}}}{{\mathtt{8}}}} = {\frac{{\mathtt{17}}}{{\mathtt{8}}}}$$ )

 

$${\mathtt{30}}{\mathtt{\,\small\textbf+\,}}{\frac{\left({\mathtt{72}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1\,071}}{\mathtt{\,-\,}}{\mathtt{224}}\right)}{{\mathtt{504}}}}$$    =  

 

$${\mathtt{30}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{919}}}{{\mathtt{504}}}} = {\mathtt{31.823\: \!412\: \!698\: \!412\: \!698\: \!4}}$$

 

$$31\frac{415}{504}$$

 

Gruß radix !

radix 28.06.2015

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