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# Mathematrix: Aufgabenbeispiele/ Bruchstrichrechnungen mit Primfaktorzerlegung

${\displaystyle {\frac {41}{120}}-3{\frac {11}{36}}+2{\frac {237}{300}}}$

Hier macht man zuerst die PFZ der Nenner:

 120 2 60 2 30 2 15 3 5 5 1
 36 2 18 2 9 3 3 3 1
 300 2 150 2 75 3 25 5 5 5 1
 120 = 2·2·2·3·5 36 = 2·2·3·3 300 = 2·2·3·5·5 kgV=2·2·2·3·3·5·5=1800

${\displaystyle {\frac {41}{120}}-3{\frac {11}{36}}+2{\frac {237}{300}}={\frac {41}{120}}-{\frac {\cancelto {119}{\ 3\cdot 36+11\ }}{36}}+{\frac {\cancelto {837}{\ 2\cdot 300+237\ }}{300}}=\dots }$

${\displaystyle \dots ={\overset {\underline {1800:120=15}}{\frac {\breve {41}}{120}}}-{\overset {\underline {1800:36=50}}{\frac {\breve {119}}{36}}}+{\overset {\underline {1800:300=6}}{\frac {\breve {837}}{300}}}={\overset {15}{\frac {\breve {41}}{120}}}-{\overset {50}{\frac {\breve {119}}{36}}}+{\overset {6}{\frac {\breve {837}}{300}}}=\dots }$

${\displaystyle \dots ={\frac {41\cdot 15}{120\cdot 15}}-{\frac {119\cdot 50}{36\cdot 50}}+{\frac {837\cdot 6}{300\cdot 6}}={\frac {615}{1800}}-{\frac {5950}{1800}}+{\frac {5022}{1800}}=\dots }$

${\displaystyle \dots ={\frac {615-5950+5022}{1800}}=-{\frac {313}{1800}}}$

Kompakt:

${\displaystyle {\frac {41}{120}}-3{\frac {11}{36}}+2{\frac {237}{300}}={\overset {15}{\frac {\breve {41}}{120}}}-{\overset {50}{\frac {\breve {119}}{36}}}+{\overset {6}{\frac {\breve {837}}{300}}}={\frac {615-5950+5022}{1800}}=-{\frac {313}{1800}}}$