Mathematrix: Aufgabenbeispiele/ Bruchstrichrechnungen mit Primfaktorzerlegung

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

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

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

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

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

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

Kompakt:

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