Lösungen: Kürzen von Brüchen I (Erweitert)

1. Kürze die folgenden Brüche durch die vorgegebenen Zahlen:

a) \( \frac{8}{24}^{\color{blue}{:2}} = \bbox[#e1ffc1,5px]{ \frac{8\color{blue}{:2}}{24\color{blue}{:2}} = \frac{4}{12} } \)

b) \( \frac{9}{27}^{\color{blue}{:3}} = \bbox[#e1ffc1,5px]{ \frac{9\color{blue}{:3}}{27\color{blue}{:3}} = \frac{3}{9} } \)

c) \( \frac{45}{9}^{\color{blue}{:3}} = \bbox[#e1ffc1,5px]{ \frac{45\color{blue}{:3}}{9\color{blue}{:3}} = \frac{15}{3} } \)

d) \( \frac{66}{99}^{\color{blue}{:3}} = \bbox[#e1ffc1,5px]{ \frac{66\color{blue}{:3}}{99\color{blue}{:3}} = \frac{22}{33} } \)

e) \( \frac{77}{154}^{\color{blue}{:7}} = \bbox[#e1ffc1,5px]{ \frac{77\color{blue}{:7}}{154\color{blue}{:7}} = \frac{11}{22} } \)

f) \( \frac{12}{72}^{\color{blue}{:6}} = \bbox[#e1ffc1,5px]{ \frac{12\color{blue}{:6}}{72\color{blue}{:6}} = \frac{2}{12} } \)

g) \( \frac{99}{9999}^{\color{blue}{:9}} = \bbox[#e1ffc1,5px]{ \frac{99\color{blue}{:9}}{9999\color{blue}{:9}} = \frac{11}{1111} } \)

h) \( \frac{90}{9990}^{\color{blue}{:9}} = \bbox[#e1ffc1,5px]{ \frac{90\color{blue}{:9}}{9990\color{blue}{:9}} = \frac{10}{1110} } \)

i) \( \frac{11}{121}^{\color{blue}{:11}} = \bbox[#e1ffc1,5px]{ \frac{11\color{blue}{:11}}{121\color{blue}{:11}} = \frac{1}{11} } \)

j) \( \frac{51}{102}^{\color{blue}{:17}} = \bbox[#e1ffc1,5px]{ \frac{51\color{blue}{:17}}{102\color{blue}{:17}} = \frac{3}{6} } \)

k) \( \frac{500}{1000}^{\color{blue}{:25}} = \bbox[#e1ffc1,5px]{ \frac{500\color{blue}{:25}}{1000\color{blue}{:25}} = \frac{20}{40} } \)

l) \( \frac{120}{4500}^{\color{blue}{:30}} = \bbox[#e1ffc1,5px]{ \frac{120\color{blue}{:30}}{4500\color{blue}{:30}} = \frac{4}{150} } \)

2. Kürze die Brüche gemäß folgender Tabelle, falls sinnvoll möglich:

Kürze mit 2 mit 3 mit 4
\( \frac{8}{24} \) \( \frac{4}{12} \) nicht
kürzbar
\( \frac{2}{6} \)
\( \frac{12}{48} \) \( \frac{6}{24} \) \( \frac{4}{16} \) \( \frac{3}{12} \)
\( \frac{48}{60} \) \( \frac{24}{30} \) \( \frac{16}{20} \) \( \frac{12}{15} \)
\( \frac{36}{80} \) \( \frac{18}{40} \) nicht
kürzbar
\( \frac{9}{20} \)
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