AB: Lektion Brüche (Teil 6)
Dividiere die folgenden Brüche miteinander:
\( \frac{1}{2} : \frac{1}{3} = \) \( \frac{1}{2} · \frac{3}{1} = \frac{1·3}{2·1} = \frac{3}{2} \)
\( \frac{4}{7} : \frac{11}{2} = \) \( \frac{4}{7} · \frac{2}{11} = \frac{4·2}{7·11} = \frac{8}{77} \)
\( \frac{4}{1} : \frac{18}{9} = \) \( \frac{4}{1} : \frac{18:9}{9:9} = \frac{4}{1} : \frac{2}{1} = 4 : 2 = 2 \)
\( \frac{15}{4} : \frac{2}{3} = \) \( \frac{15}{4} · \frac{3}{2} = \frac{15·3}{4·2} = \frac{45}{8} \)
\( \frac{4}{40} : \frac{4}{40} = \) \( 1 \)
\( \frac{5}{21} : \frac{1}{2} : 3 = \) \( \frac{5}{21} · \frac{2}{1} : 3 \\ = \frac{5·2}{21·1} : 3 = \frac{10}{21} : 3 \\ = \frac{10}{21} : \frac{3}{1} = \frac{10}{21} · \frac{1}{3} \\ = \frac{10·1}{21·3} = \frac{10}{63} \)
\( \frac{5}{21} : ( \frac{1}{2} : 3 ) = \) \( \frac{5}{21} : ( \frac{1}{2} : \frac{3}{1} ) \\ = \frac{5}{21} : ( \frac{1}{2} · \frac{1}{3} ) \\ = \frac{5}{21} : ( \frac{1·1}{2·3} ) = \frac{5}{21} : \frac{1}{6} \\ = \frac{5}{21} · \frac{6}{1} = \frac{5·6}{21·1} \\ = \frac{30}{21} = \frac{10}{7} \)