AB: Lektion Brüche (Teil 5)

\( 3 · \frac{2}{5} = \) \( \frac{3}{1} · \frac{2}{5} = \frac{3·2}{1·5} = \frac{6}{5} \)

\( \frac{4}{3} · \frac{3}{4} = \) \( \frac{4·3}{3·4} = \frac{12}{12} = 1 \)

\( \frac{8}{7} · \frac{49}{72} = \) \( \frac{8·49}{7·72} \\ = \frac{8·49}{72·7} = \frac{8}{72} · \frac{49}{7} \\ = \frac{8:8}{72:8} · \frac{49:7}{7:7} = \frac{1}{9} · \frac{7}{1} \\ = \frac{1·7}{9·1} = \frac{7}{9} \)

\( \frac{12}{22} · \frac{11}{6} = \) \( \frac{\color{blue}{2}\cancel{12}}{\color{red}{2}\cancel{22}} · \frac{\cancel{11}\color{red}{1}}{\cancel{6}\color{blue}{1}} \\ = \frac{2}{2} · \frac{1}{1} = 1 · 1 = 1 \)

\( \frac{1}{3} · \frac{3}{67} · 2 = \) \( \frac{1}{3} · \frac{3}{67} · \frac{2}{1} \\ = \frac{1·3·2}{3·67·1} = \frac{6}{201} = \frac{6:3}{201:3} \\ = \frac{2}{67} \)

\( \frac{3}{9} · \frac{42}{44} · \frac{8}{2} = \) \( \frac{3:3}{9:3} · \frac{42:2}{44:2} · \frac{8:2}{2:2} \\ = \frac{1}{3} · \frac{21}{22} · \frac{4}{1} \\ = \frac{1·21·4}{3·22·1} = \frac{84}{66} \\ = \frac{84:6}{66:6} = \frac{14}{11} \)

\( \frac{18}{70} · \frac{210}{9} · 1,5 = \) \( \frac{\color{blue}{2}\cancel{18}}{\color{red}{1}\cancel{70}} · \frac{\cancel{201}\color{red}{3}}{\cancel{9}\color{blue}{1}} · 1,5 \\ = \frac{2}{1} · \frac{3}{1} · 1,5 \\ = \frac{2}{1} · \frac{3}{1} · \frac{15}{10} \\ = \frac{2·3·15}{1·1·10} = \frac{90}{10} = 9 \)