# AB: Lektion Brüche (Teil 5)

1.

Multipliziere die folgenden Brüche und kürze das jeweilige Ergebnis.

a)

$$3 · \frac{2}{5} =$$ $$\frac{3}{1} · \frac{2}{5} = \frac{3·2}{1·5} = \frac{6}{5}$$

b)

$$\frac{4}{3} · \frac{3}{4} =$$ $$\frac{4·3}{3·4} = \frac{12}{12} = 1$$

c)

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

d)

$$\frac{12}{22} · \frac{11}{6} =$$ $$\frac{\textcolor{blue}{2}\cancel{12}}{\textcolor{red}{2}\cancel{22}} · \frac{\cancel{11}\textcolor{red}{1}}{\cancel{6}\textcolor{blue}{1}} \\ = \frac{2}{2} · \frac{1}{1} = 1 · 1 = 1$$

e)

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

f)

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

g)

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

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