# Lösungen: Erweitern von Brüchen II (Basis)

1. Bestimme die Erweiterungszahl für die folgenden Brüche:

a)  $$\frac{1}{2}^{\bbox[#e1ffc1,5px]{ ·2}} = \frac{1\color{blue}{·2}}{2\color{blue}{·2}} = \frac{2}{4}$$

b)  $$\frac{2}{5}^{\bbox[#e1ffc1,5px]{ ·3}} = \frac{2\color{blue}{·3}}{5\color{blue}{·3}} = \frac{6}{15}$$

c)  $$\frac{2}{5}^{\bbox[#e1ffc1,5px]{ ·2}} = \frac{2\color{blue}{·2}}{5\color{blue}{·2}} = \frac{4}{10}$$

d)  $$\frac{5}{8}^{\bbox[#e1ffc1,5px]{ ·3}} = \frac{5\color{blue}{·3}}{8\color{blue}{·3}} = \frac{15}{24}$$

e)  $$\frac{1}{3}^{\bbox[#e1ffc1,5px]{ ·4}} = \frac{1\color{blue}{·4}}{3\color{blue}{·4}} = \frac{4}{12}$$

f)  $$\frac{6}{7}^{\bbox[#e1ffc1,5px]{ ·3}} = \frac{6\color{blue}{·3}}{7\color{blue}{·3}} = \frac{18}{21}$$

g)  $$\frac{7}{10}^{\bbox[#e1ffc1,5px]{ ·4}} = \frac{7\color{blue}{·4}}{10\color{blue}{·4}} = \frac{28}{40}$$

h)  $$\frac{2}{15}^{\bbox[#e1ffc1,5px]{ ·7}} = \frac{2\color{blue}{·7}}{15\color{blue}{·7}} = \frac{14}{105}$$

i)  $$\frac{3}{8}^{\bbox[#e1ffc1,5px]{ ·10}} = \frac{3\color{blue}{·10}}{8\color{blue}{·10}} = \frac{30}{80}$$

j)  $$\frac{1}{15}^{\bbox[#e1ffc1,5px]{ ·100}} = \frac{1\color{blue}{·100}}{15\color{blue}{·100}} = \frac{100}{1500}$$

k)  $$\frac{12}{7}^{\bbox[#e1ffc1,5px]{ ·5}} = \frac{12\color{blue}{·5}}{7\color{blue}{·5}} = \frac{60}{35}$$

l)  $$\frac{2}{9}^{\bbox[#e1ffc1,5px]{ ·2}} = \frac{2\color{blue}{·2}}{9\color{blue}{·2}} = \frac{4}{18}$$