Lösungen: Erweitern von Brüchen I (Basis)

1. Erweitere die folgenden Brüche mit den vorgegebenen Zahlen:

a)  \( \frac{1}{3}^{\color{blue}{·2}} = \bbox[#e1ffc1,5px]{ \frac{1\color{blue}{·2}}{3\color{blue}{·2}} = \frac{2}{6} } \)

b)  \( \frac{2}{3}^{\color{blue}{·2}} = \bbox[#e1ffc1,5px]{ \frac{2\color{blue}{·2}}{3\color{blue}{·2}} = \frac{4}{6} } \)

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

d)  \( \frac{3}{7}^{\color{blue}{·3}} = \bbox[#e1ffc1,5px]{ \frac{3\color{blue}{·3}}{7\color{blue}{·3}} = \frac{9}{21} } \)

e)  \( \frac{4}{3}^{\color{blue}{·3}} = \bbox[#e1ffc1,5px]{ \frac{4\color{blue}{·3}}{3\color{blue}{·3}} = \frac{12}{9} } \)

f)  \( \frac{1}{8}^{\color{blue}{·3}} = \bbox[#e1ffc1,5px]{ \frac{1\color{blue}{·3}}{8\color{blue}{·3}} = \frac{3}{24} } \)

g)  \( \frac{8}{10}^{\color{blue}{·4}} = \bbox[#e1ffc1,5px]{ \frac{8\color{blue}{·4}}{10\color{blue}{·4}} = \frac{32}{40} } \)

h)  \( \frac{2}{5}^{\color{blue}{·4}} = \bbox[#e1ffc1,5px]{ \frac{2\color{blue}{·4}}{5\color{blue}{·4}} = \frac{8}{20} } \)

i)  \( \frac{3}{7}^{\color{blue}{·4}} = \bbox[#e1ffc1,5px]{ \frac{3\color{blue}{·4}}{7\color{blue}{·4}} = \frac{12}{28} } \)

j)  \( \frac{1}{5}^{\color{blue}{·5}} = \bbox[#e1ffc1,5px]{ \frac{1\color{blue}{·5}}{5\color{blue}{·5}} = \frac{5}{25} } \)

k)  \( \frac{2}{7}^{\color{blue}{·5}} = \bbox[#e1ffc1,5px]{ \frac{2\color{blue}{·5}}{7\color{blue}{·5}} = \frac{10}{35} } \)

l)  \( \frac{2}{9}^{\color{blue}{·5}} = \bbox[#e1ffc1,5px]{ \frac{2\color{blue}{·5}}{9\color{blue}{·5}} = \frac{10}{45} } \)

2. Erweitere die Brüche gemäß folgender Tabelle:

Erweitere mit 2 mit 3 mit 4
\( \frac{2}{4} \) \( \frac{4}{8} \) \( \frac{6}{12} \) \( \frac{8}{16} \)
\( \frac{4}{8} \) \( \frac{8}{16} \) \( \frac{12}{24} \) \( \frac{16}{32} \)
\( \frac{8}{24} \) \( \frac{16}{48} \) \( \frac{24}{72} \) \( \frac{32}{96} \)
\( \frac{12}{36} \) \( \frac{24}{72} \) \( \frac{36}{108} \) \( \frac{48}{144} \)
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