Lösungen: Erweitern von Brüchen II (Basis)

A. Bestimme die Erweiterungszahl für die folgenden Brüche:

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

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

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

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

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

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

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

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

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

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

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

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

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