Lösungen: Kürzen und Erweitern von Brüchen I (Basis)

A. Kürze die folgenden Brüche durch die vorgegebenen Zahlen:

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

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

3. \( \frac{8}{10}^{\color{blue}{:2}} = \bbox[#e1ffc1,5px]{ \frac{8\color{blue}{:2}}{10\color{blue}{:2}} = \frac{4}{5} } \)

4. \( \frac{6}{9}^{\color{blue}{:3}} = \bbox[#e1ffc1,5px]{ \frac{6\color{blue}{:3}}{9\color{blue}{:3}} = \frac{2}{3} } \)

5. \( \frac{9}{3}^{\color{blue}{:3}} = \bbox[#e1ffc1,5px]{ \frac{9\color{blue}{:3}}{3\color{blue}{:3}} = \frac{3}{1} = 3 } \)

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

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

8. \( \frac{8}{12}^{\color{blue}{:4}} = \bbox[#e1ffc1,5px]{ \frac{8\color{blue}{:4}}{12\color{blue}{:4}} = \frac{2}{3} } \)

9. \( \frac{4}{24}^{\color{blue}{:4}} = \bbox[#e1ffc1,5px]{ \frac{4\color{blue}{:4}}{24\color{blue}{:4}} = \frac{1}{6} } \)

10. Der Bruch \( \frac{1}{5} \)ist bereits vollständig gekürzt. Man kann ihn nicht weiter kürzen.

11. \( \frac{5}{10}^{\color{blue}{:5}} = \bbox[#e1ffc1,5px]{ \frac{5\color{blue}{:5}}{10\color{blue}{:5}} = \frac{1}{2} } \)

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

B. Erweitere die folgenden Brüche mit den vorgegebenen Zahlen:

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

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

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

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

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

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

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

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

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

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

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

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

C. Erweitere und kürze die Brüche gemäß folgender Tabelle:

  ·2 ·3 ·4 :2 :3 :4
\( \frac{2}{4} \) \( \frac{4}{8} \) \( \frac{6}{12} \) \( \frac{8}{16} \) \( \frac{1}{2} \) nicht
kürzbar
nicht
kürzbar
\( \frac{4}{8} \) \( \frac{8}{16} \) \( \frac{12}{24} \) \( \frac{16}{32} \) \( \frac{2}{4} \) nicht
kürzbar
\( \frac{1}{2} \)
\( \frac{8}{24} \) \( \frac{16}{48} \) \( \frac{24}{72} \) \( \frac{32}{96} \) \( \frac{4}{12} \) nicht
kürzbar
\( \frac{2}{6} \)
\( \frac{12}{36} \) \( \frac{24}{72} \) \( \frac{36}{108} \) \( \frac{48}{144} \) \( \frac{6}{18} \) \( \frac{4}{12} \) \( \frac{3}{9} \)
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