Lösungen: Kürzen und Erweitern von Brüchen II (Basis)

A. Bestimme die Zahl, die zum gekürzten Bruch führt:

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

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

3. \( \frac{6}{10}^{\bbox[#e1ffc1,5px]{:2}} = \frac{6\color{blue}{:2}}{10\color{blue}{:2}} = \frac{3}{5} \)

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

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

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

7. \( \frac{8}{16}^{\bbox[#e1ffc1,5px]{:8}} = \frac{8\color{blue}{:8}}{16\color{blue}{:8}} = \frac{1}{2} \)

8. \( \frac{10}{24}^{\bbox[#e1ffc1,5px]{:2}} = \frac{10\color{blue}{:2}}{24\color{blue}{:2}} = \frac{5}{12} \)

9. \( \frac{8}{28}^{\bbox[#e1ffc1,5px]{:4}} = \frac{8\color{blue}{:4}}{28\color{blue}{:4}} = \frac{2}{7} \)

10. \( \frac{25}{60}^{\bbox[#e1ffc1,5px]{:5}} = \frac{25\color{blue}{:5}}{60\color{blue}{:5}} = \frac{5}{12} \)

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

12. \( \frac{10}{120}^{\bbox[#e1ffc1,5px]{:10}} = \frac{10\color{blue}{:10}}{120\color{blue}{:10}} = \frac{1}{12} \)

B. 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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