# 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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