# 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 $$\frac{2}{6}$$ $$\frac{12}{36}$$ $$\frac{24}{72}$$ $$\frac{36}{108}$$ $$\frac{48}{144}$$ $$\frac{6}{18}$$ $$\frac{4}{12}$$ $$\frac{3}{9}$$