# Lösungen: Erweitern und Kürzen von Brüchen I (Erweitert)

A. Erweitere die folgenden Brüche mit den vorgegebenen Zahlen:

1. $$\frac{1}{5}^{\color{blue}{·2}} = \bbox[#e1ffc1,5px]{ \frac{1\color{blue}{·2}}{5\color{blue}{·2}} = \frac{2}{10} }$$

2. $$\frac{2}{3}^{\color{blue}{·3}} = \bbox[#e1ffc1,5px]{ \frac{2\color{blue}{·3}}{3\color{blue}{·3}} = \frac{6}{9} }$$

3. $$\frac{2}{7}^{\color{blue}{·4}} = \bbox[#e1ffc1,5px]{ \frac{2\color{blue}{·4}}{7\color{blue}{·4}} = \frac{8}{28} }$$

4. $$\frac{7}{9}^{\color{blue}{·5}} = \bbox[#e1ffc1,5px]{ \frac{7\color{blue}{·5}}{9\color{blue}{·5}} = \frac{35}{45} }$$

5. $$\frac{15}{8}^{\color{blue}{·7}} = \bbox[#e1ffc1,5px]{ \frac{15\color{blue}{·7}}{8\color{blue}{·7}} = \frac{105}{56} }$$

6. $$\frac{1}{7}^{\color{blue}{·7}} = \bbox[#e1ffc1,5px]{ \frac{1\color{blue}{·7}}{7\color{blue}{·7}} = \frac{7}{49} }$$

7. $$\frac{11}{15}^{\color{blue}{·10}} = \bbox[#e1ffc1,5px]{ \frac{11\color{blue}{·10}}{15\color{blue}{·10}} = \frac{110}{150} }$$

8. $$\frac{11}{15}^{\color{blue}{·12}} = \bbox[#e1ffc1,5px]{ \frac{11\color{blue}{·12}}{15\color{blue}{·12}} = \frac{132}{180} }$$

9. $$\frac{10}{9}^{\color{blue}{·9}} = \bbox[#e1ffc1,5px]{ \frac{10\color{blue}{·9}}{9\color{blue}{·9}} = \frac{90}{81} }$$

10. $$\frac{4}{25}^{\color{blue}{·15}} = \bbox[#e1ffc1,5px]{ \frac{4\color{blue}{·15}}{25\color{blue}{·15}} = \frac{60}{375} }$$

11. $$\frac{7}{21}^{\color{blue}{·12}} = \bbox[#e1ffc1,5px]{ \frac{7\color{blue}{·12}}{21\color{blue}{·12}} = \frac{84}{252} }$$

12. $$\frac{9}{11}^{\color{blue}{·19}} = \bbox[#e1ffc1,5px]{ \frac{9\color{blue}{·19}}{11\color{blue}{·19}} = \frac{171}{209} }$$

B. Kürze die folgenden Brüche durch die vorgegebenen Zahlen:

1. $$\frac{8}{24}^{\color{blue}{:2}} = \bbox[#e1ffc1,5px]{ \frac{8\color{blue}{:2}}{24\color{blue}{:2}} = \frac{4}{12} }$$

2. $$\frac{8}{27}$$ lässt sich nicht kürzen.

3. $$\frac{45}{9}^{\color{blue}{:3}} = \bbox[#e1ffc1,5px]{ \frac{45\color{blue}{:3}}{9\color{blue}{:3}} = \frac{15}{3} }$$

4. $$\frac{66}{99}^{\color{blue}{:3}} = \bbox[#e1ffc1,5px]{ \frac{66\color{blue}{:3}}{99\color{blue}{:3}} = \frac{22}{33} }$$

5. $$\frac{77}{154}^{\color{blue}{:7}} = \bbox[#e1ffc1,5px]{ \frac{77\color{blue}{:7}}{154\color{blue}{:7}} = \frac{11}{22} }$$

6. $$\frac{12}{72}^{\color{blue}{:6}} = \bbox[#e1ffc1,5px]{ \frac{12\color{blue}{:6}}{72\color{blue}{:6}} = \frac{2}{12} }$$

7. $$\frac{99}{9999}^{\color{blue}{:9}} = \bbox[#e1ffc1,5px]{ \frac{99\color{blue}{:9}}{9999\color{blue}{:9}} = \frac{11}{1111} }$$

8. $$\frac{90}{9990}^{\color{blue}{:9}} = \bbox[#e1ffc1,5px]{ \frac{90\color{blue}{:9}}{9990\color{blue}{:9}} = \frac{10}{1110} }$$

9. $$\frac{11}{121}^{\color{blue}{:11}} = \bbox[#e1ffc1,5px]{ \frac{11\color{blue}{:11}}{121\color{blue}{:11}} = \frac{1}{11} }$$

10. $$\frac{51}{102}^{\color{blue}{:17}} = \bbox[#e1ffc1,5px]{ \frac{51\color{blue}{:17}}{102\color{blue}{:17}} = \frac{3}{6} }$$

11. $$\frac{500}{1000}^{\color{blue}{:25}} = \bbox[#e1ffc1,5px]{ \frac{500\color{blue}{:25}}{1000\color{blue}{:25}} = \frac{20}{40} }$$

12. $$\frac{120}{4500}^{\color{blue}{:30}} = \bbox[#e1ffc1,5px]{ \frac{120\color{blue}{:30}}{4500\color{blue}{:30}} = \frac{4}{150} }$$

C. Erweitere und kürze die Brüche gemäß folgender Tabelle:

 ·2 ·3 ·4 :2 :3 :4 $$\frac{8}{24}$$ $$\frac{16}{48}$$ $$\frac{24}{72}$$ $$\frac{32}{96}$$ $$\frac{4}{12}$$ nicht kürzbar $$\frac{2}{6}$$ $$\frac{12}{48}$$ $$\frac{24}{96}$$ $$\frac{36}{144}$$ $$\frac{48}{192}$$ $$\frac{6}{24}$$ $$\frac{4}{16}$$ $$\frac{3}{12}$$ $$\frac{48}{60}$$ $$\frac{96}{120}$$ $$\frac{144}{180}$$ $$\frac{192}{240}$$ $$\frac{24}{30}$$ $$\frac{16}{20}$$ $$\frac{12}{15}$$ $$\frac{36}{80}$$ $$\frac{72}{160}$$ $$\frac{108}{240}$$ $$\frac{144}{320}$$ $$\frac{18}{40}$$ nicht kürzbar $$\frac{9}{20}$$