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
\( \frac{9}{20} \)
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