Lösungen: Kürzen und Erweitern von Brüchen II (Erweitert)

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

1. \( \frac{8}{40}^{\bbox[#e1ffc1,5px]{:4}} = \frac{8\color{blue}{:4}}{40\color{blue}{:4}} = \frac{2}{10} \)

2. \( \frac{3}{9}^{\bbox[#e1ffc1,5px]{:3}} = \frac{3\color{blue}{:3}}{9\color{blue}{:3}} = \frac{1}{3} \)

3. \( \frac{6}{16}^{\bbox[#e1ffc1,5px]{:2}} = \frac{6\color{blue}{:2}}{16\color{blue}{:2}} = \frac{3}{8} \)

4. \( \frac{8}{48}^{\bbox[#e1ffc1,5px]{:8}} = \frac{8\color{blue}{:8}}{48\color{blue}{:8}} = \frac{1}{6} \)

5. \( \frac{12}{84}^{\bbox[#e1ffc1,5px]{:12}} = \frac{12\color{blue}{:12}}{84\color{blue}{:12}} = \frac{1}{7} \)

6. \( \frac{51}{12}^{\bbox[#e1ffc1,5px]{:3}} = \frac{51\color{blue}{:3}}{12\color{blue}{:3}} = \frac{17}{4} \)

7. \( \frac{909}{54}^{\bbox[#e1ffc1,5px]{:9}} = \frac{909\color{blue}{:9}}{54\color{blue}{:9}} = \frac{101}{6} \)

8. \( \frac{155}{25}^{\bbox[#e1ffc1,5px]{:5}} = \frac{155\color{blue}{:5}}{25\color{blue}{:5}} = \frac{31}{5} \)

9. \( \frac{27}{81}^{\bbox[#e1ffc1,5px]{:9}} = \frac{27\color{blue}{:9}}{81\color{blue}{:9}} = \frac{3}{9} \)

10. \( \frac{30}{195}^{\bbox[#e1ffc1,5px]{:15}} = \frac{30\color{blue}{:15}}{195\color{blue}{:15}} = \frac{2}{13} \)

11. \( \frac{175}{205}^{\bbox[#e1ffc1,5px]{:5}} = \frac{175\color{blue}{:5}}{205\color{blue}{:5}} = \frac{35}{41} \)

12. \( \frac{210}{1020}^{\bbox[#e1ffc1,5px]{:10}} = \frac{210\color{blue}{:10}}{1020\color{blue}{:10}} = \frac{21}{102} \)

B. Bestimme die Erweiterungszahl für die folgenden Brüche:

1. \( \frac{1}{2}^{\bbox[#e1ffc1,5px]{ ·11}} = \frac{1\color{blue}{·11}}{2\color{blue}{·11}} = \frac{11}{22} \)

2. \( \frac{5}{6}^{\bbox[#e1ffc1,5px]{ ·7}} = \frac{5\color{blue}{·7}}{6\color{blue}{·7}} = \frac{35}{42} \)

3. \( \frac{1}{8}^{\bbox[#e1ffc1,5px]{ ·9}} = \frac{1\color{blue}{·9}}{8\color{blue}{·9}} = \frac{9}{72} \)

4. \( \frac{4}{9}^{\bbox[#e1ffc1,5px]{ ·13}} = \frac{4\color{blue}{·13}}{9\color{blue}{·13}} = \frac{52}{117} \)

5. \( \frac{1}{4}^{\bbox[#e1ffc1,5px]{ ·11}} = \frac{1\color{blue}{·11}}{4\color{blue}{·11}} = \frac{11}{44} \)

6. \( \frac{6}{9}^{\bbox[#e1ffc1,5px]{ ·22}} = \frac{6\color{blue}{·22}}{9\color{blue}{·22}} = \frac{132}{198} \)

7. \( \frac{9}{10}^{\bbox[#e1ffc1,5px]{ ·25}} = \frac{9\color{blue}{·25}}{10\color{blue}{·25}} = \frac{225}{250} \)

8. \( \frac{2}{11}^{\bbox[#e1ffc1,5px]{ ·7}} = \frac{2\color{blue}{·7}}{11\color{blue}{·7}} = \frac{14}{77} \)

9. \( \frac{3}{7}^{\bbox[#e1ffc1,5px]{ ·100}} = \frac{3\color{blue}{·100}}{7\color{blue}{·100}} = \frac{300}{700} \)

10. \( \frac{1}{11}^{\bbox[#e1ffc1,5px]{ ·70}} = \frac{1\color{blue}{·70}}{11\color{blue}{·70}} = \frac{70}{770} \)

11. \( \frac{12}{13}^{\bbox[#e1ffc1,5px]{ ·9}} = \frac{12\color{blue}{·9}}{13\color{blue}{·9}} = \frac{108}{117} \)

12. \( \frac{2}{11}^{\bbox[#e1ffc1,5px]{ ·201}} = \frac{2\color{blue}{·201}}{11\color{blue}{·201}} = \frac{402}{2211} \)

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