• Brüche erweitern und kürzen
  • MartinC
  • 06.10.2022
  • Mathematik
  • 6
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Du kannst einen Bruch , indem du Zähler und Nenner mit der gleichen Zahl . Beim Erweitern bleibt der vom Bruch dargestellte Anteil unverändert, dieser Anteil wird nur in Abschnitte unterteilt.
Du kannst einen Bruch , indem du Zähler und Nenner durch die gleiche Zahl . Beim Kürzen bleibt der vom Bruch dar-gestellte Anteil unverändert, dieser Anteil wird nur in Abschnitte unterteilt.

1
Kürze mit 2.
  • 812=46\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{8}{12} = \cloze{ \frac{4}{6} }
  • 818=49\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{8}{18} = \cloze{ \frac{4}{9} }
  • 220=110\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{2}{20} = \cloze{ \frac{1}{10} }
  • 1418=79\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{14}{18} = \cloze{ \frac{7}{9} }
  • 1216=68\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{12}{16} = \cloze{ \frac{6}{8} }
  • 614=37\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{6}{14} = \cloze{ \frac{3}{7} }
  • 820=410\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{8}{20} = \cloze{ \frac{4}{10} }
  • 188=94\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{18}{8} = \cloze{ \frac{9}{4} }
2
Kürze mit 3.
  • 1827=69\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{18}{27} = \cloze{ \frac{6}{9} }
  • 99=33\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{9}{9} = \cloze{ \frac{3}{3} }
  • 39=13\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{3}{9} = \cloze{ \frac{1}{3} }
  • 36=12\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{3}{6} = \cloze{ \frac{1}{2} }
  • 1521=57\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{15}{21} = \cloze{ \frac{5}{7} }
  • 912=34\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{9}{12} = \cloze{ \frac{3}{4} }
  • 624=28\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{6}{24} = \cloze{ \frac{2}{8} }
  • 1224=48\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{12}{24} = \cloze{ \frac{4}{8} }
3
Erweitere mit 2.
  • 56=1012\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{5}{6} = \cloze{ \frac{10}{12} }
  • 15=210\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{1}{5} = \cloze{ \frac{2}{10} }
  • 67=1214\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{6}{7} = \cloze{ \frac{12}{14} }
  • 23=46\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{2}{3} = \cloze{ \frac{4}{6} }
  • 22=44\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{2}{2} = \cloze{ \frac{4}{4} }
  • 89=1618\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{8}{9} = \cloze{ \frac{16}{18} }
  • 78=1416\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{7}{8} = \cloze{ \frac{14}{16} }
  • 18=216\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{1}{8} = \cloze{ \frac{2}{16} }
4
Erweitere mit 3.
  • 13=39\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{1}{3} = \cloze{ \frac{3}{9} }
  • 67=1821\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{6}{7} = \cloze{ \frac{18}{21} }
  • 68=1824\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{6}{8} = \cloze{ \frac{18}{24} }
  • 19=327\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{1}{9} = \cloze{ \frac{3}{27} }
  • 35=915\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{3}{5} = \cloze{ \frac{9}{15} }
  • 29=627\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{2}{9} = \cloze{ \frac{6}{27} }
  • 89=2427\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{8}{9} = \cloze{ \frac{24}{27} }
  • 16=318\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{1}{6} = \cloze{ \frac{3}{18} }
5
Kann ich immer kürzen und erweitern? - Begründe deine Antwort.
6
Erweitere schrittweise mit 2.
  • 29=418=836=1672\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{2}{9} = \cloze{ \frac{4}{18} } = \cloze{ \frac{8}{36} } = \cloze{ \frac{16}{72} }
  • 47=814=1628=3256\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{4}{7} = \cloze{ \frac{8}{14} } = \cloze{ \frac{16}{28} } = \cloze{ \frac{32}{56} }
  • 78=1416=2832=5664\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{7}{8} = \cloze{ \frac{14}{16} } = \cloze{ \frac{28}{32} } = \cloze{ \frac{56}{64} }
  • 35=610=1220=2440\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{3}{5} = \cloze{ \frac{6}{10} } = \cloze{ \frac{12}{20} } = \cloze{ \frac{24}{40} }
  • 13=26=412=824\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{1}{3} = \cloze{ \frac{2}{6} } = \cloze{ \frac{4}{12} } = \cloze{ \frac{8}{24} }
  • 59=1018=2036=4072\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{5}{9} = \cloze{ \frac{10}{18} } = \cloze{ \frac{20}{36} } = \cloze{ \frac{40}{72} }
7
Erweitere schrittweise mit 3.
  • 29=627=1881=54243\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{2}{9} = \cloze{ \frac{6}{27} } = \cloze{ \frac{18}{81} } = \cloze {\frac{54}{243} }
  • 68=1824=5472=162216\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{6}{8} = \cloze{ \frac{18}{24} } = \cloze{ \frac{54}{72} } = \cloze {\frac{162}{216} }
  • 23=69=1827=5481\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{2}{3} = \cloze{ \frac{6}{9} } = \cloze{ \frac{18}{27} } = \cloze {\frac{54}{81} }
  • 13=39=927=2781\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{1}{3} = \cloze{ \frac{3}{9} } = \cloze{ \frac{9}{27} } = \cloze {\frac{27}{81} }
  • 57=1521=4563=135189\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{5}{7} = \cloze{ \frac{15}{21} } = \cloze{ \frac{45}{63} } = \cloze {\frac{135}{189} }
  • 110=330=990=27270\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{1}{10} = \cloze{ \frac{3}{30} } = \cloze{ \frac{9}{90} } = \cloze {\frac{27}{270} }
8
Kürze schrittweise mit 2.
  • 2832=1416=78\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{28}{32} = \cloze{ \frac{14}{16} } = \cloze{ \frac{7}{8} }
  • 1640=820=410\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{16}{40} = \cloze{ \frac{8}{20} } = \cloze{ \frac{4}{10} }
  • 2840=1420=710\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{28}{40} = \cloze{ \frac{14}{20} } = \cloze{ \frac{7}{10} }
  • 416=28=14\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{4}{16} = \cloze{ \frac{2}{8} } = \cloze{ \frac{1}{4} }
  • 1220=610=35\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{12}{20} = \cloze{ \frac{6}{10} } = \cloze{ \frac{3}{5} }
  • 828=414=27\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{8}{28} = \cloze{ \frac{4}{14} } = \cloze{ \frac{2}{7} }
9
Kürze schrittweise mit 3.
  • 963=321=17\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{9}{63} = \cloze{ \frac{3}{21} } = \cloze{ \frac{1}{7} }
  • 5463=1821=67\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{54}{63} = \cloze{ \frac{18}{21} } = \cloze{ \frac{6}{7} }
  • 2772=924=38\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{27}{72} = \cloze{ \frac{9}{24} } = \cloze{ \frac{3}{8} }
  • 1854=618=26\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{18}{54} = \cloze{ \frac{6}{18} } = \cloze{ \frac{2}{6} }
  • 7290=2430=810\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{72}{90} = \cloze{ \frac{24}{30} } = \cloze{ \frac{8}{10} }
  • 5481=1827=69\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{54}{81} = \cloze{ \frac{18}{27} } = \cloze{ \frac{6}{9} }