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# Mathematrix: Vortrag/ Erweitern und Kürzen

 ${\displaystyle {\tfrac {2}{5}}\ }$mit 7 erweitern ${\displaystyle {\tfrac {2}{5}}={\tfrac {14}{35}}\ }$ ${\displaystyle {\tfrac {15}{35}}\ }$kürzen ${\displaystyle {\tfrac {15}{35}}={\tfrac {3}{7}}\ }$ ${\displaystyle {\tfrac {15}{35}}={\tfrac {5\cdot 3}{5\cdot 7}}={\tfrac {3}{7}}\ }$ ${\displaystyle {\tfrac {15}{35}}={\tfrac {15:5}{35:5}}={\tfrac {3}{7}}\ }$ ${\displaystyle {\tfrac {14}{35}}}$ ${\displaystyle {\tfrac {14}{35}}={\tfrac {2}{5}}}$ ${\displaystyle {\tfrac {24}{30}}}$ ${\displaystyle 2\quad 3\quad 5\quad 7\quad 11\quad 13\quad 17\quad 19.....}$ ${\displaystyle 24:2=12\quad 12:2=6\quad 6:2=3\quad 3:3=1\quad }$${\displaystyle 24=2\cdot 2\cdot 2\cdot 3}$ ${\displaystyle 30:2=15\quad 15:2=7{,}5\quad 15:3=5\quad 5:5=1\quad }$${\displaystyle 30=2\cdot 3\cdot 5}$ ${\displaystyle {\tfrac {24}{30}}={\tfrac {2\cdot 2\cdot 2\cdot 3}{2\cdot 3\cdot 5}}={\tfrac {4}{5}}}$ ${\displaystyle {\tfrac {39}{52}}}$ GeoGebra ${\displaystyle {\tfrac {38808}{15288}}}$ ${\displaystyle {\tfrac {1}{5}}\ von\ {\tfrac {3}{7}}={\text{?}}}$ ${\displaystyle {\tfrac {1}{5}}\ von\ {\tfrac {3}{7}}={\tfrac {1}{5}}\cdot {\tfrac {3}{7}}={\tfrac {3}{35}}}$ Die Hälfte von fünf neuntel ist...? ${\displaystyle {\tfrac {1}{2}}\ von\ {\tfrac {5}{9}}={\tfrac {1}{2}}\cdot {\tfrac {5}{9}}={\tfrac {5}{18}}}$ Zwei siebtel von fünf neuntel sind...? ${\displaystyle {\tfrac {2}{7}}\ von\ {\tfrac {5}{9}}={\tfrac {2}{7}}\cdot {\tfrac {5}{9}}={\tfrac {10}{63}}}$