Mathematrix: Vortrag/ Erweitern und Kürzen

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