Rechenregeln und Rechengesetze

Welches Rechengesetz hat Selina bei der Rechnung [math]\frac{2}{4}+\frac{3}{4}+\frac{2}{4}=[/math] angewendet? [br][img]data:image/png;base64,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[/img]
Jonas will die Rechnung [math]\frac{4}{5}·\frac{3}{2}·\frac{2}{3}=[/math] berechnen. [br]Gib Jonas einen Tipp, welches Rechengesetz er anwenden kann, um die Rechnung einfach zu berechnen.
Hannah berechnet das Ergebnis der Rechnung [math]\frac{3}{4}:\left(\frac{1}{4}+\frac{7}{16}-\frac{1}{8}\right)[/math].[br]Betrachte Hannahs Rechenweg und beschreibe, auf welche Rechenregeln und Rechengesetze Hannah achten musste. [br][br][img width=190,height=267]https://lh7-rt.googleusercontent.com/docsz/AD_4nXcKWZT3oLUYMYJMhdG_jpMRHypwY6DIEfvyhNvXs2Jpy84eXYPaDEW2gtDcksf0xdONinbBmGVW0ChKKSVjXPOp7OblsgemzHALXWidWSViuF0ax-FHsrFjLidBWI5jafiCrkqziWo3jN6irhh1FCkVc1hU?key=iPWyZxSwnBE__qgFAGKYbA[/img]
☆ Max hat bei der Berechnung des Ergebnisses der Rechnung [math]\frac{6}{9}+\frac{3}{11}+\frac{1}{3}[/math] ein Rechengesetz angewendet. [br]Bestimme, welches Rechengesetz Max angewendet hat und argumentiere, warum Max das Rechengesetz angewendet hat. [br][br][img width=183,height=324]https://lh7-rt.googleusercontent.com/docsz/AD_4nXe6dwnEY8E5sx_ignQBqyXdouWN529EUtMFcr_UGrOBjA0CAVhKGT5Z_N-ANqQROzXk-pS8JUXwAuIyDV1klo-jZ-So69iAk-63JLpolN4ffF_b-NZDAIuL7epku6nxEw0821oI2emVNThU6zkq-pAozjea?key=iPWyZxSwnBE__qgFAGKYbA[/img]
☆ Selina hat die Rechnung [math]\frac{9}{8}-\left(\frac{1}{4}+\frac{3}{4}·\frac{1}{2}\right)-\frac{1}{16}[/math] falsch ausgeführt. [br]Betrachte Selinas Rechenweg und beschreibe, welche Fehler Selina unterlaufen sind. [br]Berechne das richtige Ergebnis. [br][br][img width=235,height=440]https://lh7-rt.googleusercontent.com/docsz/AD_4nXc4UBEVaWufeCZ2-UJjz4HQNclfRSyTikIQdU0HCLBm5ToChW-IzzHo7-tSj7ZJLrMir6T8gyfrhmmoBxqyOi37uTmDaafoGbpm4BOjBTb_nx5enVUwyYkfUaf4_PjIzLaofDYQns2fmDrMHE1T_78rwZBw?key=iPWyZxSwnBE__qgFAGKYbA[/img]
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Information: Rechenregeln und Rechengesetze