• + / - mit natürlichen Zahlen
• MNWeG
• 28.01.2022
• Mathematik
• Bruchrechnen
• M (Mindeststandard)
• 7
• Arbeitsblatt
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1
Wandle die gemischte Zahl zuerst um und berechne dann.
Vergiss nicht zu kürzen, falls möglich!

Beispiel:

$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} 4\frac{1}{3}+3=\frac{13}{3}+\frac{3}{1}=\frac{13}{3}+\frac{9}{3}=\frac{22}{3}=\bold{\underline{\underline{7\frac{1}{3}}}}$

$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} 5+\frac{2}{3}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{5}{1}+\frac{2}{3}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{15}{3}+\frac{2}{3}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{17}{3}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} 5\frac{2}{3}$

a)

$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} 1\frac{4}{5}+7$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{9}{5}+\frac{7}{1}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{9}{5}+\frac{35}{5}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{44}{5}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} 8\frac{4}{5}$

b)

$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} 2-1\frac{2}{3}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{2}{1}-\frac{5}{3}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{6}{3}-\frac{5}{3}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{1}{3}$

c)

$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} 5\frac{3}{5}+12$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{28}{5}+\frac{12}{1}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{28}{5}+\frac{60}{5}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{88}{5}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} 17\frac{3}{5}$

d)

$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} 8-1\frac{6}{7}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{8}{1}-\frac{13}{7}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{56}{7}-\frac{13}{7}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{43}{7}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} 6\frac{1}{7}$

e)

$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} 5\frac{2}{3}-4$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{17}{3}-\frac{4}{1}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{17}{3}-\frac{12}{3}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{5}{3}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} 1\frac{2}{3}$

f)

$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} 9\frac{6}{7}+3$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{69}{7}+\frac{3}{1}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{69}{7}+\frac{21}{7}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{90}{7}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} 12\frac{6}{7}$

g)

$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} 6-2\frac{2}{3}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{6}{1}-\frac{8}{3}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{18}{3}-\frac{8}{3}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{10}{3}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} 3\frac{1}{3}$

h)

$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} 5\frac{3}{8}+2\frac{1}{2}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{43}{8}+\frac{5}{2}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{43}{8}+\frac{20}{8}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{63}{8}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} 7\frac{7}{8}$

i)

$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} 3-1\frac{1}{7}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{3}{1}-\frac{8}{7}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{21}{7}-\frac{8}{7}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{13}{7}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} 1\frac{6}{7}$

j)

$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} 2-1\frac{3}{9}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{2}{1}-\frac{12}{9}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{18}{9}-\frac{12}{9}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{6}{9}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{2}{3}$

k)

$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} 3-2\frac{4}{5}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{3}{1}-\frac{14}{5}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{15}{5}-\frac{14}{5}$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{\displaystyle #1}}}}}} =$ $\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{\displaystyle #1}}}}}} \frac{1}{5}$

l)