• Terme ordnen & zusammenfassen
  • MNWeG
  • 13.05.2022
  • Mathematik
  • Gleichungen
  • M (Mindeststandard)
  • 7
  • Arbeitsblatt
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1
Ordne den Term und fasse ihn dann zusammen.
a+b+3a+a+2b+a=a+3a+a+a+b+2b=6a+3b\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} a+b+3a+a+2b+a&=a+3a+a+a+b+2b\\ &=6a+3b \end{aligned}

Beispiel:

a)   b+a+a+b+b+b+a=a+a+a+b+b+b+b=3a+4b\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} a)\ \ \ b+a+a+b+b+b+a&=\cloze{a+a+a+b+b+b+b}\\ &=\cloze{3a+4b} \end{aligned}
b)   x+y+x+xy=x+x+x+yy=3x0y=3x\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} b)\ \ \ x+y+x+x-y&=\cloze{x+x+x+y-y}\\ &=\cloze{3x-0y}\\ &=\cloze{3x} \end{aligned}
c)   2z+3rz+2r+r=2zz+3r+2r+r=1z+6r=z+6r\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} c)\ \ \ 2z+3r-z+2r+r&=\cloze{2z-z+3r+2r+r}\\ &=\cloze{1z+6r}\\ &=\cloze{z+6r} \end{aligned}
d)   12u3w10u+6w=12u10u3w+6w=2u+3w\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} d)\ \ \ 12u-3w-10u+6w&=\cloze{12u-10u-3w+6w}\\ &=\cloze{2u+3w} \end{aligned}
e)   4t+5f+3e2t3f=4t2t+5f3f+3e=2t+2f+3e\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} e)\ \ \ 4t+5f+3e-2t-3f&=\cloze{4t-2t+5f-3f+3e}\\ &=\cloze{2t+2f+3e} \end{aligned}
f)   3l5i6l+2i+4i=3l6l5i+2i+4i=3l+1i=3l+i\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} f)\ \ \ 3l-5i-6l+2i+4i&=\cloze{3l-6l-5i+2i+4i}\\ &=\cloze{-3l+1i}\\ &=\cloze{-3l+i} \end{aligned}
g)   6z+3r2s+3z+6s=6z+3z+3r2s+6s=9z+3r+4s\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} g)\ \ \ 6z+3r-2s+3z+6s&=\cloze{6z+3z+3r-2s+6s}\\ &=\cloze{9z+3r+4s} \end{aligned}
h)   13+3a+4b3+2a=133+3a+2a+4b=10+5a+4b\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} h)\ \ \ 13+3a+4b-3+2a&=\cloze{13-3+3a+2a+4b}\\ &=\cloze{10+5a+4b} \end{aligned}
i)   53x+4+5x2=5+423x+5x=7+2x\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} i)\ \ \ 5-3x+4+5x-2&=\cloze{5+4-2-3x+5x}\\ &=\cloze{7+2x} \end{aligned}
j)   77f4+3r+20f+145r=77f+20f4+14+3r5r=97f+102r\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} j)\ \ \ 77f-4+3r+20f+14-5r&=\cloze{77f+20f-4+14+3r-5r}\\ &=\cloze{97f+10-2r} \end{aligned}
k)   77f4+3r+20f+145r=77f+20f4+14+3r5r=97f+102r\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} k)\ \ \ 77f-4+3r+20f+14-5r&=\cloze{77f+20f-4+14+3r-5r}\\ &=\cloze{97f+10-2r} \end{aligned}
l)   2d13d4+7z+613z=2d13d4+6+7z13z=11d+26z\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} l)\ \ \ 2d-13d-4+7z+6-13z&=\cloze{2d-13d-4+6+7z-13z}\\ &=\cloze{-11d+2-6z} \end{aligned}
m)   5k+45l4k+9946l=5k4k+45l46l+99=1k1l+99=kl+99\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} m)\ \ \ 5k+45l-4k+99-46l&=\cloze{5k-4k+45l-46l+99}\\ &=\cloze{1k-1l+99}\\ &=\cloze{k-l+99} \end{aligned}
n)   12o4m2o4o2m=12o2o4o4m2m=18o6m\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} n)\ \ \ -12o-4m-2o-4o-2m&=\cloze{-12o-2o-4o-4m-2m}\\ &=\cloze{-18o-6m} \end{aligned}
o)   3+15u98+387u=398+3+15u87u=9872u\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} o)\ \ \ -3+15u-98+3-87u&=\cloze{–3-98+3+15u-87u}\\ &=\cloze{-98-72u} \end{aligned}
n)   0z+28p5z+129p=0z5z+2+128p9p=5z+1417p\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} n)\ \ \ 0z+2-8p-5z+12-9p&=\cloze{0z-5z+2+12-8p-9p}\\ &=\cloze{-5z+14-17p} \end{aligned}