• Grundrechenarten bei Termen
  • MNWeG
  • 18.12.2021
  • Mathematik
  • Terme
  • M (Mindeststandard)
  • 8
  • Einzelarbeit
  • Arbeitsblatt
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1
Fasse die Terme so weit wie möglich zusammen.
  • x+x+x+z+x+z\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} x+x+x+z+x+z
  • a+b+c+c+b+a+b+c+a+a\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} a+b+c+c+b+a+b+c+a+a
  • 2x+y+3x+4y+2x\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 2x+y+3x+4y+2x
  • 3x2y+5x7y+x12y\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 3x-2y+5x-7y+x-12y
  • 8x4x+2y5x+12y+13x21y\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 8x-4x+2y-5x+12y+13x-21y
  • 14h+9f13j+12h+22f29j54h\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 14h+9f-13j+12h+22f-29j-54h
  • 23+17x45z+18y19+24z+18y\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 23+17x-45z+18y-19+24z+18y
  • g+14o12p+19r+12g14r12o+19g8p+17o\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} g+14o-12p+19r+12g-14r-12o+19g-8p+17o
  • 2+4a+f+7h+23l4l+2h+1619f+2228l+15a31h\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 2+4a+f+7h+23l-4l+2h+16-19f+22-28l+15a-31h   +9a26l+2012l+100a\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \;+9a-26l+20-12l+100a
  • 2,6x+1,7r+12,3b22,4+17,2r18,3+13,4b+31,3x44,5r\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 2{,}6x+1{,}7r+12{,}3b-22{,}4+17{,}2r-18{,}3+13{,}4b+31{,}3x-44{,}5r

Nicht vergessen:

Markiere Gleiches mit Farbe.

Sortiere alles hintereinander.

Achte darauf, dass du das Vorzeichen mitnimmst.

Lösung1
Fasse die Terme so weit wie möglich zusammen.
a) 4x+2z\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 4x+2z
b) 4a+3b+3c\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 4a+3b+3c
c) 7x+5y\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 7x+5y
d) 9x21y\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 9x-21y
e) 12x7y\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 12x-7y
f) 31f28h42j\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 31f-28h-42j
g) 4+17x+36y21z\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 4+17x+36y-21z
h) 32g+19o20p+5r\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 32g+19o-20p+5r
i) 60+128a18f22h47l\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 60 +128a -18f -22h -47l
j) 40,7+25,7b+33,9x26,4r\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} -40{,}7+25{,}7b+33{,}9x-26{,}4r
Platzprobleme ?

Wenn du alle Aufgaben lösen willst, dann nutze am besten ein extra Blatt.

2
Vereinfache die Terme, indem du multiplizierst.
  • 27a\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 2\cdot7a
  • 12b3\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 12b\cdot3
  • xyz\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} x\cdot y\cdot z
  • 2hfg\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 2h\cdot f\cdot g
  • 8d3f\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 8d\cdot 3f
  • 14l2k\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 14l\cdot 2k
  • 12xx3x\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 12x\cdot x\cdot 3x
  • 2m3n4o\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 2m\cdot 3n\cdot 4o
  • 3b2n3b2n2b\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 3b\cdot 2n\cdot 3b\cdot 2n\cdot2b
  • abde3abee2d\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} a\cdot b\cdot d\cdot e\cdot 3a\cdot b\cdot e\cdot e\cdot 2d
  • 2b(5a)2b(a)a\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 2b\cdot (-5a)\cdot 2b\cdot(-a)\cdot a
Versteckte Informationen!

Das Pluszeichen, eine 1 vor einer Variable oder auch ein Malzeichen dazwischen.

ab\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} ab ist ganz ausführlich 1a1b\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 1\cdot a\cdot1\cdot b

Tipp:

Sortiere auch hier nach Zahlen und nach Buchstaben.

Alle Zahlen multiplizieren, alle Variablen zusammenschreiben und nach dem Alphabet aufschreiben.

Lösung2
a) 14a\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 14a
b)36b\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 36b
c)xyz\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} xyz
d) 2fgh\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 2fgh
e) 18df\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 18df
f) 28kl\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 28kl
g) 36x3\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 36x^{3}
h) 24mno\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 24mno
i)72b3n2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 72b^{3}n^{2}
j) 6a2b2d2e3\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 6a^{2}b^{2}d^{2}e^{3}
k)(+)20a3b2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} (+)20a^{3}b^{2}
3
Schreibe diese Divisionen erst als Bruch und kürze sie dann so weit wie möglich.
  • 18x:2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 18x : 2
  • 25b:5\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 25b : 5
  • 64c:8\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 64c : 8
  • 12d:3d\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 12d:3d
  • 81e:9e\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 81e: 9e
  • 196f:14f\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 196f:14f
  • 9gh:gh\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 9gh:gh
  • 12hij:2hij\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 12hij:2hij
  • 49ijk:7ij\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 49ijk:7ij
  • 15jk:3j\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 15jk:3j
  • 22x2:11x\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 22x^{2}:11x
  • 16a3b2c6:4a3b2c2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 16a^{3}b^{2}c^{6}:4a^{3}b^{2}c^{2}
  • 24xv:48xvz\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 24xv:48xvz
  • 125x2y3:1000xy3\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} 125x^{2}y^{3}:1000xy^{3}

Tipp:

Schreibe Zähler und Nenner ganz ausführlich und sortiert untereinander. Dann kannst du Gleiches einfach streichen.

Lösung3
a) 918x12=9x\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{^{9}\cancel{18}x}{_{1}\cancel{2}}=\underline{9x}
b) 525b15=5b\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{^{5}\cancel{25}b}{_{1}\cancel{5}}=\underline{5b}
c) 864c18=8c\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{^{8}\cancel{64}c}{_{1}\cancel{8}}=\underline{8c}
d) 412d13d=4\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{^{4}\cancel{12}\cancel{d}}{_{1}\cancel{3}\cancel{d}}=\underline{4}
e) 981e19e=9\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{^{9}\cancel{81}\cancel{e}}{_{1}\cancel{9}\cancel{e}}=\underline{9}
f) 14196f114f=14\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{^{14}\cancel{196}\cancel{f}}{_{1}\cancel{14}\cancel{f}}=\underline{14}
g) 9gh1gh=9\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{9\cancel{g}\cancel{h}}{_{1}\cancel{g}\cancel{h}}=\underline{9}
h)212hij12hij=2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{^{2}\cancel{12}\cancel{h}\cancel{i}\cancel{j}}{_{1}\cancel{2}\cancel{h}\cancel{i}\cancel{j}}=\underline{2}
i)749ijk17ij=7k\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{^{7}\cancel{49}\cancel{i}\cancel{j}k}{_{1}\cancel{7}\cancel{i}\cancel{j}}=\underline{7k}
j)515jk13j=5k\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{^{5}\cancel{15}\cancel{j}k}{_{1}\cancel{3}\cancel{j}}=\underline{5k}
k)222xx111x=2x\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{^{2}\cancel{22}\cancel{x}x}{_{1}\cancel{11}\cancel{x}}=\underline{2x}
l)416aaabbcccccc14aaabbcc=4c4\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{^{4}\cancel{16}\cancel{a}\cancel{a}\cancel{a}\cancel{b}\cancel{b}\cancel{c}\cancel{c}cccc}{_{1}\cancel{4}\cancel{a}\cancel{a}\cancel{a}\cancel{b}\cancel{b}\cancel{c}\cancel{c}}=\underline{4c^{4}}
m)124xv248xvz=12z      oder      0,5z\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{^{1}\cancel{24}\cancel{x}\cancel{v}}{_{2}\cancel{48}\cancel{x}\cancel{v}z}=\underline{\frac{1}{2}z\;\;\; oder\;\;\; 0{,}5z}
n)1125xxyyy81000xyyy=x8      oder      0,125x\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{^{1}\cancel{125}\cancel{x}x\cancel{y}\cancel{y}\cancel{y}}{_{8}\cancel{1000}\cancel{x}\cancel{y}\cancel{y}\cancel{y}}=\underline{\frac{x}{8}\;\;\; oder\;\;\; 0{,}125x}