TitelProzentzahlen
Autoranonym
veröffentlicht04.07.2021
FachMathematik
Klassenstufen5, 6

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Prozentzahlen und Brüche

Schreibe als Prozentzahl.

$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{7}{10} = \cloze{7 0} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{2}{10} = \cloze{2 0} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{1}{10} = \cloze{1 0} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{9}{10} = \cloze{9 0} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{8}{10} = \cloze{8 0} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{4}{10} = \cloze{4 0} \%$

Die Prozentzahlen in den nächsten beiden Aufgaben sind entweder Vielfache von 5 oder von 2. Dadurch können die Brüche in jedem Fall gekürzt werden.

Schreibe die Prozentzahl zunächst als Dezimalbruch und kürze dann soweit wie möglich.

$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 42 \% = \frac{ \cloze{42} }{100} = \cloze{ \frac{21}{50} }$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 10 \% = \frac{ \cloze{10} }{100} = \cloze{ \frac{1}{10} }$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 55 \% = \frac{ \cloze{55} }{100} = \cloze{ \frac{11}{20} }$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 80 \% = \frac{ \cloze{80} }{100} = \cloze{ \frac{4}{5} }$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 34 \% = \frac{ \cloze{34} }{100} = \cloze{ \frac{17}{50} }$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 32 \% = \frac{ \cloze{32} }{100} = \cloze{ \frac{8}{25} }$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 56 \% = \frac{ \cloze{56} }{100} = \cloze{ \frac{14}{25} }$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 65 \% = \frac{ \cloze{65} }{100} = \cloze{ \frac{13}{20} }$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 20 \% = \frac{ \cloze{20} }{100} = \cloze{ \frac{1}{5} }$

Erweitere den Bruch zunächst auf Hundertstel und schreibe dann als Prozentzahl.

$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{13}{20} = \frac{ \cloze{65} }{100} = \cloze{65} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{3}{20} = \frac{ \cloze{15} }{100} = \cloze{15} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{1}{10} = \frac{ \cloze{10} }{100} = \cloze{10} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{17}{20} = \frac{ \cloze{85} }{100} = \cloze{85} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{1}{20} = \frac{ \cloze{5} }{100} = \cloze{5} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{1}{4} = \frac{ \cloze{25} }{100} = \cloze{25} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{23}{25} = \frac{ \cloze{92} }{100} = \cloze{92} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{1}{5} = \frac{ \cloze{20} }{100} = \cloze{20} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{2}{5} = \frac{ \cloze{40} }{100} = \cloze{40} \%$

Prozentzahlen und Dezimalzahlen

Fülle die Lücken.

$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \cloze{0{,}5} = 5 0 \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 0{,}7 = \cloze{7 0} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \cloze{0{,}8} = 8 0 \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \cloze{0{,}3} = 3 0 \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 0{,}5 = \cloze{5 0} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 0{,}2 = \cloze{2 0} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 0{,}6 = \cloze{6 0} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 0{,}4 = \cloze{4 0} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \cloze{0{,}9} = 9 0 \%$

Schreibe als Prozentzahl.

$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 0{,}01 = \cloze{1} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 0{,}05 = \cloze{5} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 0{,}88 = \cloze{88} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 0{,}65 = \cloze{65} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 0{,}84 = \cloze{84} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 0{,}04 = \cloze{4} \%$

Hier kommen zunächst nur ganze Prozentzahlen vor. Durch die beiden Textausgaben lassen sich ein- und zweistellige Prozentzahlen mit gleicher Wahrscheinlichkeit generieren.

Schreibe als Kommazahl.

$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 8 \% = \cloze{0{,}08}$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 4 \% = \cloze{0{,}04}$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 9 \% = \cloze{0{,}09}$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 63 \% = \cloze{0{,}63}$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 74 \% = \cloze{0{,}74}$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 85 \% = \cloze{0{,}85}$

Schreibe als Prozentzahl.

$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 0{,}839 = \cloze{83{,}9} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 0{,}9754 = \cloze{97{,}54} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 0{,}5991 = \cloze{59{,}91} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 0{,}0878 = \cloze{8{,}78} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 0{,}668 = \cloze{66{,}8} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 0{,}032 = \cloze{3{,}2} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 0{,}816 = \cloze{81{,}6} \%$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 0{,}028 = \cloze{2{,}8} \%$

Hier werden die Prozentzahlen gebrochen ausgegeben.

Schreibe als Dezimalzahl.

$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 4{,}63 \% = \cloze{0{,}0463}$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 93{,}3 \% = \cloze{0{,}933}$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 7{,}3 \% = \cloze{0{,}073}$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 3{,}64 \% = \cloze{0{,}0364}$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 16{,}6 \% = \cloze{0{,}166}$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 69{,}67 \% = \cloze{0{,}6967}$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 37{,}1 \% = \cloze{0{,}371}$
$\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 72{,}54 \% = \cloze{0{,}7254}$

Man beachte die angepassten Nachkommastellen bei den #d-Variablen.