MathemaTriX ⋅ Grundrechenarten und Bruchrechnungen

Hoch

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AUFGABEN

KAPITEL Grundrechenarten Bruchrechnungen $-{\tfrac {\cdot \ +}{\ :\ }}$ Schlussrechnung Prozentrechnung Exponentialfunktion Logarithmus Arbeiten mit Termen $\mathbb {X} ^{2}$ Zahlendarstellungen Mengentheorie Aussagenlogik ${\begin{matrix}\mathbb {R} :=\\\mathbb {Q} \cup \mathbb {I} \end{matrix}}$ Einheiten $cm^{2}$ Statistik und Wahrscheinlichkeit Geometrische Konstruktionen Geometrie der Ebene Geometrie des Raums Diagramme Funktionen $f(x)$ Lineare Gleichungssysteme ${\begin{smallmatrix}{a_{1}\ b_{2}}\\{a_{2}\ b_{2}}\end{smallmatrix}}$ Trigonometrische Funktionen Vektoren Differentialrechnung $^{dy}/_{dx}$ Integralrechnung $\textstyle \int _{a}^{b}dx$ Folgen $a_{n}$ Beweise $a\rightarrow b$

Grundrechnungen

Textaufgaben zu den Grundrechenarten

Typ A

1. 1. 3
   2. 42
   3. 41
   4. −4
2. 1. 5
   2. 21
   3. 19
   4. −42
3. 1. 4
   2. 28
   3. 12
   4. −46
4. 1. 33
   2. 10
   3. -18
   4. 26
5. 1. 3
   2. 42
   3. 41
   4. −4
6. 1. 5
   2. 21
   3. 19
   4. −42
7. 1. 4
   2. 28
   3. 12
   4. −46
8. 1. 33
   2. 10
   3. -18
   4. 26

Typ B

1. 1C, 2A, 3B
2. 1C, 2B, 3A
3. 1A, 2B, 3C
4. 1B, 2A, 3C
5. 1C, 2A, 3B
6. 1C, 2B, 3A
7. 1A, 2B, 3C
8. 1B, 2A, 3C

Sachaufgaben zu den Grundrechenarten

Grundaufgaben

1. 1. An:18, Fr:26
   2. 12:Ä, 5:O, 20:E, 35 K
2. 1. Pe:5,8, Fr:5,7 kg
   2. 19:S, 7:G, 42:R, 27:B
3. 1. Su:22, Fr:12
   2. W:1,5 kg, G:0,8 kg, D:2,4 kg, H:4,3 kg
4. 1. Sa:2, Fr:27:T-S
   2. 33:R, 4:S, 32:W, 30:B
5. 1. Mi:5, Fr:26
   2. 14:Ä, 15:K, 30:E, 25:B
6. 1. Sa:3,1 kg, Da:1,3 kg (Sa:1,9 kg, Da:2,5 kg)
   2. G: 0,6 kg, B:0,5 kg, E:2,5 kg, R:0,6 kg
7. 1. An:31, Fr:31
   2. w:3, s:2, br:8, bu:5
8. 1. As:13, Fr:13
   2. r:22, s:5, w:40, b:21

Kombinationsaufgaben

1. 1. 50,4 €
   2. das 4-Fache
2. 1. 9
   2. 3
3. 1. 12
   2. 6
4. 1. 9
   2. 3
5. 1. P:8, M:7, A:11, W:7
   2. 4
6. 1. I:15, P:12, N:24, S:8, W:10
   2. 5
7. 1. 6
   2. 6
8. 1. V:20, F:5, L:4
   2. 1

Vorrang der Rechenarten

Grundrechenartenvorrang

O

1. 1. $24$
   2. $9$
2. 1. $-9$
   2. $0$
3. 1. $-27$
   2. $7$
4. 1. $49$
   2. $8$
5. 1. $10$
   2. $21$
6. 1. $98$
   2. $15$
7. 1. $-27$
   2. $13$
8. 1. $-14$
   2. $-1$

A

1. $-17$
2. $73$
3. $39$
4. $-5$
5. $29$
6. $-5$
7. $-13$
8. $0$

B

1. $9$
2. $0$
3. $-15$
4. $16$
5. $21$
6. $0$
7. $-13$
8. $-1$

C

1. $-7$
2. $0$
3. $3$
4. $-1$
5. $3$
6. $1$
7. $1$
8. $1$

D

1. 1. ${\color {red}21+56}:7-(79-2\cdot 5):3=$
      ${\color {red}77}:7-(79-10):3=$
      ...→ Punkt vor Strich
   2. 6
2. 1. $43+56:8-({\color {red}30-2}\cdot 5):4=$
      $43+7-({\color {red}28}\cdot 5):4=$
      ...→ Punkt vor Strich
   2. 45
3. 1. $43+72:8-(56-2\cdot {\color {red}20}):{\color {red}4}=$
      $43+9-(56-2\cdot {\color {red}5})=$
      ... → Klammer vor Punkt
   2. 48
4. 1. $63-(56:7-2)\cdot {\color {red}9+72}:3=$
      $63-(8-2)\cdot {\color {red}81}:3=$
      ...→ Punkt vor Strich
   2. 33
5. 1. $21+56:7-({\color {red}77-2\cdot 4}):3=$
      $21+8-({\color {red}75}\cdot 4):3=$
      ...→ Punkt vor Strich
   2. 6
6. 1. ${\color {red}40+56:8}(30-2\cdot 5):4=$
      ${\color {red}96:8}(30-10):4=$
      ...→ Punkt vor Strich
   2. 45
7. 1. $33+72:8-(56-2\cdot 20):4=$
      $33+9-(56-2\cdot {\color {red}40}):{\color {red}4}=$
      $33+9-(56-2\cdot {\color {red}10})=$
      ... → Klammer vor Punkt
   2. 38
8. 1. $63-(56:7-2):3+72:6=$
      $63-(8-2):3+72:6=$
      ${\color {red}63-6}:3+72:6=$
      ${\color {red}57}:3-12=$
      ...→ Punkt vor Strich
   2. 73

Vorrang mit Klammern in Klammern

1. $\ 22$
2. $\ -10$
3. $\ -25$
4. $\ 51$
5. $\ -37$
6. $\ 55$
7. $\ 53$
8. $\ 49$

Bruchrechnungen

Definitionen

Gemischte Zahlen

1. $\ {\tfrac {40}{9}}\qquad$$\ {\tfrac {120}{13}}\qquad$$\ {\tfrac {12}{7}}$
   $\ 35{\tfrac {7}{11}}\qquad$$\ 7\qquad$$\ 11{\tfrac {1}{12}}$
   $\ {\tfrac {11}{9}}\qquad$$\ 8{\tfrac {10}{13}}\qquad$$\ -1{\tfrac {1}{7}}\qquad$$\ 3{\tfrac {3}{5}}$
2. $\ {\tfrac {53}{7}}\qquad$$\ {\tfrac {9}{5}}\qquad$$\ {\tfrac {35}{3}}$
   $\ 37{\tfrac {3}{12}}\qquad$$\ 6{\tfrac {3}{5}}\qquad$$\ 11$
   $\ 3{\tfrac {4}{7}}\qquad$$\ {\tfrac {1}{5}}\qquad$$\ {\tfrac {11}{3}}\qquad$$\ -2{\tfrac {1}{4}}$
3. $\ {\tfrac {11}{3}}\qquad$$\ {\tfrac {76}{11}}\qquad$$\ {\tfrac {17}{9}}$
   $\ 34\qquad$$\ 1{\tfrac {4}{5}}\qquad$$\ 12{\tfrac {1}{8}}$
   $\ -5{\tfrac {1}{3}}\qquad$$\ {\tfrac {56}{11}}\qquad$$\ {\tfrac {1}{9}}\qquad$$\ -4{\tfrac {8}{13}}$
4. $\ {\tfrac {37}{7}}\qquad$$\ {\tfrac {7}{6}}\qquad$$\ {\tfrac {89}{9}}$
   $\ 40{\tfrac {7}{11}}\qquad$$\ 1{\tfrac {2}{7}}\qquad$$\ 7$
   $\ -{\tfrac {17}{7}}\qquad$$\ {\tfrac {5}{6}}\qquad$$\ {\tfrac {53}{9}}\qquad$$\ -{\tfrac {1}{17}}$
5. $\ {\tfrac {37}{9}}\qquad$$\ {\tfrac {111}{13}}\qquad$$\ {\tfrac {36}{7}}$
   $\ 35{\tfrac {4}{11}}\qquad$$\ 9\qquad$$\ 11{\tfrac {3}{12}}$
   $\ -{\tfrac {2}{9}}\qquad$$\ -{\tfrac {1}{8}}\qquad$$\ {\tfrac {34}{7}}\qquad$$\ -{\tfrac {6}{7}}$
6. $\ {\tfrac {60}{7}}\qquad$$\ {\tfrac {19}{5}}\qquad$$\ {\tfrac {32}{3}}$
   $\ 37{\tfrac {7}{12}}\qquad$$\ 7{\tfrac {4}{5}}\qquad$$\ 11$
   $\ {\tfrac {52}{7}}\qquad$$\ -1{\tfrac {4}{5}}\qquad$$\ {\tfrac {9}{11}}\qquad$$\ -3{\tfrac {5}{14}}$
7. $\ {\tfrac {5}{3}}\qquad$$\ {\tfrac {72}{11}}\qquad$$\ {\tfrac {25}{13}}$
   $\ 35\qquad$$\ 2{\tfrac {1}{5}}\qquad$$\ 11{\tfrac {7}{8}}$
   $\ {\tfrac {5}{7}}\qquad$$\ -{\tfrac {1}{11}}\qquad$$\ 4{\tfrac {1}{13}}\qquad$$\ -1{\tfrac {1}{9}}$
8. $\ {\tfrac {47}{7}}\qquad$$\ {\tfrac {13}{12}}\qquad$$\ {\tfrac {82}{9}}$
   $\ 37\qquad$$\ 1{\tfrac {1}{7}}\qquad$$\ 7{\tfrac {3}{5}}$
   $\ -2{\tfrac {3}{7}}\qquad$$\ {\tfrac {11}{12}}\qquad$$\ 8{\tfrac {1}{9}}\qquad$$\ -{\tfrac {1}{3}}$

Erweitern und Kürzen

Erweitern

1. 1. $\ {\frac {18}{30}}\qquad$
   2. $\ {\frac {14}{49}}\qquad$
   3. $\ {\frac {15}{12}}\qquad$
   4. $\ {\frac {77}{154}}\qquad$
   5. $\ {\frac {3b}{4b}}\qquad$
   
   
   
2. 1. $\ {\frac {12}{16}}\qquad$
   2. $\ {\frac {12}{21}}\qquad$
   3. $\ {\frac {25}{20}}\qquad$
   4. $\ {\frac {91}{104}}\qquad$
   5. $\ {\frac {3w}{11w}}\qquad$
   
   
   
3. 1. $\ {\frac {49}{35}}\qquad$
   2. $\ {\frac {10}{15}}\qquad$
   3. $\ {\frac {72}{54}}\qquad$
   4. $\ {\frac {66}{84}}\qquad$
   5. $\ {\frac {7x}{4x}}\qquad$
   
   
   
4. 1. $\ {\frac {36}{24}}\qquad$
   2. $\ {\frac {60}{35}}\qquad$
   3. $\ {\frac {40}{64}}\qquad$
   4. $\ {\frac {66}{24}}\qquad$
   5. $\ {\frac {5m}{7m}}\qquad$
   
   
   

Bruchkürzen

1. 1. $\ {\frac {2}{5}}\qquad$
   2. $\ {\frac {3}{7}}\qquad$
   3. $\ {\frac {3}{2}}\qquad$
   
   
   
   4. $\ {\frac {5}{2}}\qquad$
   5. $\ {\frac {7}{4}}\qquad$
   
   
   
2. 1. $\ {\frac {2}{3}}\qquad$
   2. $\ {\frac {3}{5}}\qquad$
   3. $\ {\frac {3}{4}}\qquad$
   
   
   
   4. $\ {\frac {5}{6}}\qquad$
   5. $\ {\frac {2}{3}}\qquad$
   
   
   
3. 1. $\ {\frac {2}{3}}\qquad$
   2. $\ {\frac {10}{11}}\qquad$
   3. $\ {\frac {9}{11}}\qquad$
   
   
   
   4. $\ {\frac {5}{6}}\qquad$
   5. $\ {\frac {3}{2}}\qquad$
   
   
   
4. 1. $\ {\frac {3}{2}}\qquad$
   2. $\ {\frac {7}{4}}\qquad$
   3. $\ {\frac {4}{13}}\qquad$
   
   
   
   4. $\ {\frac {3}{4}}\qquad$
   5. $\ {\frac {1}{3}}\qquad$
   
   
   

Strich und Punkt Bruchrechnungen

Übungen

1. 1. $\textstyle \ {\frac {3}{13}}\qquad$
   2. $\textstyle \ {\frac {23}{12}}\qquad$
   3. $\textstyle \ {\frac {15}{28}}\qquad$
   4. $\textstyle \ {\frac {35}{12}}\qquad$
   
   
   
2. 1. $\textstyle \ -{\frac {57}{44}}\qquad$
   2. $\textstyle \ {\frac {35}{44}}\qquad$
   3. $\textstyle \ -{\frac {12}{11}}\qquad$
   4. $\textstyle \ {\frac {20}{77}}\qquad$
   
   
   
3. 1. $\textstyle \ {\frac {63}{55}}\qquad$
   2. $\textstyle \ -{\frac {8}{45}}\qquad$
   3. $\textstyle \ {\frac {77}{45}}\qquad$
   4. $\textstyle \ {\frac {18}{9}}(=2)\qquad$
   
   
   
4. 1. $\textstyle \ {\frac {143}{24}}\qquad$
   2. $\textstyle \ {\frac {119}{39}}\qquad$
   3. $\textstyle \ -{\frac {13}{13}}(=-1)\qquad$
   4. $\textstyle \ {\frac {88}{39}}\qquad$
   
   
   
5. 1. $\textstyle \ {\frac {4}{7}}\qquad$
   2. $\textstyle \ {\frac {60}{77}}\qquad$
   3. $\textstyle \ {\frac {137}{28}}\qquad$
   4. $\textstyle \ {\frac {165}{28}}\qquad$
   
   
   
6. 1. $\textstyle \ {\frac {26}{13}}(=2)\qquad$
   2. $\textstyle \ {\frac {165}{104}}\qquad$
   3. $\textstyle \ {\frac {143}{120}}\qquad$
   4. $\textstyle \ {\frac {23}{104}}\qquad$
   
   
   
7. 1. $\textstyle \ {\frac {3}{13}}\qquad$
   2. $\textstyle \ {\frac {23}{20}}\qquad$
   3. $\textstyle \ {\frac {28}{15}}\qquad$
   4. $\textstyle \ {\frac {12}{35}}\qquad$
   
   
   
8. 1. $\textstyle \ -{\frac {57}{55}}\qquad$
   2. $\textstyle \ {\frac {44}{35}}\qquad$
   3. $\textstyle \ -{\frac {12}{11}}\qquad$
   4. $\textstyle \ {\frac {77}{20}}\qquad$
   
   
   

Testaufgaben

1. 1. $\textstyle \ {\frac {15}{16}}$
   2. $\textstyle \ -{\frac {1}{77}}$
   3. $\textstyle \ {\frac {599}{210}}$
2. 1. $\textstyle \ {\frac {20}{21}}$
   2. $\textstyle \ -{\frac {35}{104}}$
   3. $\textstyle \ -{\frac {23}{60}}$
3. 1. $\textstyle \ {\frac {63}{40}}$
   2. $\textstyle \ -{\frac {31}{221}}$
   3. $\textstyle \ -{\frac {58}{63}}$
4. 1. $\textstyle \ {\frac {20}{33}}$
   2. $\textstyle \ -{\frac {11}{195}}$
   3. $\textstyle \ -{\frac {27}{22}}$
5. 1. $\textstyle \ {\frac {15}{14}}$
   2. $\textstyle \ {\frac {14}{99}}$
   3. $\textstyle \ {\frac {74}{27}}$
6. 1. $\textstyle \ {\frac {5}{6}}$
   2. $\textstyle {\frac {28}{165}}$
   3. $\textstyle \ -{\frac {4}{21}}$
7. 1. $\textstyle \ {\frac {21}{20}}$
   2. $\textstyle \ -{\frac {30}{143}}$
   3. $\textstyle \ -{\frac {38}{33}}$
8. 1. $\textstyle \ {\frac {20}{33}}$
   2. $\textstyle \ {\frac {73}{273}}$
   3. $\textstyle \ -{\frac {197}{180}}$

Doppelbrüche

1. $\textstyle {\frac {5}{9}}$
2. $\textstyle 1{,}5$
3. $\textstyle -{\frac {1}{8}}$
4. $\textstyle 1{\frac {1}{3}}$
5. $\textstyle {\frac {5}{6}}$
6. $\textstyle -{\frac {3}{2}}$
7. $\textstyle -2$
8. $\textstyle -{\frac {3}{4}}$

Arbeiten mit ganzen Zahlen und Brüchen

Multiplikation Bruch-Ganze Zahl

1. 1. $\textstyle \ {\frac {30}{3}}=10\qquad$
   2. $\textstyle \ {\frac {1275}{12}}=106,25\qquad$
   3. $\textstyle \ {\frac {63}{7}}=9\qquad$
   4. $\textstyle \ {\frac {6}{13}}\approx 0,46\qquad$
   
   
   
2. 1. $\textstyle \ {\frac {14}{20}}=0,7\qquad$
   2. $\textstyle \ {\frac {1515}{24}}=63,125\qquad$
   3. $\textstyle \ {\frac {231}{11}}=21\qquad$
   4. $\textstyle \ {\frac {156}{13}}=12\qquad$
   
   
   
3. 1. $\textstyle \ {\frac {3}{4}}=0,75\qquad$
   2. $\textstyle \ {\frac {924}{8}}=115,5\qquad$
   3. $\textstyle \ {\frac {56}{7}}=8\qquad$
   4. $\textstyle \ {\frac {156}{4}}=39\qquad$
   
   
   
4. 1. $\textstyle \ {\frac {60}{5}}=12\qquad$
   2. $\textstyle \ {\frac {12}{27}}=0,{\dot {4}}\qquad$
   3. $\textstyle \ {\frac {105}{6}}=17,5\qquad$
   4. $\textstyle \ {\frac {627}{11}}=57\qquad$
   
   
   
5. 1. $\textstyle \ {\frac {510}{5}}=102\qquad$
   2. $\textstyle \ {\frac {3}{5}}=0,6\qquad$
   3. $\textstyle \ {\frac {66}{11}}=6\qquad$
   4. $\textstyle \ {\frac {35}{12}}=2,91{\dot {6}}\qquad$
   
   
   
6. 1. $\textstyle \ {\frac {4}{5}}=0,8\qquad$
   2. $\textstyle \ {\frac {1001}{13}}=77\qquad$
   3. $\textstyle \ {\frac {210}{7}}=30\qquad$
   4. $\textstyle \ {\frac {21}{10}}=2,1\qquad$
   
   
   
7. 1. $\textstyle \ {\frac {1422}{3}}=474\qquad$
   2. $\textstyle \ {\frac {28}{20}}=1,4\qquad$
   3. $\textstyle \ {\frac {6}{11}}=0,{\overline {54}}\qquad$
   4. $\textstyle \ {\frac {12}{5}}=2,4\qquad$
   
   
   
8. 1. $\textstyle \ {\frac {10}{16}}=0,625\qquad$
   2. $\textstyle \ {\frac {50}{5}}=10\qquad$
   3. $\textstyle \ {\frac {651}{7}}=93\qquad$
   4. $\textstyle \ {\frac {78}{13}}=6\qquad$

Division Bruch-Ganze Zahl

1. 1. $\textstyle \ {\frac {30}{3}}=10\qquad$
   2. $\textstyle \ {\frac {7}{63}}=0,{\dot {1}}\qquad$
   3. $\textstyle \ {\frac {3}{26}}\approx 0,1154\qquad$
   4. $\textstyle \ {\frac {6}{13}}\approx 0,46\qquad$
   
   
   
2. 1. $\textstyle \ {\frac {14}{20}}=0,7\qquad$
   2. $\textstyle \ {\frac {1515}{24}}=63,125\qquad$
   3. $\textstyle \ {\frac {22}{231}}\approx 0,0952\qquad$
   4. $\textstyle \ {\frac {65}{156}}\approx 0,41{\dot {6}}\qquad$
   
   
   
3. 1. $\textstyle \ {\frac {15}{4}}=3,75\qquad$
   2. $\textstyle \ {\frac {924}{8}}=115,5\qquad$
   3. $\textstyle \ {\frac {7}{112}}=0,0625\qquad$
   4. $\textstyle \ {\frac {11}{220}}=0,05\qquad$
   
   
   
4. 1. $\textstyle \ {\frac {60}{5}}=12\qquad$
   2. $\textstyle \ {\frac {12}{27}}=0,{\dot {4}}\qquad$
   3. $\textstyle \ {\frac {6}{105}}\approx 0,057\qquad$
   4. $\textstyle \ {\frac {11}{627}}\approx 0,0175\qquad$
   
   
   
5. 1. $\textstyle \ {\frac {510}{5}}=102\qquad$
   2. $\textstyle \ {\frac {3}{5}}=0,6\qquad$
   3. $\textstyle \ {\frac {66}{11}}=6\qquad$
   4. $\textstyle \ {\frac {35}{12}}=2,91{\dot {6}}\qquad$
   
   
   
6. 1. $\textstyle \ {\frac {4}{5}}=0,8\qquad$
   2. $\textstyle \ {\frac {1001}{13}}=77\qquad$
   3. $\textstyle \ {\frac {210}{7}}=30\qquad$
   4. $\textstyle \ {\frac {21}{10}}=2,1\qquad$
   
   
   
7. 1. $\textstyle \ {\frac {1422}{3}}=474\qquad$
   2. $\textstyle \ {\frac {28}{20}}=1,4\qquad$
   3. $\textstyle \ {\frac {11}{6}}=1,8{\overline {3}}\qquad$
   4. $\textstyle \ {\frac {3}{20}}=0,15\qquad$
   
   
   
8. 1. $\textstyle \ {\frac {10}{16}}=0,625\qquad$
   2. $\textstyle \ {\frac {50}{5}}=10\qquad$
   3. $\textstyle \ {\frac {93}{124}}=0,75\qquad$
   4. $\textstyle \ {\frac {13}{78}}=0,1{\dot {6}}\qquad$

Bruchrechnungen und Vorrang

1. ${\frac {16}{15}}$
2. $-{\frac {1}{4}}$
3. $-{\frac {383}{180}}$
4. $-{\frac {35}{11}}$
5. $-{\frac {1}{6}}$
6. $-{\frac {1}{15}}$
7. ${\frac {4}{15}}$
8. $0$

Textaufgaben zu den Bruchrechnungen

1. 1. 360 t Kart., 280 t Tom., 189 t Gur.,
      11 t Karot., 420 t Getr.
   2. $\textstyle {\frac {1}{3}}\ {\text{der Ernte}}$
   
   
   
2. 1. 462 Öst., 168 Serb., 132 Türk., 162 Rest
   2. $\textstyle {\frac {27}{154}}\ {\text{der SchülerInnen}}$
   
   
   
3. 1. $\ 3{,}76\ {\text{Mill. Liter}}\qquad \ 30080{\text{€}}\$
   2. $A\ 42000\ {\text{€}}\qquad B\ 35000\ {\text{€}}\$$C\ und\ D\ je\ 14000\ {\text{€}}\$
   
   
   
4. 1. $\textstyle {\frac {1}{98000}}\ {\text{der Menschen}}\qquad \ 3,52\ {\text{Milliarden €}}\$
   2. $\textstyle {\frac {1}{3675}}\ {\text{der Menschen}}\qquad \ 4\ {\text{Milliarden €}}\$
   3. $\textstyle {\frac {4}{11}}\ {\text{der Menschen}}\qquad \ 4,8\ {\text{Milliarden €}}\$
   4. $\textstyle {\text{fast}}\ {\frac {7}{11}}\ {\text{der Menschen}}\qquad \ 880\ {\text{Millionen €}}\$
   
   
   
5. 1. die Orangen
   2. $128\ kg$
6. 1. Saskia
   2. $5\ Punkte$
7. 1. die Hosen
   2. $28$
8. 1. Elektrolytkondensatoren
   2. $313\ g$

Primfaktorzerlegung

Definitionen

Anwendungen

Kürzen mit Primfaktorzerlegung

1. 1. $\ {\frac {34}{45}}\qquad$
   2. $\ {\frac {91}{99}}\qquad$
   3. $\ {\frac {77}{68}}$
   
   
   
2. 1. $\ {\frac {10}{9}}\qquad$
   2. $\ {\frac {121}{225}}\qquad$
   3. $\ {\frac {56}{55}}$
   
   
   
3. 1. $\ {\frac {21}{22}}\qquad$
   2. $\ {\frac {65}{77}}\qquad$
   3. $\ {\frac {136}{273}}$
   
   
   
4. 1. $\ {\frac {52}{35}}\qquad$
   2. $\ {\frac {13}{33}}\qquad$
   3. $\ {\frac {77}{45}}$
   
   
   
5. 1. $\ {\frac {17}{9}}\qquad$
   2. $\ {\frac {455}{297}}\qquad$
   3. $\ {\frac {385}{306}}$
   
   
   
6. 1. $\ {\frac {4}{9}}\qquad$
   2. $\ {\frac {121}{25}}\qquad$
   3. $\ {\frac {168}{275}}$
   
   
   
7. 1. $\ {\frac {27}{22}}\qquad$
   2. $\ {\frac {65}{77}}\qquad$
   3. $\ {\frac {4}{3}}$
   
   
   
8. 1. $\ {\frac {136}{245}}\qquad$
   2. $\ {\frac {13}{33}}\qquad$
   3. $\ {\frac {11}{5}}$
   
   
   

Bruchstrichrechnungen mit Primfaktorzerlegung

1. $-{\frac {313}{1800}}$
2. ${\frac {296}{60}}\left(={\frac {74}{15}}\right)$
3. $-{\frac {232}{252}}\left(=-{\frac {58}{63}}\right)$
4. ${\frac {649}{504}}$
5. $-{\frac {85}{100}}\left(=-{\frac {17}{20}}\right)$
6. $-{\frac {32}{36}}\left(=-{\frac {8}{9}}\right)$
7. $-{\frac {37}{300}}$
8. ${\frac {1082}{180}}\left(={\frac {541}{90}}\right)$

Textaufgaben Primfaktorzerlegung

1. ${\frac {90}{31}}\approx 2{,}9\ \Omega$
2. Jede 231 min, also nach 21 bzw. 22 mal, 4 mal am Tag
3. 3 cm, 462 Teile
4. 1009008 Tage
5. 7 cm, 88 Teile
6. Jede 42 min, also nach 3 bzw. 4 mal, 23 mal am Tag gemeinsam
7. ${\frac {8}{3}}=2{,}{\dot {6}}\ \Omega$
8. 13 bzw. 22 Umdrehungen

Teilbarkeit

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