# AB: Lektion Brüche (Teil 2)

1.

Wandle die Brüche in Gemischte Zahlen um:

a)

$$\frac{5}{2} =$$ $$\frac{4+1}{2} = \frac{4}{2} + \frac{1}{2} = 2 + \frac{1}{2} = 2 \frac{1}{2}$$

b)

$$\frac{8}{3} =$$ $$\frac{6+2}{3} = \frac{6}{3} + \frac{2}{3} = 2 + \frac{2}{3} = 2 \frac{2}{3}$$

c)

$$\frac{75}{6} =$$ $$\frac{72+3}{6} = \frac{72}{6} + \frac{3}{6} = 12 + \frac{3:3}{6:3} = 12 \frac{1}{2}$$

d)

$$\frac{88}{3} =$$ $$\frac{87+1}{3} = \frac{87}{3} + \frac{1}{3} = 29 + \frac{1}{3} = 29 \frac{1}{3}$$

e)

$$\frac{100}{15} =$$ $$\frac{90+10}{15} = \frac{90}{15} + \frac{10:5}{15:5} = 6 + \frac{2}{3} = 6 \frac{2}{3}$$

f)

$$\frac{85}{15} =$$ $$\frac{75+10}{15} = \frac{75}{15} + \frac{10:5}{15:5} = 5 + \frac{2}{3} = 5 \frac{2}{3}$$

2.

Wandle die folgenden Gemischten Zahlen zurück in Brüche:

a)

$$3\frac{1}{2} =$$ $$3 + \frac{1}{2} = \frac{3}{1} + \frac{1}{2} \\ = \frac{3·2}{1·2} + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} \\ = \frac{6+1}{2} = \frac{7}{2}$$

b)

$$1\frac{1}{10} =$$ $$\frac{1}{1} + \frac{1}{10} \\ = \frac{10}{10} + \frac{1}{10} = \frac{10+1}{10} \\ = \frac{11}{10}$$

c)

$$8\frac{4}{7} =$$ $$\frac{8}{1} + \frac{4}{7} = \frac{8·7}{1·7} + \frac{4}{7} \\ = \frac{56}{7} + \frac{4}{7} = \frac{56+4}{7} \\ = \frac{60}{7}$$

d)

$$6\frac{3}{8} =$$ $$\frac{6}{1} + \frac{3}{8} = \frac{6·8}{1·8} + \frac{3}{8} \\ = \frac{48}{8} + \frac{3}{8} = \frac{48+3}{8} \\ = \frac{51}{8}$$

e)

$$12\frac{1}{3} =$$ $$\frac{12}{1} + \frac{1}{3} = \frac{12·3}{1·3} + \frac{1}{3} \\ = \frac{36}{3} + \frac{1}{3} = \frac{36+1}{3} \\ = \frac{37}{3}$$

f)

$$2\frac{2}{3} =$$ $$\frac{2}{1} + \frac{2}{3} = \frac{2·3}{1·3} + \frac{2}{3} \\ = \frac{6}{3} + \frac{2}{3} = \frac{6+2}{3} \\ = \frac{8}{3}$$

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