AB: Lektion Brüche (Teil 2)

1.

Wandle die Brüche in Gemischte Zahlen um:

a)

\( \frac{5}{2} = \) \( \bbox[#e1ffc1,5px]{ \frac{4+1}{2} = \frac{4}{2} + \frac{1}{2} = 2 + \frac{1}{2} = 2 \frac{1}{2} } \)

b)

\( \frac{8}{3} = \) \( \bbox[#e1ffc1,5px]{ \frac{6+2}{3} = \frac{6}{3} + \frac{2}{3} = 2 + \frac{2}{3} = 2 \frac{2}{3} } \)

c)

\( \frac{75}{6} = \) \( \bbox[#e1ffc1,5px]{ \frac{72+3}{6} = \frac{72}{6} + \frac{3}{6} = 12 + \frac{3:3}{6:3} = 12 \frac{1}{2} } \)

d)

\( \frac{88}{3} = \) \( \bbox[#e1ffc1,5px]{ \frac{87+1}{3} = \frac{87}{3} + \frac{1}{3} = 29 + \frac{1}{3} = 29 \frac{1}{3} } \)

e)

\( \frac{100}{15} = \) \( \bbox[#e1ffc1,5px]{ \frac{90+10}{15} = \frac{90}{15} + \frac{10:5}{15:5} = 6 + \frac{2}{3} = 6 \frac{2}{3} } \)

f)

\( \frac{85}{15} = \) \( \bbox[#e1ffc1,5px]{ \frac{75+10}{15} = \frac{75}{15} + \frac{10:5}{15:5} = 5 + \frac{2}{3} = 5 \frac{2}{3} } \)

2.

Wandle die folgenden Gemischten Zahlen zurück in Brüche:

a)

\( 3\frac{1}{2} = \) \( \bbox[#e1ffc1,5px]{ 3 + \frac{1}{2} = \frac{3}{1} + \frac{1}{2} \\ = \frac{3·2}{1·2} + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} \\ = \frac{6+1}{2} = \frac{7}{2} } \)

b)

\( 1\frac{1}{10} = \) \( \bbox[#e1ffc1,5px]{ \frac{1}{1} + \frac{1}{10} \\ = \frac{10}{10} + \frac{1}{10} = \frac{10+1}{10} \\ = \frac{11}{10} } \)

c)

\( 8\frac{4}{7} = \) \( \bbox[#e1ffc1,5px]{ \frac{8}{1} + \frac{4}{7} = \frac{8·7}{1·7} + \frac{4}{7} \\ = \frac{56}{7} + \frac{4}{7} = \frac{56+4}{7} \\ = \frac{60}{7} } \)

d)

\( 6\frac{3}{8} = \) \( \bbox[#e1ffc1,5px]{ \frac{6}{1} + \frac{3}{8} = \frac{6·8}{1·8} + \frac{3}{8} \\ = \frac{48}{8} + \frac{3}{8} = \frac{48+3}{8} \\ = \frac{51}{8} } \)

e)

\( 12\frac{1}{3} = \) \( \bbox[#e1ffc1,5px]{ \frac{12}{1} + \frac{1}{3} = \frac{12·3}{1·3} + \frac{1}{3} \\ = \frac{36}{3} + \frac{1}{3} = \frac{36+1}{3} \\ = \frac{37}{3} } \)

f)

\( 2\frac{2}{3} = \) \( \bbox[#e1ffc1,5px]{ \frac{2}{1} + \frac{2}{3} = \frac{2·3}{1·3} + \frac{2}{3} \\ = \frac{6}{3} + \frac{2}{3} = \frac{6+2}{3} \\ = \frac{8}{3} } \)

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