AB: Lektion Brüche (Teil 4)

1.

Subtrahiere folgende Brüche und kürze das Ergebnis. Wandle in eine gemischte Zahl nur bei den Aufgaben e, f und g um.

a)

\( \frac{4}{2} - \frac{3}{2} = \) \( \bbox[#e1ffc1,5px]{ \frac{4-3}{2} = \frac{1}{2} } \)

b)

\( \frac{11}{12} - \frac{1}{12} = \) \( \bbox[#e1ffc1,5px]{ \frac{11-1}{12} = \frac{10}{12} = \frac{10:2}{12:2} = \frac{5}{6} } \)

c)

\( \frac{11}{3} - \frac{5}{2} = \) \( \bbox[#e1ffc1,5px]{ \frac{11·2}{3·2} - \frac{5·3}{2·3} \\ = \frac{22}{6} - \frac{15}{6} = \frac{22-15}{6} \\ = \frac{7}{6} = 1 \frac{1}{6} } \)

d)

\( \frac{8}{3} - \frac{2}{6} = \) \( \bbox[#e1ffc1,5px]{ \frac{8}{3} - \frac{2:2}{6:2} = \frac{8}{3} - \frac{1}{3} = \frac{8-1}{3} = \frac{7}{3} } \)

e)

\( \frac{14}{3} - \frac{3}{2} - \frac{4}{2} = \) \( \bbox[#e1ffc1,5px]{ = \frac{14·2}{3·2} - \frac{3·3}{2·3} - \frac{4·3}{2·3} \\ = \frac{28}{6} - \frac{9}{6} - \frac{12}{6} \\ = \frac{28-9-12}{6} = \frac{7}{6} = 1 \frac{1}{6} } \)

f)

\( \frac{9}{8} - \frac{8}{7} - \frac{7}{4} = \) \( \bbox[#e1ffc1,5px]{ = \frac{9·7}{8·7} - \frac{8·8}{7·8} - \frac{7·14}{4·14} \\ = \frac{63}{56} - \frac{64}{56} - \frac{98}{56} \\ = \frac{63-64-98}{56} = \frac{-99}{56} \\ = -1 · \frac{99}{56} = -1 · ( \frac{56+43}{56} ) \\ = -( \frac{56}{56}+\frac{43}{56} ) = -( 1\frac{43}{56} ) \\ = -1\frac{43}{56} } \)

g)

\( \frac{43}{4} - \frac{12}{5} - 4 = \) \( \bbox[#e1ffc1,5px]{ = \frac{43}{4} - \frac{12}{5} - \frac{4}{1} \\ = \frac{43·5}{4·5} - \frac{12·4}{5·4} - \frac{4·20}{1·20} \\ = \frac{215}{20} - \frac{48}{20} - \frac{80}{20} \\ = \frac{215-48-80}{20} = \frac{87}{20} \\ = \frac{80 + 7}{20} = \frac{80}{20} + \frac{7}{20} \\ = 4 \frac{7}{20} } \)

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