| Ausrechnen, Resultat als gekürzter Bruch:<JS>miniAufgabe("#exonumbercrunch2","#solnumbercrunch2", | Ausrechnen, Resultat als gekürzter Bruch:<JS>miniAufgabe("#exonumbercrunch2","#solnumbercrunch2", |
| [["$\\displaystyle \\frac{\\frac{-\\frac{15}{7}}{5}+\\frac{\\frac{20}{7}}{-2}}{\\frac{-5}{-\\frac{15}{4}}+\\frac{\\frac{10}{3}}{4}}$", "$\\displaystyle \\frac{\\frac{-\\frac{15}{7}}{5}+\\frac{\\frac{20}{7}}{-2}}{\\frac{-5}{-\\frac{15}{4}}+\\frac{\\frac{10}{3}}{4}} = \\frac{-\\frac{15}{7}\\cdot\\frac{1}{5}+\\frac{20}{7}\\cdot-\\frac{1}{2}}{-5\\cdot-\\frac{4}{15}+\\frac{10}{3}\\cdot\\frac{1}{4}} = \\frac{-\\frac{3}{7}-\\frac{10}{7}}{\\frac{4}{3}+\\frac{5}{6}} = \\frac{\\frac{13}{6}}{-\\frac{13}{7}} = \\frac{13}{6} \\cdot -\\frac{7}{13} = -\\frac{7}{6}$"], ["$\\displaystyle \\frac{\\frac{-\\frac{4}{5}}{-6}+\\frac{-\\frac{16}{15}}{-8}}{\\frac{6}{-\\frac{15}{2}}+\\frac{-\\frac{5}{3}}{-5}}$", "$\\displaystyle \\frac{\\frac{-\\frac{4}{5}}{-6}+\\frac{-\\frac{16}{15}}{-8}}{\\frac{6}{-\\frac{15}{2}}+\\frac{-\\frac{5}{3}}{-5}} = \\frac{-\\frac{4}{5}\\cdot-\\frac{1}{6}+-\\frac{16}{15}\\cdot-\\frac{1}{8}}{6\\cdot-\\frac{2}{15}+-\\frac{5}{3}\\cdot-\\frac{1}{5}} = \\frac{\\frac{2}{15}+\\frac{2}{15}}{-\\frac{4}{5}+\\frac{1}{3}} = \\frac{-\\frac{7}{15}}{\\frac{4}{15}} = -\\frac{7}{15} \\cdot \\frac{15}{4} = -\\frac{7}{4}$"], ["$\\displaystyle \\frac{\\frac{8}{\\frac{20}{7}}+\\frac{\\frac{12}{5}}{-6}}{\\frac{\\frac{11}{5}}{2}+\\frac{-\\frac{7}{5}}{2}}$", "$\\displaystyle \\frac{\\frac{8}{\\frac{20}{7}}+\\frac{\\frac{12}{5}}{-6}}{\\frac{\\frac{11}{5}}{2}+\\frac{-\\frac{7}{5}}{2}} = \\frac{8\\cdot\\frac{7}{20}+\\frac{12}{5}\\cdot-\\frac{1}{6}}{\\frac{11}{5}\\cdot\\frac{1}{2}+-\\frac{7}{5}\\cdot\\frac{1}{2}} = \\frac{\\frac{14}{5}-\\frac{2}{5}}{\\frac{11}{10}-\\frac{7}{10}} = \\frac{\\frac{2}{5}}{\\frac{12}{5}} = \\frac{2}{5} \\cdot \\frac{5}{12} = \\frac{1}{6}$"], ["$\\displaystyle \\frac{\\frac{-\\frac{3}{2}}{-4}+\\frac{-2}{-\\frac{16}{3}}}{\\frac{-\\frac{17}{5}}{-4}+\\frac{-\\frac{5}{2}}{5}}$", "$\\displaystyle \\frac{\\frac{-\\frac{3}{2}}{-4}+\\frac{-2}{-\\frac{16}{3}}}{\\frac{-\\frac{17}{5}}{-4}+\\frac{-\\frac{5}{2}}{5}} = \\frac{-\\frac{3}{2}\\cdot-\\frac{1}{4}+-2\\cdot-\\frac{3}{16}}{-\\frac{17}{5}\\cdot-\\frac{1}{4}+-\\frac{5}{2}\\cdot\\frac{1}{5}} = \\frac{\\frac{3}{8}+\\frac{3}{8}}{\\frac{17}{20}-\\frac{1}{2}} = \\frac{\\frac{7}{20}}{\\frac{3}{4}} = \\frac{7}{20} \\cdot \\frac{4}{3} = \\frac{7}{15}$"], ["$\\displaystyle \\frac{\\frac{-\\frac{13}{3}}{-3}+\\frac{\\frac{17}{3}}{-3}}{\\frac{-\\frac{19}{3}}{-7}+\\frac{\\frac{7}{3}}{-7}}$", "$\\displaystyle \\frac{\\frac{-\\frac{13}{3}}{-3}+\\frac{\\frac{17}{3}}{-3}}{\\frac{-\\frac{19}{3}}{-7}+\\frac{\\frac{7}{3}}{-7}} = \\frac{-\\frac{13}{3}\\cdot-\\frac{1}{3}+\\frac{17}{3}\\cdot-\\frac{1}{3}}{-\\frac{19}{3}\\cdot-\\frac{1}{7}+\\frac{7}{3}\\cdot-\\frac{1}{7}} = \\frac{\\frac{13}{9}-\\frac{17}{9}}{\\frac{19}{21}-\\frac{1}{3}} = \\frac{\\frac{4}{7}}{-\\frac{4}{9}} = \\frac{4}{7} \\cdot -\\frac{9}{4} = -\\frac{9}{7}$"], ["$\\displaystyle \\frac{\\frac{-2}{-\\frac{26}{19}}+\\frac{\\frac{14}{13}}{-2}}{\\frac{-3}{-\\frac{13}{4}}+\\frac{-\\frac{8}{13}}{2}}$", "$\\displaystyle \\frac{\\frac{-2}{-\\frac{26}{19}}+\\frac{\\frac{14}{13}}{-2}}{\\frac{-3}{-\\frac{13}{4}}+\\frac{-\\frac{8}{13}}{2}} = \\frac{-2\\cdot-\\frac{19}{26}+\\frac{14}{13}\\cdot-\\frac{1}{2}}{-3\\cdot-\\frac{4}{13}+-\\frac{8}{13}\\cdot\\frac{1}{2}} = \\frac{\\frac{19}{13}-\\frac{7}{13}}{\\frac{12}{13}-\\frac{4}{13}} = \\frac{\\frac{8}{13}}{\\frac{12}{13}} = \\frac{8}{13} \\cdot \\frac{13}{12} = \\frac{2}{3}$"], ["$\\displaystyle \\frac{\\frac{-\\frac{10}{7}}{-3}+\\frac{\\frac{16}{21}}{-4}}{\\frac{2}{-\\frac{14}{5}}+\\frac{\\frac{15}{7}}{2}}$", "$\\displaystyle \\frac{\\frac{-\\frac{10}{7}}{-3}+\\frac{\\frac{16}{21}}{-4}}{\\frac{2}{-\\frac{14}{5}}+\\frac{\\frac{15}{7}}{2}} = \\frac{-\\frac{10}{7}\\cdot-\\frac{1}{3}+\\frac{16}{21}\\cdot-\\frac{1}{4}}{2\\cdot-\\frac{5}{14}+\\frac{15}{7}\\cdot\\frac{1}{2}} = \\frac{\\frac{10}{21}-\\frac{4}{21}}{-\\frac{5}{7}+\\frac{15}{14}} = \\frac{\\frac{5}{14}}{\\frac{2}{7}} = \\frac{5}{14} \\cdot \\frac{7}{2} = \\frac{5}{4}$"], ["$\\displaystyle \\frac{\\frac{\\frac{13}{2}}{-7}+\\frac{-\\frac{4}{7}}{4}}{\\frac{-3}{-\\frac{9}{2}}+\\frac{8}{-\\frac{16}{3}}}$", "$\\displaystyle \\frac{\\frac{\\frac{13}{2}}{-7}+\\frac{-\\frac{4}{7}}{4}}{\\frac{-3}{-\\frac{9}{2}}+\\frac{8}{-\\frac{16}{3}}} = \\frac{\\frac{13}{2}\\cdot-\\frac{1}{7}+-\\frac{4}{7}\\cdot\\frac{1}{4}}{-3\\cdot-\\frac{2}{9}+8\\cdot-\\frac{3}{16}} = \\frac{-\\frac{13}{14}-\\frac{1}{7}}{\\frac{2}{3}-\\frac{3}{2}} = \\frac{-\\frac{5}{6}}{-\\frac{15}{14}} = -\\frac{5}{6} \\cdot -\\frac{14}{15} = \\frac{7}{9}$"], ["$\\displaystyle \\frac{\\frac{\\frac{7}{3}}{8}+\\frac{-\\frac{5}{3}}{-5}}{\\frac{\\frac{7}{4}}{6}+\\frac{-\\frac{5}{4}}{3}}$", "$\\displaystyle \\frac{\\frac{\\frac{7}{3}}{8}+\\frac{-\\frac{5}{3}}{-5}}{\\frac{\\frac{7}{4}}{6}+\\frac{-\\frac{5}{4}}{3}} = \\frac{\\frac{7}{3}\\cdot\\frac{1}{8}+-\\frac{5}{3}\\cdot-\\frac{1}{5}}{\\frac{7}{4}\\cdot\\frac{1}{6}+-\\frac{5}{4}\\cdot\\frac{1}{3}} = \\frac{\\frac{7}{24}+\\frac{1}{3}}{\\frac{7}{24}-\\frac{5}{12}} = \\frac{-\\frac{1}{8}}{\\frac{5}{8}} = -\\frac{1}{8} \\cdot \\frac{8}{5} = -\\frac{1}{5}$"], ["$\\displaystyle \\frac{\\frac{-2}{-\\frac{19}{8}}+\\frac{\\frac{18}{19}}{-3}}{\\frac{-2}{\\frac{19}{4}}+\\frac{5}{\\frac{19}{2}}}$", "$\\displaystyle \\frac{\\frac{-2}{-\\frac{19}{8}}+\\frac{\\frac{18}{19}}{-3}}{\\frac{-2}{\\frac{19}{4}}+\\frac{5}{\\frac{19}{2}}} = \\frac{-2\\cdot-\\frac{8}{19}+\\frac{18}{19}\\cdot-\\frac{1}{3}}{-2\\cdot\\frac{4}{19}+5\\cdot\\frac{2}{19}} = \\frac{\\frac{16}{19}-\\frac{6}{19}}{-\\frac{8}{19}+\\frac{10}{19}} = \\frac{\\frac{2}{19}}{\\frac{10}{19}} = \\frac{2}{19} \\cdot \\frac{19}{10} = \\frac{1}{5}$"]], | [["$\\displaystyle \\frac{\\frac{-\\frac{13}{2}}{8}+\\frac{-\\frac{7}{8}}{7}}{\\frac{-\\frac{19}{2}}{6}+\\frac{\\frac{5}{2}}{3}}$", "$\\displaystyle \\frac{\\frac{-\\frac{13}{2}}{8}+\\frac{-\\frac{7}{8}}{7}}{\\frac{-\\frac{19}{2}}{6}+\\frac{\\frac{5}{2}}{3}} = \\frac{-\\frac{13}{2}\\cdot\\frac{1}{8}+-\\frac{7}{8}\\cdot\\frac{1}{7}}{-\\frac{19}{2}\\cdot\\frac{1}{6}+\\frac{5}{2}\\cdot\\frac{1}{3}} = \\frac{-\\frac{13}{16}-\\frac{1}{8}}{-\\frac{19}{12}+\\frac{5}{6}} = \\frac{-\\frac{13}{16}-\\frac{2}{16}}{-\\frac{19}{12}+\\frac{10}{12}} = \\frac{-\\frac{15}{16}}{-\\frac{3}{4}} = -\\frac{15}{16} \\cdot -\\frac{4}{3} = \\frac{5}{4}$"], ["$\\displaystyle \\frac{\\frac{\\frac{16}{5}}{4}+\\frac{-\\frac{8}{3}}{8}}{\\frac{\\frac{14}{3}}{-10}+\\frac{\\frac{7}{3}}{-7}}$", "$\\displaystyle \\frac{\\frac{\\frac{16}{5}}{4}+\\frac{-\\frac{8}{3}}{8}}{\\frac{\\frac{14}{3}}{-10}+\\frac{\\frac{7}{3}}{-7}} = \\frac{\\frac{16}{5}\\cdot\\frac{1}{4}+-\\frac{8}{3}\\cdot\\frac{1}{8}}{\\frac{14}{3}\\cdot-\\frac{1}{10}+\\frac{7}{3}\\cdot-\\frac{1}{7}} = \\frac{\\frac{4}{5}-\\frac{1}{3}}{-\\frac{7}{15}-\\frac{1}{3}} = \\frac{\\frac{12}{15}-\\frac{5}{15}}{-\\frac{7}{15}-\\frac{5}{15}} = \\frac{\\frac{7}{15}}{-\\frac{4}{5}} = \\frac{7}{15} \\cdot -\\frac{5}{4} = -\\frac{7}{12}$"], ["$\\displaystyle \\frac{\\frac{-2}{-\\frac{5}{4}}+\\frac{-9}{\\frac{15}{4}}}{\\frac{-9}{\\frac{5}{2}}+\\frac{-6}{-\\frac{15}{2}}}$", "$\\displaystyle \\frac{\\frac{-2}{-\\frac{5}{4}}+\\frac{-9}{\\frac{15}{4}}}{\\frac{-9}{\\frac{5}{2}}+\\frac{-6}{-\\frac{15}{2}}} = \\frac{-2\\cdot-\\frac{4}{5}+-9\\cdot\\frac{4}{15}}{-9\\cdot\\frac{2}{5}+-6\\cdot-\\frac{2}{15}} = \\frac{\\frac{8}{5}-\\frac{12}{5}}{-\\frac{18}{5}+\\frac{4}{5}} = \\frac{\\frac{8}{5}-\\frac{12}{5}}{-\\frac{18}{5}+\\frac{4}{5}} = \\frac{-\\frac{4}{5}}{-\\frac{14}{5}} = -\\frac{4}{5} \\cdot -\\frac{5}{14} = \\frac{2}{7}$"], ["$\\displaystyle \\frac{\\frac{\\frac{11}{2}}{5}+\\frac{-\\frac{9}{2}}{9}}{\\frac{-\\frac{19}{2}}{7}+\\frac{-\\frac{3}{2}}{-3}}$", "$\\displaystyle \\frac{\\frac{\\frac{11}{2}}{5}+\\frac{-\\frac{9}{2}}{9}}{\\frac{-\\frac{19}{2}}{7}+\\frac{-\\frac{3}{2}}{-3}} = \\frac{\\frac{11}{2}\\cdot\\frac{1}{5}+-\\frac{9}{2}\\cdot\\frac{1}{9}}{-\\frac{19}{2}\\cdot\\frac{1}{7}+-\\frac{3}{2}\\cdot-\\frac{1}{3}} = \\frac{\\frac{11}{10}-\\frac{1}{2}}{-\\frac{19}{14}+\\frac{1}{2}} = \\frac{\\frac{11}{10}-\\frac{5}{10}}{-\\frac{19}{14}+\\frac{7}{14}} = \\frac{\\frac{3}{5}}{-\\frac{6}{7}} = \\frac{3}{5} \\cdot -\\frac{7}{6} = -\\frac{7}{10}$"], ["$\\displaystyle \\frac{\\frac{\\frac{8}{3}}{-4}+\\frac{-\\frac{4}{3}}{3}}{\\frac{-\\frac{8}{3}}{3}+\\frac{\\frac{16}{3}}{-8}}$", "$\\displaystyle \\frac{\\frac{\\frac{8}{3}}{-4}+\\frac{-\\frac{4}{3}}{3}}{\\frac{-\\frac{8}{3}}{3}+\\frac{\\frac{16}{3}}{-8}} = \\frac{\\frac{8}{3}\\cdot-\\frac{1}{4}+-\\frac{4}{3}\\cdot\\frac{1}{3}}{-\\frac{8}{3}\\cdot\\frac{1}{3}+\\frac{16}{3}\\cdot-\\frac{1}{8}} = \\frac{-\\frac{2}{3}-\\frac{4}{9}}{-\\frac{8}{9}-\\frac{2}{3}} = \\frac{-\\frac{6}{9}-\\frac{4}{9}}{-\\frac{8}{9}-\\frac{6}{9}} = \\frac{-\\frac{10}{9}}{-\\frac{14}{9}} = -\\frac{10}{9} \\cdot -\\frac{9}{14} = \\frac{5}{7}$"], ["$\\displaystyle \\frac{\\frac{-5}{\\frac{9}{2}}+\\frac{-\\frac{11}{9}}{-2}}{\\frac{-\\frac{13}{5}}{-2}+\\frac{\\frac{5}{2}}{-5}}$", "$\\displaystyle \\frac{\\frac{-5}{\\frac{9}{2}}+\\frac{-\\frac{11}{9}}{-2}}{\\frac{-\\frac{13}{5}}{-2}+\\frac{\\frac{5}{2}}{-5}} = \\frac{-5\\cdot\\frac{2}{9}+-\\frac{11}{9}\\cdot-\\frac{1}{2}}{-\\frac{13}{5}\\cdot-\\frac{1}{2}+\\frac{5}{2}\\cdot-\\frac{1}{5}} = \\frac{-\\frac{10}{9}+\\frac{11}{18}}{\\frac{13}{10}-\\frac{1}{2}} = \\frac{-\\frac{20}{18}+\\frac{11}{18}}{\\frac{13}{10}-\\frac{5}{10}} = \\frac{-\\frac{1}{2}}{\\frac{4}{5}} = -\\frac{1}{2} \\cdot \\frac{5}{4} = -\\frac{5}{8}$"], ["$\\displaystyle \\frac{\\frac{-6}{-\\frac{13}{2}}+\\frac{-\\frac{18}{13}}{2}}{\\frac{-\\frac{14}{13}}{-2}+\\frac{-2}{\\frac{13}{8}}}$", "$\\displaystyle \\frac{\\frac{-6}{-\\frac{13}{2}}+\\frac{-\\frac{18}{13}}{2}}{\\frac{-\\frac{14}{13}}{-2}+\\frac{-2}{\\frac{13}{8}}} = \\frac{-6\\cdot-\\frac{2}{13}+-\\frac{18}{13}\\cdot\\frac{1}{2}}{-\\frac{14}{13}\\cdot-\\frac{1}{2}+-2\\cdot\\frac{8}{13}} = \\frac{\\frac{12}{13}-\\frac{9}{13}}{\\frac{7}{13}-\\frac{16}{13}} = \\frac{\\frac{12}{13}-\\frac{9}{13}}{\\frac{7}{13}-\\frac{16}{13}} = \\frac{\\frac{3}{13}}{-\\frac{9}{13}} = \\frac{3}{13} \\cdot -\\frac{13}{9} = -\\frac{1}{3}$"], ["$\\displaystyle \\frac{\\frac{\\frac{19}{10}}{2}+\\frac{-\\frac{5}{2}}{5}}{\\frac{-\\frac{19}{2}}{10}+\\frac{\\frac{8}{5}}{8}}$", "$\\displaystyle \\frac{\\frac{\\frac{19}{10}}{2}+\\frac{-\\frac{5}{2}}{5}}{\\frac{-\\frac{19}{2}}{10}+\\frac{\\frac{8}{5}}{8}} = \\frac{\\frac{19}{10}\\cdot\\frac{1}{2}+-\\frac{5}{2}\\cdot\\frac{1}{5}}{-\\frac{19}{2}\\cdot\\frac{1}{10}+\\frac{8}{5}\\cdot\\frac{1}{8}} = \\frac{\\frac{19}{20}-\\frac{1}{2}}{-\\frac{19}{20}+\\frac{1}{5}} = \\frac{\\frac{19}{20}-\\frac{10}{20}}{-\\frac{19}{20}+\\frac{4}{20}} = \\frac{\\frac{9}{20}}{-\\frac{3}{4}} = \\frac{9}{20} \\cdot -\\frac{4}{3} = -\\frac{3}{5}$"], ["$\\displaystyle \\frac{\\frac{-4}{-\\frac{12}{7}}+\\frac{7}{\\frac{21}{4}}}{\\frac{\\frac{13}{3}}{-2}+\\frac{\\frac{7}{2}}{7}}$", "$\\displaystyle \\frac{\\frac{-4}{-\\frac{12}{7}}+\\frac{7}{\\frac{21}{4}}}{\\frac{\\frac{13}{3}}{-2}+\\frac{\\frac{7}{2}}{7}} = \\frac{-4\\cdot-\\frac{7}{12}+7\\cdot\\frac{4}{21}}{\\frac{13}{3}\\cdot-\\frac{1}{2}+\\frac{7}{2}\\cdot\\frac{1}{7}} = \\frac{\\frac{7}{3}+\\frac{4}{3}}{-\\frac{13}{6}+\\frac{1}{2}} = \\frac{\\frac{7}{3}+\\frac{4}{3}}{-\\frac{13}{6}+\\frac{3}{6}} = \\frac{\\frac{11}{3}}{-\\frac{5}{3}} = \\frac{11}{3} \\cdot -\\frac{3}{5} = -\\frac{11}{5}$"], ["$\\displaystyle \\frac{\\frac{\\frac{11}{7}}{-2}+\\frac{-2}{-\\frac{7}{4}}}{\\frac{-\\frac{5}{4}}{-3}+\\frac{-\\frac{5}{3}}{-2}}$", "$\\displaystyle \\frac{\\frac{\\frac{11}{7}}{-2}+\\frac{-2}{-\\frac{7}{4}}}{\\frac{-\\frac{5}{4}}{-3}+\\frac{-\\frac{5}{3}}{-2}} = \\frac{\\frac{11}{7}\\cdot-\\frac{1}{2}+-2\\cdot-\\frac{4}{7}}{-\\frac{5}{4}\\cdot-\\frac{1}{3}+-\\frac{5}{3}\\cdot-\\frac{1}{2}} = \\frac{-\\frac{11}{14}+\\frac{8}{7}}{\\frac{5}{12}+\\frac{5}{6}} = \\frac{-\\frac{11}{14}+\\frac{16}{14}}{\\frac{5}{12}+\\frac{10}{12}} = \\frac{\\frac{5}{14}}{\\frac{5}{4}} = \\frac{5}{14} \\cdot \\frac{4}{5} = \\frac{2}{7}$"]], |