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