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