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