| Ausrechnen, Resultat als gekürzter Bruch:<JS>miniAufgabe("#exonumbercrunch2","#solnumbercrunch2", | Ausrechnen, Resultat als gekürzter Bruch:<JS>miniAufgabe("#exonumbercrunch2","#solnumbercrunch2", |
| [["$\\displaystyle \\frac{\\frac{-\\frac{15}{7}}{5}+\\frac{\\frac{20}{7}}{-2}}{\\frac{-5}{-\\frac{15}{4}}+\\frac{\\frac{10}{3}}{4}}$", "$\\displaystyle \\frac{\\frac{-\\frac{15}{7}}{5}+\\frac{\\frac{20}{7}}{-2}}{\\frac{-5}{-\\frac{15}{4}}+\\frac{\\frac{10}{3}}{4}} = \\frac{-\\frac{15}{7}\\cdot\\frac{1}{5}+\\frac{20}{7}\\cdot-\\frac{1}{2}}{-5\\cdot-\\frac{4}{15}+\\frac{10}{3}\\cdot\\frac{1}{4}} = \\frac{-\\frac{3}{7}-\\frac{10}{7}}{\\frac{4}{3}+\\frac{5}{6}} = \\frac{\\frac{13}{6}}{-\\frac{13}{7}} = \\frac{13}{6} \\cdot -\\frac{7}{13} = -\\frac{7}{6}$"], ["$\\displaystyle \\frac{\\frac{-\\frac{4}{5}}{-6}+\\frac{-\\frac{16}{15}}{-8}}{\\frac{6}{-\\frac{15}{2}}+\\frac{-\\frac{5}{3}}{-5}}$", "$\\displaystyle \\frac{\\frac{-\\frac{4}{5}}{-6}+\\frac{-\\frac{16}{15}}{-8}}{\\frac{6}{-\\frac{15}{2}}+\\frac{-\\frac{5}{3}}{-5}} = \\frac{-\\frac{4}{5}\\cdot-\\frac{1}{6}+-\\frac{16}{15}\\cdot-\\frac{1}{8}}{6\\cdot-\\frac{2}{15}+-\\frac{5}{3}\\cdot-\\frac{1}{5}} = \\frac{\\frac{2}{15}+\\frac{2}{15}}{-\\frac{4}{5}+\\frac{1}{3}} = \\frac{-\\frac{7}{15}}{\\frac{4}{15}} = -\\frac{7}{15} \\cdot \\frac{15}{4} = -\\frac{7}{4}$"], ["$\\displaystyle \\frac{\\frac{8}{\\frac{20}{7}}+\\frac{\\frac{12}{5}}{-6}}{\\frac{\\frac{11}{5}}{2}+\\frac{-\\frac{7}{5}}{2}}$", "$\\displaystyle \\frac{\\frac{8}{\\frac{20}{7}}+\\frac{\\frac{12}{5}}{-6}}{\\frac{\\frac{11}{5}}{2}+\\frac{-\\frac{7}{5}}{2}} = \\frac{8\\cdot\\frac{7}{20}+\\frac{12}{5}\\cdot-\\frac{1}{6}}{\\frac{11}{5}\\cdot\\frac{1}{2}+-\\frac{7}{5}\\cdot\\frac{1}{2}} = \\frac{\\frac{14}{5}-\\frac{2}{5}}{\\frac{11}{10}-\\frac{7}{10}} = \\frac{\\frac{2}{5}}{\\frac{12}{5}} = \\frac{2}{5} \\cdot \\frac{5}{12} = \\frac{1}{6}$"], ["$\\displaystyle \\frac{\\frac{-\\frac{3}{2}}{-4}+\\frac{-2}{-\\frac{16}{3}}}{\\frac{-\\frac{17}{5}}{-4}+\\frac{-\\frac{5}{2}}{5}}$", "$\\displaystyle \\frac{\\frac{-\\frac{3}{2}}{-4}+\\frac{-2}{-\\frac{16}{3}}}{\\frac{-\\frac{17}{5}}{-4}+\\frac{-\\frac{5}{2}}{5}} = \\frac{-\\frac{3}{2}\\cdot-\\frac{1}{4}+-2\\cdot-\\frac{3}{16}}{-\\frac{17}{5}\\cdot-\\frac{1}{4}+-\\frac{5}{2}\\cdot\\frac{1}{5}} = \\frac{\\frac{3}{8}+\\frac{3}{8}}{\\frac{17}{20}-\\frac{1}{2}} = \\frac{\\frac{7}{20}}{\\frac{3}{4}} = \\frac{7}{20} \\cdot \\frac{4}{3} = \\frac{7}{15}$"], ["$\\displaystyle \\frac{\\frac{-\\frac{13}{3}}{-3}+\\frac{\\frac{17}{3}}{-3}}{\\frac{-\\frac{19}{3}}{-7}+\\frac{\\frac{7}{3}}{-7}}$", "$\\displaystyle \\frac{\\frac{-\\frac{13}{3}}{-3}+\\frac{\\frac{17}{3}}{-3}}{\\frac{-\\frac{19}{3}}{-7}+\\frac{\\frac{7}{3}}{-7}} = \\frac{-\\frac{13}{3}\\cdot-\\frac{1}{3}+\\frac{17}{3}\\cdot-\\frac{1}{3}}{-\\frac{19}{3}\\cdot-\\frac{1}{7}+\\frac{7}{3}\\cdot-\\frac{1}{7}} = \\frac{\\frac{13}{9}-\\frac{17}{9}}{\\frac{19}{21}-\\frac{1}{3}} = \\frac{\\frac{4}{7}}{-\\frac{4}{9}} = \\frac{4}{7} \\cdot -\\frac{9}{4} = -\\frac{9}{7}$"], ["$\\displaystyle \\frac{\\frac{-2}{-\\frac{26}{19}}+\\frac{\\frac{14}{13}}{-2}}{\\frac{-3}{-\\frac{13}{4}}+\\frac{-\\frac{8}{13}}{2}}$", "$\\displaystyle \\frac{\\frac{-2}{-\\frac{26}{19}}+\\frac{\\frac{14}{13}}{-2}}{\\frac{-3}{-\\frac{13}{4}}+\\frac{-\\frac{8}{13}}{2}} = \\frac{-2\\cdot-\\frac{19}{26}+\\frac{14}{13}\\cdot-\\frac{1}{2}}{-3\\cdot-\\frac{4}{13}+-\\frac{8}{13}\\cdot\\frac{1}{2}} = \\frac{\\frac{19}{13}-\\frac{7}{13}}{\\frac{12}{13}-\\frac{4}{13}} = \\frac{\\frac{8}{13}}{\\frac{12}{13}} = \\frac{8}{13} \\cdot \\frac{13}{12} = \\frac{2}{3}$"], ["$\\displaystyle \\frac{\\frac{-\\frac{10}{7}}{-3}+\\frac{\\frac{16}{21}}{-4}}{\\frac{2}{-\\frac{14}{5}}+\\frac{\\frac{15}{7}}{2}}$", "$\\displaystyle \\frac{\\frac{-\\frac{10}{7}}{-3}+\\frac{\\frac{16}{21}}{-4}}{\\frac{2}{-\\frac{14}{5}}+\\frac{\\frac{15}{7}}{2}} = \\frac{-\\frac{10}{7}\\cdot-\\frac{1}{3}+\\frac{16}{21}\\cdot-\\frac{1}{4}}{2\\cdot-\\frac{5}{14}+\\frac{15}{7}\\cdot\\frac{1}{2}} = \\frac{\\frac{10}{21}-\\frac{4}{21}}{-\\frac{5}{7}+\\frac{15}{14}} = \\frac{\\frac{5}{14}}{\\frac{2}{7}} = \\frac{5}{14} \\cdot \\frac{7}{2} = \\frac{5}{4}$"], ["$\\displaystyle \\frac{\\frac{\\frac{13}{2}}{-7}+\\frac{-\\frac{4}{7}}{4}}{\\frac{-3}{-\\frac{9}{2}}+\\frac{8}{-\\frac{16}{3}}}$", "$\\displaystyle \\frac{\\frac{\\frac{13}{2}}{-7}+\\frac{-\\frac{4}{7}}{4}}{\\frac{-3}{-\\frac{9}{2}}+\\frac{8}{-\\frac{16}{3}}} = \\frac{\\frac{13}{2}\\cdot-\\frac{1}{7}+-\\frac{4}{7}\\cdot\\frac{1}{4}}{-3\\cdot-\\frac{2}{9}+8\\cdot-\\frac{3}{16}} = \\frac{-\\frac{13}{14}-\\frac{1}{7}}{\\frac{2}{3}-\\frac{3}{2}} = \\frac{-\\frac{5}{6}}{-\\frac{15}{14}} = -\\frac{5}{6} \\cdot -\\frac{14}{15} = \\frac{7}{9}$"], ["$\\displaystyle \\frac{\\frac{\\frac{7}{3}}{8}+\\frac{-\\frac{5}{3}}{-5}}{\\frac{\\frac{7}{4}}{6}+\\frac{-\\frac{5}{4}}{3}}$", "$\\displaystyle \\frac{\\frac{\\frac{7}{3}}{8}+\\frac{-\\frac{5}{3}}{-5}}{\\frac{\\frac{7}{4}}{6}+\\frac{-\\frac{5}{4}}{3}} = \\frac{\\frac{7}{3}\\cdot\\frac{1}{8}+-\\frac{5}{3}\\cdot-\\frac{1}{5}}{\\frac{7}{4}\\cdot\\frac{1}{6}+-\\frac{5}{4}\\cdot\\frac{1}{3}} = \\frac{\\frac{7}{24}+\\frac{1}{3}}{\\frac{7}{24}-\\frac{5}{12}} = \\frac{-\\frac{1}{8}}{\\frac{5}{8}} = -\\frac{1}{8} \\cdot \\frac{8}{5} = -\\frac{1}{5}$"], ["$\\displaystyle \\frac{\\frac{-2}{-\\frac{19}{8}}+\\frac{\\frac{18}{19}}{-3}}{\\frac{-2}{\\frac{19}{4}}+\\frac{5}{\\frac{19}{2}}}$", "$\\displaystyle \\frac{\\frac{-2}{-\\frac{19}{8}}+\\frac{\\frac{18}{19}}{-3}}{\\frac{-2}{\\frac{19}{4}}+\\frac{5}{\\frac{19}{2}}} = \\frac{-2\\cdot-\\frac{8}{19}+\\frac{18}{19}\\cdot-\\frac{1}{3}}{-2\\cdot\\frac{4}{19}+5\\cdot\\frac{2}{19}} = \\frac{\\frac{16}{19}-\\frac{6}{19}}{-\\frac{8}{19}+\\frac{10}{19}} = \\frac{\\frac{2}{19}}{\\frac{10}{19}} = \\frac{2}{19} \\cdot \\frac{19}{10} = \\frac{1}{5}$"]], | [["$\\displaystyle \\frac{\\frac{\\frac{9}{5}}{6}+\\frac{-2}{\\frac{10}{3}}}{\\frac{-\\frac{11}{3}}{-7}+\\frac{\\frac{8}{7}}{8}}$", "$\\displaystyle \\frac{\\frac{\\frac{9}{5}}{6}+\\frac{-2}{\\frac{10}{3}}}{\\frac{-\\frac{11}{3}}{-7}+\\frac{\\frac{8}{7}}{8}} = \\frac{\\frac{9}{5}\\cdot\\frac{1}{6}+-2\\cdot\\frac{3}{10}}{-\\frac{11}{3}\\cdot-\\frac{1}{7}+\\frac{8}{7}\\cdot\\frac{1}{8}} = \\frac{\\frac{3}{10}-\\frac{3}{5}}{\\frac{11}{21}+\\frac{1}{7}} = \\frac{\\frac{3}{10}-\\frac{6}{10}{\\frac{11}{21}+\\frac{3}{21}} = \\frac{-\\frac{3}{10}}{\\frac{2}{3}} = -\\frac{3}{10} \\cdot \\frac{3}{2} = -\\frac{9}{20}$"], ["$\\displaystyle \\frac{\\frac{-2}{\\frac{26}{19}}+\\frac{2}{\\frac{26}{17}}}{\\frac{-\\frac{16}{13}}{4}+\\frac{7}{\\frac{13}{2}}}$", "$\\displaystyle \\frac{\\frac{-2}{\\frac{26}{19}}+\\frac{2}{\\frac{26}{17}}}{\\frac{-\\frac{16}{13}}{4}+\\frac{7}{\\frac{13}{2}}} = \\frac{-2\\cdot\\frac{19}{26}+2\\cdot\\frac{17}{26}}{-\\frac{16}{13}\\cdot\\frac{1}{4}+7\\cdot\\frac{2}{13}} = \\frac{-\\frac{19}{13}+\\frac{17}{13}}{-\\frac{4}{13}+\\frac{14}{13}} = \\frac{-\\frac{19}{13}+\\frac{17}{13}{-\\frac{4}{13}+\\frac{14}{13}} = \\frac{-\\frac{2}{13}}{\\frac{10}{13}} = -\\frac{2}{13} \\cdot \\frac{13}{10} = -\\frac{1}{5}$"], ["$\\displaystyle \\frac{\\frac{-3}{-\\frac{19}{4}}+\\frac{-\\frac{12}{19}}{3}}{\\frac{-8}{-\\frac{15}{2}}+\\frac{-\\frac{18}{5}}{9}}$", "$\\displaystyle \\frac{\\frac{-3}{-\\frac{19}{4}}+\\frac{-\\frac{12}{19}}{3}}{\\frac{-8}{-\\frac{15}{2}}+\\frac{-\\frac{18}{5}}{9}} = \\frac{-3\\cdot-\\frac{4}{19}+-\\frac{12}{19}\\cdot\\frac{1}{3}}{-8\\cdot-\\frac{2}{15}+-\\frac{18}{5}\\cdot\\frac{1}{9}} = \\frac{\\frac{12}{19}-\\frac{4}{19}}{\\frac{16}{15}-\\frac{2}{5}} = \\frac{\\frac{12}{19}-\\frac{4}{19}{\\frac{16}{15}-\\frac{6}{15}} = \\frac{\\frac{8}{19}}{\\frac{2}{3}} = \\frac{8}{19} \\cdot \\frac{3}{2} = \\frac{12}{19}$"], ["$\\displaystyle \\frac{\\frac{-\\frac{18}{17}}{-6}+\\frac{-\\frac{14}{17}}{-7}}{\\frac{\\frac{5}{2}}{6}+\\frac{2}{\\frac{8}{5}}}$", "$\\displaystyle \\frac{\\frac{-\\frac{18}{17}}{-6}+\\frac{-\\frac{14}{17}}{-7}}{\\frac{\\frac{5}{2}}{6}+\\frac{2}{\\frac{8}{5}}} = \\frac{-\\frac{18}{17}\\cdot-\\frac{1}{6}+-\\frac{14}{17}\\cdot-\\frac{1}{7}}{\\frac{5}{2}\\cdot\\frac{1}{6}+2\\cdot\\frac{5}{8}} = \\frac{\\frac{3}{17}+\\frac{2}{17}}{\\frac{5}{12}+\\frac{5}{4}} = \\frac{\\frac{3}{17}+\\frac{2}{17}{\\frac{5}{12}+\\frac{15}{12}} = \\frac{\\frac{5}{17}}{\\frac{5}{3}} = \\frac{5}{17} \\cdot \\frac{3}{5} = \\frac{3}{17}$"], ["$\\displaystyle \\frac{\\frac{\\frac{11}{8}}{-3}+\\frac{\\frac{3}{4}}{6}}{\\frac{\\frac{3}{4}}{5}+\\frac{-\\frac{2}{5}}{-4}}$", "$\\displaystyle \\frac{\\frac{\\frac{11}{8}}{-3}+\\frac{\\frac{3}{4}}{6}}{\\frac{\\frac{3}{4}}{5}+\\frac{-\\frac{2}{5}}{-4}} = \\frac{\\frac{11}{8}\\cdot-\\frac{1}{3}+\\frac{3}{4}\\cdot\\frac{1}{6}}{\\frac{3}{4}\\cdot\\frac{1}{5}+-\\frac{2}{5}\\cdot-\\frac{1}{4}} = \\frac{-\\frac{11}{24}+\\frac{1}{8}}{\\frac{3}{20}+\\frac{1}{10}} = \\frac{-\\frac{11}{24}+\\frac{3}{24}{\\frac{3}{20}+\\frac{2}{20}} = \\frac{-\\frac{1}{3}}{\\frac{1}{4}} = -\\frac{1}{3} \\cdot 4 = -\\frac{4}{3}$"], ["$\\displaystyle \\frac{\\frac{-\\frac{19}{4}}{4}+\\frac{\\frac{13}{8}}{2}}{\\frac{\\frac{15}{8}}{-6}+\\frac{-\\frac{3}{2}}{3}}$", "$\\displaystyle \\frac{\\frac{-\\frac{19}{4}}{4}+\\frac{\\frac{13}{8}}{2}}{\\frac{\\frac{15}{8}}{-6}+\\frac{-\\frac{3}{2}}{3}} = \\frac{-\\frac{19}{4}\\cdot\\frac{1}{4}+\\frac{13}{8}\\cdot\\frac{1}{2}}{\\frac{15}{8}\\cdot-\\frac{1}{6}+-\\frac{3}{2}\\cdot\\frac{1}{3}} = \\frac{-\\frac{19}{16}+\\frac{13}{16}}{-\\frac{5}{16}-\\frac{1}{2}} = \\frac{-\\frac{19}{16}+\\frac{13}{16}{-\\frac{5}{16}-\\frac{8}{16}} = \\frac{-\\frac{3}{8}}{-\\frac{13}{16}} = -\\frac{3}{8} \\cdot -\\frac{16}{13} = \\frac{6}{13}$"], ["$\\displaystyle \\frac{\\frac{7}{-\\frac{9}{2}}+\\frac{-\\frac{7}{3}}{-3}}{\\frac{\\frac{10}{3}}{-6}+\\frac{-4}{\\frac{9}{2}}}$", "$\\displaystyle \\frac{\\frac{7}{-\\frac{9}{2}}+\\frac{-\\frac{7}{3}}{-3}}{\\frac{\\frac{10}{3}}{-6}+\\frac{-4}{\\frac{9}{2}}} = \\frac{7\\cdot-\\frac{2}{9}+-\\frac{7}{3}\\cdot-\\frac{1}{3}}{\\frac{10}{3}\\cdot-\\frac{1}{6}+-4\\cdot\\frac{2}{9}} = \\frac{-\\frac{14}{9}+\\frac{7}{9}}{-\\frac{5}{9}-\\frac{8}{9}} = \\frac{-\\frac{14}{9}+\\frac{7}{9}{-\\frac{5}{9}-\\frac{8}{9}} = \\frac{-\\frac{7}{9}}{-\\frac{13}{9}} = -\\frac{7}{9} \\cdot -\\frac{9}{13} = \\frac{7}{13}$"], ["$\\displaystyle \\frac{\\frac{-\\frac{14}{3}}{6}+\\frac{\\frac{2}{3}}{4}}{\\frac{-2}{\\frac{12}{17}}+\\frac{2}{\\frac{4}{5}}}$", "$\\displaystyle \\frac{\\frac{-\\frac{14}{3}}{6}+\\frac{\\frac{2}{3}}{4}}{\\frac{-2}{\\frac{12}{17}}+\\frac{2}{\\frac{4}{5}}} = \\frac{-\\frac{14}{3}\\cdot\\frac{1}{6}+\\frac{2}{3}\\cdot\\frac{1}{4}}{-2\\cdot\\frac{17}{12}+2\\cdot\\frac{5}{4}} = \\frac{-\\frac{7}{9}+\\frac{1}{6}}{-\\frac{17}{6}+\\frac{5}{2}} = \\frac{-\\frac{14}{18}+\\frac{3}{18}{-\\frac{17}{6}+\\frac{15}{6}} = \\frac{-\\frac{11}{18}}{-\\frac{1}{3}} = -\\frac{11}{18} \\cdot -3 = \\frac{11}{6}$"], ["$\\displaystyle \\frac{\\frac{-\\frac{34}{19}}{-2}+\\frac{-3}{\\frac{19}{5}}}{\\frac{\\frac{8}{5}}{6}+\\frac{\\frac{18}{5}}{-9}}$", "$\\displaystyle \\frac{\\frac{-\\frac{34}{19}}{-2}+\\frac{-3}{\\frac{19}{5}}}{\\frac{\\frac{8}{5}}{6}+\\frac{\\frac{18}{5}}{-9}} = \\frac{-\\frac{34}{19}\\cdot-\\frac{1}{2}+-3\\cdot\\frac{5}{19}}{\\frac{8}{5}\\cdot\\frac{1}{6}+\\frac{18}{5}\\cdot-\\frac{1}{9}} = \\frac{\\frac{17}{19}-\\frac{15}{19}}{\\frac{4}{15}-\\frac{2}{5}} = \\frac{\\frac{17}{19}-\\frac{15}{19}{\\frac{4}{15}-\\frac{6}{15}} = \\frac{\\frac{2}{19}}{-\\frac{2}{15}} = \\frac{2}{19} \\cdot -\\frac{15}{2} = -\\frac{15}{19}$"], ["$\\displaystyle \\frac{\\frac{-4}{-\\frac{18}{7}}+\\frac{\\frac{16}{3}}{-6}}{\\frac{-2}{-\\frac{6}{5}}+\\frac{-3}{-\\frac{9}{2}}}$", "$\\displaystyle \\frac{\\frac{-4}{-\\frac{18}{7}}+\\frac{\\frac{16}{3}}{-6}}{\\frac{-2}{-\\frac{6}{5}}+\\frac{-3}{-\\frac{9}{2}}} = \\frac{-4\\cdot-\\frac{7}{18}+\\frac{16}{3}\\cdot-\\frac{1}{6}}{-2\\cdot-\\frac{5}{6}+-3\\cdot-\\frac{2}{9}} = \\frac{\\frac{14}{9}-\\frac{8}{9}}{\\frac{5}{3}+\\frac{2}{3}} = \\frac{\\frac{14}{9}-\\frac{8}{9}{\\frac{5}{3}+\\frac{2}{3}} = \\frac{\\frac{2}{3}}{\\frac{7}{3}} = \\frac{2}{3} \\cdot \\frac{3}{7} = \\frac{2}{7}$"]], |