Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

1. \(+\left(\frac{2}{-7}\right) -\left(\frac{4}{-5}\right) -\left(\frac{6}{-7}\right)\)
2. \(-\left(\frac{8}{-3}\right) -\left(\frac{-10}{10}\right) -\left(\frac{11}{-9}\right)\)
3. \(-\left(\frac{-10}{7}\right) -\left(\frac{6}{6}\right) +\left(\frac{-4}{-6}\right)\)
4. \(+\left(\frac{5}{-9}\right) +\left(\frac{3}{8}\right) -\left(\frac{3}{-10}\right)\)
5. \(+\left(\frac{5}{-6}\right) -\left(\frac{6}{8}\right) -\left(\frac{-7}{6}\right)\)
6. \(+\left(\frac{10}{3}\right) +\left(\frac{-2}{9}\right) -\left(\frac{-12}{3}\right)\)
7. \(-\left(\frac{6}{7}\right) +\left(\frac{4}{-10}\right) -\left(\frac{-9}{-4}\right)\)
8. \(+\left(\frac{-10}{-9}\right) +\left(\frac{-2}{5}\right) -\left(\frac{-11}{-12}\right)\)
9. \(+\left(\frac{8}{5}\right) -\left(\frac{9}{8}\right) +\left(\frac{2}{8}\right)\)
10. \(-\left(\frac{-4}{5}\right) +\left(\frac{2}{-8}\right) +\left(\frac{-3}{3}\right)\)
11. \(-\left(\frac{7}{9}\right) +\left(\frac{10}{-9}\right) +\left(\frac{-6}{-12}\right)\)
12. \(-\left(\frac{-7}{-3}\right) -\left(\frac{9}{2}\right) -\left(\frac{-7}{-12}\right)\)

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Bereken

Verbetersleutel

1. \(+\left(\frac{2}{-7}\right) -\left(\frac{4}{-5}\right) -\left(\frac{6}{-7}\right)\\= \frac{-2}{7}+ \frac{4}{5}+\frac{6}{7}\\=\frac{-10}{35}+\frac{28}{35}+\frac{30}{35}\\=\frac{-10+28+30}{35}\\=\frac{48}{35}\)
2. \(-\left(\frac{8}{-3}\right) -\left(\frac{-10}{10}\right) -\left(\frac{11}{-9}\right)\\= \frac{8}{3}+ \frac{10}{10}+\frac{11}{9}\\=\frac{8}{3}+\frac{1}{1}+\frac{11}{9}\\=\frac{24}{9}+\frac{9}{9}+\frac{11}{9}\\=\frac{24+9+11}{9}\\=\frac{44}{9}\)
3. \(-\left(\frac{-10}{7}\right) -\left(\frac{6}{6}\right) +\left(\frac{-4}{-6}\right)\\= \frac{10}{7}- \frac{6}{6}+\frac{4}{6}\\=\frac{10}{7}-\frac{1}{1}+\frac{2}{3}\\=\frac{30}{21}-\frac{21}{21}+\frac{14}{21}\\=\frac{30-21+14}{21}\\=\frac{23}{21}\)
4. \(+\left(\frac{5}{-9}\right) +\left(\frac{3}{8}\right) -\left(\frac{3}{-10}\right)\\= \frac{-5}{9}+ \frac{3}{8}+\frac{3}{10}\\=\frac{-200}{360}+\frac{135}{360}+\frac{108}{360}\\=\frac{-200+135+108}{360}\\=\frac{43}{360}\)
5. \(+\left(\frac{5}{-6}\right) -\left(\frac{6}{8}\right) -\left(\frac{-7}{6}\right)\\= \frac{-5}{6}- \frac{6}{8}+\frac{7}{6}\\=\frac{-5}{6}-\frac{3}{4}+\frac{7}{6}\\=\frac{-10}{12}-\frac{9}{12}+\frac{14}{12}\\=\frac{-10-9+14}{12}\\=\frac{-5}{12}\)
6. \(+\left(\frac{10}{3}\right) +\left(\frac{-2}{9}\right) -\left(\frac{-12}{3}\right)\\= \frac{10}{3}- \frac{2}{9}+\frac{12}{3}\\=\frac{10}{3}-\frac{2}{9}+\frac{4}{1}\\=\frac{30}{9}-\frac{2}{9}+\frac{36}{9}\\=\frac{30-2+36}{9}\\=\frac{64}{9}\)
7. \(-\left(\frac{6}{7}\right) +\left(\frac{4}{-10}\right) -\left(\frac{-9}{-4}\right)\\= \frac{-6}{7}- \frac{4}{10}-\frac{9}{4}\\=\frac{-6}{7}-\frac{2}{5}-\frac{9}{4}\\=\frac{-120}{140}-\frac{56}{140}-\frac{315}{140}\\=\frac{-120-56-315}{140}\\=\frac{-491}{140}\)
8. \(+\left(\frac{-10}{-9}\right) +\left(\frac{-2}{5}\right) -\left(\frac{-11}{-12}\right)\\= \frac{10}{9}- \frac{2}{5}-\frac{11}{12}\\=\frac{200}{180}-\frac{72}{180}-\frac{165}{180}\\=\frac{200-72-165}{180}\\=\frac{-37}{180}\)
9. \(+\left(\frac{8}{5}\right) -\left(\frac{9}{8}\right) +\left(\frac{2}{8}\right)\\= \frac{8}{5}- \frac{9}{8}+\frac{2}{8}\\=\frac{8}{5}-\frac{9}{8}+\frac{1}{4}\\=\frac{64}{40}-\frac{45}{40}+\frac{10}{40}\\=\frac{64-45+10}{40}\\=\frac{29}{40}\)
10. \(-\left(\frac{-4}{5}\right) +\left(\frac{2}{-8}\right) +\left(\frac{-3}{3}\right)\\= \frac{4}{5}- \frac{2}{8}-\frac{3}{3}\\=\frac{4}{5}-\frac{1}{4}-\frac{1}{1}\\=\frac{16}{20}-\frac{5}{20}-\frac{20}{20}\\=\frac{16-5-20}{20}\\=\frac{-9}{20}\)
11. \(-\left(\frac{7}{9}\right) +\left(\frac{10}{-9}\right) +\left(\frac{-6}{-12}\right)\\= \frac{-7}{9}- \frac{10}{9}+\frac{6}{12}\\=\frac{-7}{9}-\frac{10}{9}+\frac{1}{2}\\=\frac{-14}{18}-\frac{20}{18}+\frac{9}{18}\\=\frac{-14-20+9}{18}\\=\frac{-25}{18}\)
12. \(-\left(\frac{-7}{-3}\right) -\left(\frac{9}{2}\right) -\left(\frac{-7}{-12}\right)\\= \frac{-7}{3}- \frac{9}{2}-\frac{7}{12}\\=\frac{-28}{12}-\frac{54}{12}-\frac{7}{12}\\=\frac{-28-54-7}{12}\\=\frac{-89}{12}\)