Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{5}{-6}\right) -\left(\frac{10}{7}\right) -\left(\frac{-3}{5}\right)\\= \frac{-5}{6}- \frac{10}{7}+\frac{3}{5}\\=\frac{-175}{210}-\frac{300}{210}+\frac{126}{210}\\=\frac{-175-300+126}{210}\\=\frac{-349}{210}\)
2. \(-\left(\frac{-9}{4}\right) +\left(\frac{5}{-3}\right) +\left(\frac{-2}{-2}\right)\\= \frac{9}{4}- \frac{5}{3}+\frac{2}{2}\\=\frac{9}{4}-\frac{5}{3}+\frac{1}{1}\\=\frac{27}{12}-\frac{20}{12}+\frac{12}{12}\\=\frac{27-20+12}{12}\\=\frac{19}{12}\)
3. \(+\left(\frac{-9}{4}\right) +\left(\frac{4}{-2}\right) +\left(\frac{-2}{3}\right)\\= \frac{-9}{4}- \frac{4}{2}-\frac{2}{3}\\=\frac{-9}{4}-\frac{2}{1}-\frac{2}{3}\\=\frac{-27}{12}-\frac{24}{12}-\frac{8}{12}\\=\frac{-27-24-8}{12}\\=\frac{-59}{12}\)
4. \(+\left(\frac{10}{-7}\right) -\left(\frac{3}{4}\right) -\left(\frac{2}{7}\right)\\= \frac{-10}{7}- \frac{3}{4}-\frac{2}{7}\\=\frac{-40}{28}-\frac{21}{28}-\frac{8}{28}\\=\frac{-40-21-8}{28}\\=\frac{-69}{28}\)
5. \(+\left(\frac{-2}{-9}\right) -\left(\frac{-5}{3}\right) -\left(\frac{5}{2}\right)\\= \frac{2}{9}+ \frac{5}{3}-\frac{5}{2}\\=\frac{4}{18}+\frac{30}{18}-\frac{45}{18}\\=\frac{4+30-45}{18}\\=\frac{-11}{18}\)
6. \(-\left(\frac{-3}{-2}\right) +\left(\frac{8}{-2}\right) -\left(\frac{-7}{10}\right)\\= \frac{-3}{2}- \frac{8}{2}+\frac{7}{10}\\=\frac{-3}{2}-\frac{4}{1}+\frac{7}{10}\\=\frac{-15}{10}-\frac{40}{10}+\frac{7}{10}\\=\frac{-15-40+7}{10}\\=\frac{-48}{10}\\=\frac{-24}{5}\)
7. \(-\left(\frac{5}{-2}\right) -\left(\frac{-3}{-5}\right) +\left(\frac{10}{6}\right)\\= \frac{5}{2}- \frac{3}{5}+\frac{10}{6}\\=\frac{5}{2}-\frac{3}{5}+\frac{5}{3}\\=\frac{75}{30}-\frac{18}{30}+\frac{50}{30}\\=\frac{75-18+50}{30}\\=\frac{107}{30}\)
8. \(+\left(\frac{-4}{5}\right) +\left(\frac{-8}{2}\right) +\left(\frac{-10}{7}\right)\\= \frac{-4}{5}- \frac{8}{2}-\frac{10}{7}\\=\frac{-4}{5}-\frac{4}{1}-\frac{10}{7}\\=\frac{-28}{35}-\frac{140}{35}-\frac{50}{35}\\=\frac{-28-140-50}{35}\\=\frac{-218}{35}\)
9. \(+\left(\frac{-8}{-3}\right) +\left(\frac{8}{-2}\right) -\left(\frac{9}{-6}\right)\\= \frac{8}{3}- \frac{8}{2}+\frac{9}{6}\\=\frac{8}{3}-\frac{4}{1}+\frac{3}{2}\\=\frac{16}{6}-\frac{24}{6}+\frac{9}{6}\\=\frac{16-24+9}{6}\\=\frac{1}{6}\)
10. \(-\left(\frac{-5}{-4}\right) -\left(\frac{-10}{-10}\right) -\left(\frac{-7}{-3}\right)\\= \frac{-5}{4}- \frac{10}{10}-\frac{7}{3}\\=\frac{-5}{4}-\frac{1}{1}-\frac{7}{3}\\=\frac{-15}{12}-\frac{12}{12}-\frac{28}{12}\\=\frac{-15-12-28}{12}\\=\frac{-55}{12}\)
11. \(-\left(\frac{8}{-5}\right) -\left(\frac{-6}{10}\right) -\left(\frac{-9}{-8}\right)\\= \frac{8}{5}+ \frac{6}{10}-\frac{9}{8}\\=\frac{8}{5}+\frac{3}{5}-\frac{9}{8}\\=\frac{64}{40}+\frac{24}{40}-\frac{45}{40}\\=\frac{64+24-45}{40}\\=\frac{43}{40}\)
12. \(-\left(\frac{-9}{-7}\right) +\left(\frac{-5}{3}\right) -\left(\frac{-9}{-4}\right)\\= \frac{-9}{7}- \frac{5}{3}-\frac{9}{4}\\=\frac{-108}{84}-\frac{140}{84}-\frac{189}{84}\\=\frac{-108-140-189}{84}\\=\frac{-437}{84}\)