Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-9}{-4}\right) -\left(\frac{3}{-4}\right) -\left(\frac{2}{-2}\right)\\= \frac{9}{4}+ \frac{3}{4}+\frac{2}{2}\\=\frac{9}{4}+\frac{3}{4}+\frac{1}{1}\\=\frac{9+3+1}{4}\\=\frac{13}{4}\)
2. \(-\left(\frac{3}{4}\right) -\left(\frac{2}{2}\right) +\left(\frac{4}{-5}\right)\\= \frac{-3}{4}- \frac{2}{2}-\frac{4}{5}\\=\frac{-3}{4}-\frac{1}{1}-\frac{4}{5}\\=\frac{-15}{20}-\frac{20}{20}-\frac{16}{20}\\=\frac{-15-20-16}{20}\\=\frac{-51}{20}\)
3. \(+\left(\frac{9}{-8}\right) -\left(\frac{4}{3}\right) -\left(\frac{3}{-9}\right)\\= \frac{-9}{8}- \frac{4}{3}+\frac{3}{9}\\=\frac{-9}{8}-\frac{4}{3}+\frac{1}{3}\\=\frac{-27}{24}-\frac{32}{24}+\frac{8}{24}\\=\frac{-27-32+8}{24}\\=\frac{-51}{24}\\=\frac{-17}{8}\)
4. \(-\left(\frac{-4}{3}\right) -\left(\frac{-6}{2}\right) -\left(\frac{-8}{-11}\right)\\= \frac{4}{3}+ \frac{6}{2}-\frac{8}{11}\\=\frac{4}{3}+\frac{3}{1}-\frac{8}{11}\\=\frac{44}{33}+\frac{99}{33}-\frac{24}{33}\\=\frac{44+99-24}{33}\\=\frac{119}{33}\)
5. \(+\left(\frac{-5}{2}\right) +\left(\frac{-9}{-10}\right) +\left(\frac{4}{7}\right)\\= \frac{-5}{2}+ \frac{9}{10}+\frac{4}{7}\\=\frac{-175}{70}+\frac{63}{70}+\frac{40}{70}\\=\frac{-175+63+40}{70}\\=\frac{-72}{70}\\=\frac{-36}{35}\)
6. \(+\left(\frac{3}{2}\right) +\left(\frac{2}{-6}\right) -\left(\frac{7}{-9}\right)\\= \frac{3}{2}- \frac{2}{6}+\frac{7}{9}\\=\frac{3}{2}-\frac{1}{3}+\frac{7}{9}\\=\frac{27}{18}-\frac{6}{18}+\frac{14}{18}\\=\frac{27-6+14}{18}\\=\frac{35}{18}\)
7. \(+\left(\frac{-9}{8}\right) -\left(\frac{9}{5}\right) +\left(\frac{-8}{-10}\right)\\= \frac{-9}{8}- \frac{9}{5}+\frac{8}{10}\\=\frac{-9}{8}-\frac{9}{5}+\frac{4}{5}\\=\frac{-45}{40}-\frac{72}{40}+\frac{32}{40}\\=\frac{-45-72+32}{40}\\=\frac{-85}{40}\\=\frac{-17}{8}\)
8. \(+\left(\frac{8}{-7}\right) +\left(\frac{3}{-6}\right) +\left(\frac{-9}{-2}\right)\\= \frac{-8}{7}- \frac{3}{6}+\frac{9}{2}\\=\frac{-8}{7}-\frac{1}{2}+\frac{9}{2}\\=\frac{-16}{14}-\frac{7}{14}+\frac{63}{14}\\=\frac{-16-7+63}{14}\\=\frac{40}{14}\\=\frac{20}{7}\)
9. \(-\left(\frac{-7}{-2}\right) -\left(\frac{3}{-10}\right) -\left(\frac{8}{8}\right)\\= \frac{-7}{2}+ \frac{3}{10}-\frac{8}{8}\\=\frac{-7}{2}+\frac{3}{10}-\frac{1}{1}\\=\frac{-35}{10}+\frac{3}{10}-\frac{10}{10}\\=\frac{-35+3-10}{10}\\=\frac{-42}{10}\\=\frac{-21}{5}\)
10. \(-\left(\frac{-6}{-5}\right) -\left(\frac{9}{-4}\right) -\left(\frac{-10}{12}\right)\\= \frac{-6}{5}+ \frac{9}{4}+\frac{10}{12}\\=\frac{-6}{5}+\frac{9}{4}+\frac{5}{6}\\=\frac{-72}{60}+\frac{135}{60}+\frac{50}{60}\\=\frac{-72+135+50}{60}\\=\frac{113}{60}\)
11. \(+\left(\frac{6}{5}\right) -\left(\frac{-4}{3}\right) -\left(\frac{10}{-3}\right)\\= \frac{6}{5}+ \frac{4}{3}+\frac{10}{3}\\=\frac{18}{15}+\frac{20}{15}+\frac{50}{15}\\=\frac{18+20+50}{15}\\=\frac{88}{15}\)
12. \(+\left(\frac{-9}{-7}\right) +\left(\frac{-8}{6}\right) +\left(\frac{3}{-3}\right)\\= \frac{9}{7}- \frac{8}{6}-\frac{3}{3}\\=\frac{9}{7}-\frac{4}{3}-\frac{1}{1}\\=\frac{27}{21}-\frac{28}{21}-\frac{21}{21}\\=\frac{27-28-21}{21}\\=\frac{-22}{21}\)