Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{9}{-7}\right) -\left(\frac{4}{2}\right) +\left(\frac{-3}{-6}\right)\\= \frac{9}{7}- \frac{4}{2}+\frac{3}{6}\\=\frac{9}{7}-\frac{2}{1}+\frac{1}{2}\\=\frac{18}{14}-\frac{28}{14}+\frac{7}{14}\\=\frac{18-28+7}{14}\\=\frac{-3}{14}\)
2. \(-\left(\frac{-4}{3}\right) -\left(\frac{-2}{-3}\right) +\left(\frac{3}{6}\right)\\= \frac{4}{3}- \frac{2}{3}+\frac{3}{6}\\=\frac{4}{3}-\frac{2}{3}+\frac{1}{2}\\=\frac{8}{6}-\frac{4}{6}+\frac{3}{6}\\=\frac{8-4+3}{6}\\=\frac{7}{6}\)
3. \(+\left(\frac{-3}{2}\right) +\left(\frac{4}{-4}\right) +\left(\frac{12}{-10}\right)\\= \frac{-3}{2}- \frac{4}{4}-\frac{12}{10}\\=\frac{-3}{2}-\frac{1}{1}-\frac{6}{5}\\=\frac{-15}{10}-\frac{10}{10}-\frac{12}{10}\\=\frac{-15-10-12}{10}\\=\frac{-37}{10}\)
4. \(-\left(\frac{-9}{4}\right) -\left(\frac{10}{-4}\right) +\left(\frac{-10}{6}\right)\\= \frac{9}{4}+ \frac{10}{4}-\frac{10}{6}\\=\frac{9}{4}+\frac{5}{2}-\frac{5}{3}\\=\frac{27}{12}+\frac{30}{12}-\frac{20}{12}\\=\frac{27+30-20}{12}\\=\frac{37}{12}\)
5. \(+\left(\frac{10}{3}\right) -\left(\frac{-6}{-9}\right) +\left(\frac{-6}{-7}\right)\\= \frac{10}{3}- \frac{6}{9}+\frac{6}{7}\\=\frac{10}{3}-\frac{2}{3}+\frac{6}{7}\\=\frac{70}{21}-\frac{14}{21}+\frac{18}{21}\\=\frac{70-14+18}{21}\\=\frac{74}{21}\)
6. \(-\left(\frac{7}{8}\right) -\left(\frac{-9}{5}\right) -\left(\frac{5}{-8}\right)\\= \frac{-7}{8}+ \frac{9}{5}+\frac{5}{8}\\=\frac{-35}{40}+\frac{72}{40}+\frac{25}{40}\\=\frac{-35+72+25}{40}\\=\frac{62}{40}\\=\frac{31}{20}\)
7. \(+\left(\frac{3}{4}\right) +\left(\frac{8}{6}\right) -\left(\frac{10}{-3}\right)\\= \frac{3}{4}+ \frac{8}{6}+\frac{10}{3}\\=\frac{3}{4}+\frac{4}{3}+\frac{10}{3}\\=\frac{9}{12}+\frac{16}{12}+\frac{40}{12}\\=\frac{9+16+40}{12}\\=\frac{65}{12}\)
8. \(+\left(\frac{-4}{3}\right) +\left(\frac{-5}{5}\right) +\left(\frac{-5}{-10}\right)\\= \frac{-4}{3}- \frac{5}{5}+\frac{5}{10}\\=\frac{-4}{3}-\frac{1}{1}+\frac{1}{2}\\=\frac{-8}{6}-\frac{6}{6}+\frac{3}{6}\\=\frac{-8-6+3}{6}\\=\frac{-11}{6}\)
9. \(-\left(\frac{-10}{9}\right) -\left(\frac{9}{-6}\right) +\left(\frac{-9}{6}\right)\\= \frac{10}{9}+ \frac{9}{6}-\frac{9}{6}\\=\frac{10}{9}+\frac{3}{2}-\frac{3}{2}\\=\frac{20}{18}+\frac{27}{18}-\frac{27}{18}\\=\frac{20+27-27}{18}\\=\frac{20}{18}\\=\frac{10}{9}\)
10. \(-\left(\frac{-7}{-3}\right) +\left(\frac{-6}{-3}\right) -\left(\frac{8}{-8}\right)\\= \frac{-7}{3}+ \frac{6}{3}+\frac{8}{8}\\=\frac{-7}{3}+\frac{2}{1}+\frac{1}{1}\\=\frac{-7+2+1}{3}\\=\frac{-4}{3}\)
11. \(+\left(\frac{-5}{9}\right) +\left(\frac{7}{-5}\right) -\left(\frac{12}{-12}\right)\\= \frac{-5}{9}- \frac{7}{5}+\frac{12}{12}\\=\frac{-5}{9}-\frac{7}{5}+\frac{1}{1}\\=\frac{-25}{45}-\frac{63}{45}+\frac{45}{45}\\=\frac{-25-63+45}{45}\\=\frac{-43}{45}\)
12. \(-\left(\frac{-2}{7}\right) +\left(\frac{-7}{3}\right) -\left(\frac{7}{9}\right)\\= \frac{2}{7}- \frac{7}{3}-\frac{7}{9}\\=\frac{18}{63}-\frac{147}{63}-\frac{49}{63}\\=\frac{18-147-49}{63}\\=\frac{-178}{63}\)