Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{-7}{2}\right) +\left(\frac{5}{-7}\right) -\left(\frac{-8}{8}\right)\\= \frac{-7}{2}- \frac{5}{7}+\frac{8}{8}\\=\frac{-7}{2}-\frac{5}{7}+\frac{1}{1}\\=\frac{-49}{14}-\frac{10}{14}+\frac{14}{14}\\=\frac{-49-10+14}{14}\\=\frac{-45}{14}\)
2. \(-\left(\frac{-10}{9}\right) +\left(\frac{-9}{-2}\right) -\left(\frac{10}{-4}\right)\\= \frac{10}{9}+ \frac{9}{2}+\frac{10}{4}\\=\frac{10}{9}+\frac{9}{2}+\frac{5}{2}\\=\frac{20}{18}+\frac{81}{18}+\frac{45}{18}\\=\frac{20+81+45}{18}\\=\frac{146}{18}\\=\frac{73}{9}\)
3. \(-\left(\frac{-10}{-9}\right) -\left(\frac{-7}{-3}\right) -\left(\frac{-9}{-9}\right)\\= \frac{-10}{9}- \frac{7}{3}-\frac{9}{9}\\=\frac{-10}{9}-\frac{7}{3}-\frac{1}{1}\\=\frac{-10-7-1}{9}\\=\frac{-18}{9}\\=\frac{-2}{1}\)
4. \(-\left(\frac{-3}{4}\right) -\left(\frac{9}{9}\right) +\left(\frac{-2}{-3}\right)\\= \frac{3}{4}- \frac{9}{9}+\frac{2}{3}\\=\frac{3}{4}-\frac{1}{1}+\frac{2}{3}\\=\frac{9}{12}-\frac{12}{12}+\frac{8}{12}\\=\frac{9-12+8}{12}\\=\frac{5}{12}\)
5. \(-\left(\frac{4}{9}\right) +\left(\frac{-8}{-7}\right) -\left(\frac{4}{-7}\right)\\= \frac{-4}{9}+ \frac{8}{7}+\frac{4}{7}\\=\frac{-28}{63}+\frac{72}{63}+\frac{36}{63}\\=\frac{-28+72+36}{63}\\=\frac{80}{63}\)
6. \(+\left(\frac{2}{-3}\right) -\left(\frac{2}{-9}\right) -\left(\frac{-9}{9}\right)\\= \frac{-2}{3}+ \frac{2}{9}+\frac{9}{9}\\=\frac{-2}{3}+\frac{2}{9}+\frac{1}{1}\\=\frac{-6}{9}+\frac{2}{9}+\frac{9}{9}\\=\frac{-6+2+9}{9}\\=\frac{5}{9}\)
7. \(-\left(\frac{4}{-3}\right) +\left(\frac{-7}{7}\right) -\left(\frac{2}{4}\right)\\= \frac{4}{3}- \frac{7}{7}-\frac{2}{4}\\=\frac{4}{3}-\frac{1}{1}-\frac{1}{2}\\=\frac{8}{6}-\frac{6}{6}-\frac{3}{6}\\=\frac{8-6-3}{6}\\=\frac{-1}{6}\)
8. \(+\left(\frac{6}{7}\right) -\left(\frac{-4}{10}\right) +\left(\frac{-6}{10}\right)\\= \frac{6}{7}+ \frac{4}{10}-\frac{6}{10}\\=\frac{6}{7}+\frac{2}{5}-\frac{3}{5}\\=\frac{30}{35}+\frac{14}{35}-\frac{21}{35}\\=\frac{30+14-21}{35}\\=\frac{23}{35}\)
9. \(-\left(\frac{-7}{8}\right) -\left(\frac{3}{-10}\right) +\left(\frac{-9}{-10}\right)\\= \frac{7}{8}+ \frac{3}{10}+\frac{9}{10}\\=\frac{35}{40}+\frac{12}{40}+\frac{36}{40}\\=\frac{35+12+36}{40}\\=\frac{83}{40}\)
10. \(+\left(\frac{-9}{-2}\right) +\left(\frac{-4}{2}\right) -\left(\frac{-10}{7}\right)\\= \frac{9}{2}- \frac{4}{2}+\frac{10}{7}\\=\frac{9}{2}-\frac{2}{1}+\frac{10}{7}\\=\frac{63}{14}-\frac{28}{14}+\frac{20}{14}\\=\frac{63-28+20}{14}\\=\frac{55}{14}\)
11. \(-\left(\frac{9}{-4}\right) +\left(\frac{-2}{3}\right) -\left(\frac{-5}{4}\right)\\= \frac{9}{4}- \frac{2}{3}+\frac{5}{4}\\=\frac{27}{12}-\frac{8}{12}+\frac{15}{12}\\=\frac{27-8+15}{12}\\=\frac{34}{12}\\=\frac{17}{6}\)
12. \(-\left(\frac{-2}{-9}\right) -\left(\frac{6}{-5}\right) +\left(\frac{-9}{12}\right)\\= \frac{-2}{9}+ \frac{6}{5}-\frac{9}{12}\\=\frac{-2}{9}+\frac{6}{5}-\frac{3}{4}\\=\frac{-40}{180}+\frac{216}{180}-\frac{135}{180}\\=\frac{-40+216-135}{180}\\=\frac{41}{180}\)