Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{7}{-2}\right) +\left(\frac{-9}{-4}\right) -\left(\frac{-10}{-5}\right)\\= \frac{-7}{2}+ \frac{9}{4}-\frac{10}{5}\\=\frac{-7}{2}+\frac{9}{4}-\frac{2}{1}\\=\frac{-14}{4}+\frac{9}{4}-\frac{8}{4}\\=\frac{-14+9-8}{4}\\=\frac{-13}{4}\)
2. \(-\left(\frac{5}{-6}\right) -\left(\frac{-7}{-7}\right) +\left(\frac{3}{-3}\right)\\= \frac{5}{6}- \frac{7}{7}-\frac{3}{3}\\=\frac{5}{6}-\frac{1}{1}-\frac{1}{1}\\=\frac{5-1-1}{6}\\=\frac{3}{6}\\=\frac{1}{2}\)
3. \(-\left(\frac{-4}{-3}\right) +\left(\frac{2}{9}\right) -\left(\frac{4}{-7}\right)\\= \frac{-4}{3}+ \frac{2}{9}+\frac{4}{7}\\=\frac{-84}{63}+\frac{14}{63}+\frac{36}{63}\\=\frac{-84+14+36}{63}\\=\frac{-34}{63}\)
4. \(-\left(\frac{8}{5}\right) +\left(\frac{4}{-9}\right) -\left(\frac{8}{11}\right)\\= \frac{-8}{5}- \frac{4}{9}-\frac{8}{11}\\=\frac{-792}{495}-\frac{220}{495}-\frac{360}{495}\\=\frac{-792-220-360}{495}\\=\frac{-1372}{495}\)
5. \(+\left(\frac{4}{-3}\right) -\left(\frac{-8}{6}\right) -\left(\frac{6}{6}\right)\\= \frac{-4}{3}+ \frac{8}{6}-\frac{6}{6}\\=\frac{-4}{3}+\frac{4}{3}-\frac{1}{1}\\=\frac{-4+4-1}{3}\\=\frac{-1}{3}\)
6. \(+\left(\frac{-9}{-2}\right) +\left(\frac{9}{2}\right) -\left(\frac{-5}{-3}\right)\\= \frac{9}{2}+ \frac{9}{2}-\frac{5}{3}\\=\frac{27}{6}+\frac{27}{6}-\frac{10}{6}\\=\frac{27+27-10}{6}\\=\frac{44}{6}\\=\frac{22}{3}\)
7. \(+\left(\frac{10}{-3}\right) +\left(\frac{-7}{6}\right) +\left(\frac{3}{-6}\right)\\= \frac{-10}{3}- \frac{7}{6}-\frac{3}{6}\\=\frac{-10}{3}-\frac{7}{6}-\frac{1}{2}\\=\frac{-20}{6}-\frac{7}{6}-\frac{3}{6}\\=\frac{-20-7-3}{6}\\=\frac{-30}{6}\\=\frac{-5}{1}\)
8. \(+\left(\frac{-3}{-7}\right) -\left(\frac{5}{9}\right) +\left(\frac{-4}{9}\right)\\= \frac{3}{7}- \frac{5}{9}-\frac{4}{9}\\=\frac{27}{63}-\frac{35}{63}-\frac{28}{63}\\=\frac{27-35-28}{63}\\=\frac{-36}{63}\\=\frac{-4}{7}\)
9. \(+\left(\frac{-10}{7}\right) +\left(\frac{3}{2}\right) +\left(\frac{5}{8}\right)\\= \frac{-10}{7}+ \frac{3}{2}+\frac{5}{8}\\=\frac{-80}{56}+\frac{84}{56}+\frac{35}{56}\\=\frac{-80+84+35}{56}\\=\frac{39}{56}\)
10. \(-\left(\frac{10}{-3}\right) -\left(\frac{-2}{5}\right) +\left(\frac{6}{-11}\right)\\= \frac{10}{3}+ \frac{2}{5}-\frac{6}{11}\\=\frac{550}{165}+\frac{66}{165}-\frac{90}{165}\\=\frac{550+66-90}{165}\\=\frac{526}{165}\)
11. \(+\left(\frac{-7}{-2}\right) +\left(\frac{10}{-7}\right) -\left(\frac{-5}{3}\right)\\= \frac{7}{2}- \frac{10}{7}+\frac{5}{3}\\=\frac{147}{42}-\frac{60}{42}+\frac{70}{42}\\=\frac{147-60+70}{42}\\=\frac{157}{42}\)
12. \(+\left(\frac{-8}{5}\right) -\left(\frac{-4}{-2}\right) +\left(\frac{12}{2}\right)\\= \frac{-8}{5}- \frac{4}{2}+\frac{12}{2}\\=\frac{-8}{5}-\frac{2}{1}+\frac{6}{1}\\=\frac{-8-2+6}{5}\\=\frac{-4}{5}\)