Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{-7}{8}\right) +\left(\frac{-3}{-7}\right) -\left(\frac{-4}{-11}\right)\\= \frac{7}{8}+ \frac{3}{7}-\frac{4}{11}\\=\frac{539}{616}+\frac{264}{616}-\frac{224}{616}\\=\frac{539+264-224}{616}\\=\frac{579}{616}\)
2. \(+\left(\frac{4}{-3}\right) +\left(\frac{-8}{10}\right) -\left(\frac{-11}{10}\right)\\= \frac{-4}{3}- \frac{8}{10}+\frac{11}{10}\\=\frac{-4}{3}-\frac{4}{5}+\frac{11}{10}\\=\frac{-40}{30}-\frac{24}{30}+\frac{33}{30}\\=\frac{-40-24+33}{30}\\=\frac{-31}{30}\)
3. \(-\left(\frac{10}{3}\right) -\left(\frac{-9}{-6}\right) +\left(\frac{2}{-2}\right)\\= \frac{-10}{3}- \frac{9}{6}-\frac{2}{2}\\=\frac{-10}{3}-\frac{3}{2}-\frac{1}{1}\\=\frac{-20}{6}-\frac{9}{6}-\frac{6}{6}\\=\frac{-20-9-6}{6}\\=\frac{-35}{6}\)
4. \(-\left(\frac{-10}{9}\right) +\left(\frac{2}{9}\right) +\left(\frac{-6}{3}\right)\\= \frac{10}{9}+ \frac{2}{9}-\frac{6}{3}\\=\frac{10}{9}+\frac{2}{9}-\frac{2}{1}\\=\frac{10+2-2}{9}\\=\frac{10}{9}\)
5. \(-\left(\frac{-5}{6}\right) +\left(\frac{-2}{3}\right) -\left(\frac{2}{-3}\right)\\= \frac{5}{6}- \frac{2}{3}+\frac{2}{3}\\=\frac{5-2+2}{6}\\=\frac{5}{6}\)
6. \(-\left(\frac{-2}{-9}\right) -\left(\frac{-2}{4}\right) -\left(\frac{-11}{-4}\right)\\= \frac{-2}{9}+ \frac{2}{4}-\frac{11}{4}\\=\frac{-2}{9}+\frac{1}{2}-\frac{11}{4}\\=\frac{-8}{36}+\frac{18}{36}-\frac{99}{36}\\=\frac{-8+18-99}{36}\\=\frac{-89}{36}\)
7. \(+\left(\frac{8}{-9}\right) +\left(\frac{-7}{-9}\right) -\left(\frac{-5}{3}\right)\\= \frac{-8}{9}+ \frac{7}{9}+\frac{5}{3}\\=\frac{-8+7+5}{9}\\=\frac{4}{9}\)
8. \(-\left(\frac{3}{-7}\right) +\left(\frac{-10}{-9}\right) +\left(\frac{6}{-8}\right)\\= \frac{3}{7}+ \frac{10}{9}-\frac{6}{8}\\=\frac{3}{7}+\frac{10}{9}-\frac{3}{4}\\=\frac{108}{252}+\frac{280}{252}-\frac{189}{252}\\=\frac{108+280-189}{252}\\=\frac{199}{252}\)
9. \(+\left(\frac{8}{-3}\right) +\left(\frac{-2}{-7}\right) +\left(\frac{3}{5}\right)\\= \frac{-8}{3}+ \frac{2}{7}+\frac{3}{5}\\=\frac{-280}{105}+\frac{30}{105}+\frac{63}{105}\\=\frac{-280+30+63}{105}\\=\frac{-187}{105}\)
10. \(-\left(\frac{6}{-5}\right) +\left(\frac{-7}{-6}\right) +\left(\frac{2}{3}\right)\\= \frac{6}{5}+ \frac{7}{6}+\frac{2}{3}\\=\frac{36}{30}+\frac{35}{30}+\frac{20}{30}\\=\frac{36+35+20}{30}\\=\frac{91}{30}\)
11. \(+\left(\frac{-4}{5}\right) +\left(\frac{-4}{-2}\right) -\left(\frac{12}{-12}\right)\\= \frac{-4}{5}+ \frac{4}{2}+\frac{12}{12}\\=\frac{-4}{5}+\frac{2}{1}+\frac{1}{1}\\=\frac{-4+2+1}{5}\\=\frac{-1}{5}\)
12. \(-\left(\frac{3}{2}\right) +\left(\frac{5}{-2}\right) -\left(\frac{-5}{3}\right)\\= \frac{-3}{2}- \frac{5}{2}+\frac{5}{3}\\=\frac{-9}{6}-\frac{15}{6}+\frac{10}{6}\\=\frac{-9-15+10}{6}\\=\frac{-14}{6}\\=\frac{-7}{3}\)