Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{-7}\right) +\left(\frac{-4}{-2}\right) -\left(\frac{12}{12}\right)\\= \frac{-10}{7}+ \frac{4}{2}-\frac{12}{12}\\=\frac{-10}{7}+\frac{2}{1}-\frac{1}{1}\\=\frac{-10+2-1}{7}\\=\frac{-9}{7}\)
2. \(-\left(\frac{7}{-3}\right) -\left(\frac{6}{-10}\right) +\left(\frac{-6}{8}\right)\\= \frac{7}{3}+ \frac{6}{10}-\frac{6}{8}\\=\frac{7}{3}+\frac{3}{5}-\frac{3}{4}\\=\frac{140}{60}+\frac{36}{60}-\frac{45}{60}\\=\frac{140+36-45}{60}\\=\frac{131}{60}\)
3. \(-\left(\frac{-2}{-5}\right) +\left(\frac{-7}{2}\right) +\left(\frac{-4}{-12}\right)\\= \frac{-2}{5}- \frac{7}{2}+\frac{4}{12}\\=\frac{-2}{5}-\frac{7}{2}+\frac{1}{3}\\=\frac{-12}{30}-\frac{105}{30}+\frac{10}{30}\\=\frac{-12-105+10}{30}\\=\frac{-107}{30}\)
4. \(-\left(\frac{-6}{5}\right) -\left(\frac{8}{10}\right) +\left(\frac{-3}{10}\right)\\= \frac{6}{5}- \frac{8}{10}-\frac{3}{10}\\=\frac{6}{5}-\frac{4}{5}-\frac{3}{10}\\=\frac{12}{10}-\frac{8}{10}-\frac{3}{10}\\=\frac{12-8-3}{10}\\=\frac{1}{10}\)
5. \(-\left(\frac{5}{4}\right) +\left(\frac{-4}{4}\right) +\left(\frac{8}{-5}\right)\\= \frac{-5}{4}- \frac{4}{4}-\frac{8}{5}\\=\frac{-5}{4}-\frac{1}{1}-\frac{8}{5}\\=\frac{-25}{20}-\frac{20}{20}-\frac{32}{20}\\=\frac{-25-20-32}{20}\\=\frac{-77}{20}\)
6. \(-\left(\frac{-8}{3}\right) +\left(\frac{-8}{-2}\right) +\left(\frac{2}{-11}\right)\\= \frac{8}{3}+ \frac{8}{2}-\frac{2}{11}\\=\frac{8}{3}+\frac{4}{1}-\frac{2}{11}\\=\frac{88}{33}+\frac{132}{33}-\frac{6}{33}\\=\frac{88+132-6}{33}\\=\frac{214}{33}\)
7. \(+\left(\frac{2}{-3}\right) -\left(\frac{6}{6}\right) -\left(\frac{4}{4}\right)\\= \frac{-2}{3}- \frac{6}{6}-\frac{4}{4}\\=\frac{-2}{3}-\frac{1}{1}-\frac{1}{1}\\=\frac{-2-1-1}{3}\\=\frac{-4}{3}\)
8. \(+\left(\frac{4}{5}\right) +\left(\frac{-6}{-4}\right) -\left(\frac{-2}{8}\right)\\= \frac{4}{5}+ \frac{6}{4}+\frac{2}{8}\\=\frac{4}{5}+\frac{3}{2}+\frac{1}{4}\\=\frac{16}{20}+\frac{30}{20}+\frac{5}{20}\\=\frac{16+30+5}{20}\\=\frac{51}{20}\)
9. \(+\left(\frac{5}{-3}\right) +\left(\frac{-5}{4}\right) +\left(\frac{-10}{6}\right)\\= \frac{-5}{3}- \frac{5}{4}-\frac{10}{6}\\=\frac{-5}{3}-\frac{5}{4}-\frac{5}{3}\\=\frac{-20}{12}-\frac{15}{12}-\frac{20}{12}\\=\frac{-20-15-20}{12}\\=\frac{-55}{12}\)
10. \(-\left(\frac{2}{-9}\right) +\left(\frac{-5}{10}\right) -\left(\frac{5}{10}\right)\\= \frac{2}{9}- \frac{5}{10}-\frac{5}{10}\\=\frac{2}{9}-\frac{1}{2}-\frac{1}{2}\\=\frac{4}{18}-\frac{9}{18}-\frac{9}{18}\\=\frac{4-9-9}{18}\\=\frac{-14}{18}\\=\frac{-7}{9}\)
11. \(-\left(\frac{-8}{-3}\right) +\left(\frac{6}{-3}\right) -\left(\frac{-5}{2}\right)\\= \frac{-8}{3}- \frac{6}{3}+\frac{5}{2}\\=\frac{-8}{3}-\frac{2}{1}+\frac{5}{2}\\=\frac{-16}{6}-\frac{12}{6}+\frac{15}{6}\\=\frac{-16-12+15}{6}\\=\frac{-13}{6}\)
12. \(+\left(\frac{-3}{-4}\right) -\left(\frac{4}{-8}\right) +\left(\frac{-4}{4}\right)\\= \frac{3}{4}+ \frac{4}{8}-\frac{4}{4}\\=\frac{3}{4}+\frac{1}{2}-\frac{1}{1}\\=\frac{3+1-1}{4}\\=\frac{3}{4}\)