Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{-8}{3}\right) +\left(\frac{-10}{4}\right) +\left(\frac{-8}{-9}\right)\\= \frac{-8}{3}- \frac{10}{4}+\frac{8}{9}\\=\frac{-8}{3}-\frac{5}{2}+\frac{8}{9}\\=\frac{-48}{18}-\frac{45}{18}+\frac{16}{18}\\=\frac{-48-45+16}{18}\\=\frac{-77}{18}\)
2. \(+\left(\frac{-9}{4}\right) +\left(\frac{10}{7}\right) +\left(\frac{11}{9}\right)\\= \frac{-9}{4}+ \frac{10}{7}+\frac{11}{9}\\=\frac{-567}{252}+\frac{360}{252}+\frac{308}{252}\\=\frac{-567+360+308}{252}\\=\frac{101}{252}\)
3. \(+\left(\frac{-8}{-7}\right) -\left(\frac{3}{-9}\right) -\left(\frac{4}{2}\right)\\= \frac{8}{7}+ \frac{3}{9}-\frac{4}{2}\\=\frac{8}{7}+\frac{1}{3}-\frac{2}{1}\\=\frac{24}{21}+\frac{7}{21}-\frac{42}{21}\\=\frac{24+7-42}{21}\\=\frac{-11}{21}\)
4. \(-\left(\frac{7}{6}\right) +\left(\frac{4}{10}\right) -\left(\frac{11}{-3}\right)\\= \frac{-7}{6}+ \frac{4}{10}+\frac{11}{3}\\=\frac{-7}{6}+\frac{2}{5}+\frac{11}{3}\\=\frac{-35}{30}+\frac{12}{30}+\frac{110}{30}\\=\frac{-35+12+110}{30}\\=\frac{87}{30}\\=\frac{29}{10}\)
5. \(-\left(\frac{-10}{7}\right) +\left(\frac{-7}{7}\right) +\left(\frac{11}{2}\right)\\= \frac{10}{7}- \frac{7}{7}+\frac{11}{2}\\=\frac{10}{7}-\frac{1}{1}+\frac{11}{2}\\=\frac{20}{14}-\frac{14}{14}+\frac{77}{14}\\=\frac{20-14+77}{14}\\=\frac{83}{14}\)
6. \(+\left(\frac{-3}{4}\right) +\left(\frac{-8}{3}\right) +\left(\frac{6}{-6}\right)\\= \frac{-3}{4}- \frac{8}{3}-\frac{6}{6}\\=\frac{-3}{4}-\frac{8}{3}-\frac{1}{1}\\=\frac{-9}{12}-\frac{32}{12}-\frac{12}{12}\\=\frac{-9-32-12}{12}\\=\frac{-53}{12}\)
7. \(-\left(\frac{8}{-9}\right) +\left(\frac{-3}{-10}\right) +\left(\frac{-3}{-6}\right)\\= \frac{8}{9}+ \frac{3}{10}+\frac{3}{6}\\=\frac{8}{9}+\frac{3}{10}+\frac{1}{2}\\=\frac{80}{90}+\frac{27}{90}+\frac{45}{90}\\=\frac{80+27+45}{90}\\=\frac{152}{90}\\=\frac{76}{45}\)
8. \(+\left(\frac{7}{-2}\right) +\left(\frac{-2}{2}\right) +\left(\frac{9}{11}\right)\\= \frac{-7}{2}- \frac{2}{2}+\frac{9}{11}\\=\frac{-7}{2}-\frac{1}{1}+\frac{9}{11}\\=\frac{-77}{22}-\frac{22}{22}+\frac{18}{22}\\=\frac{-77-22+18}{22}\\=\frac{-81}{22}\)
9. \(+\left(\frac{9}{4}\right) -\left(\frac{5}{-6}\right) -\left(\frac{6}{10}\right)\\= \frac{9}{4}+ \frac{5}{6}-\frac{6}{10}\\=\frac{9}{4}+\frac{5}{6}-\frac{3}{5}\\=\frac{135}{60}+\frac{50}{60}-\frac{36}{60}\\=\frac{135+50-36}{60}\\=\frac{149}{60}\)
10. \(-\left(\frac{8}{-3}\right) -\left(\frac{-8}{-10}\right) +\left(\frac{-10}{12}\right)\\= \frac{8}{3}- \frac{8}{10}-\frac{10}{12}\\=\frac{8}{3}-\frac{4}{5}-\frac{5}{6}\\=\frac{80}{30}-\frac{24}{30}-\frac{25}{30}\\=\frac{80-24-25}{30}\\=\frac{31}{30}\)
11. \(+\left(\frac{6}{5}\right) -\left(\frac{-3}{3}\right) +\left(\frac{2}{4}\right)\\= \frac{6}{5}+ \frac{3}{3}+\frac{2}{4}\\=\frac{6}{5}+\frac{1}{1}+\frac{1}{2}\\=\frac{12}{10}+\frac{10}{10}+\frac{5}{10}\\=\frac{12+10+5}{10}\\=\frac{27}{10}\)
12. \(-\left(\frac{5}{8}\right) -\left(\frac{-2}{-5}\right) -\left(\frac{6}{-4}\right)\\= \frac{-5}{8}- \frac{2}{5}+\frac{6}{4}\\=\frac{-5}{8}-\frac{2}{5}+\frac{3}{2}\\=\frac{-25}{40}-\frac{16}{40}+\frac{60}{40}\\=\frac{-25-16+60}{40}\\=\frac{19}{40}\)