Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{10}{3}\right) +\left(\frac{-6}{8}\right) +\left(\frac{-11}{3}\right)\\= \frac{10}{3}- \frac{6}{8}-\frac{11}{3}\\=\frac{10}{3}-\frac{3}{4}-\frac{11}{3}\\=\frac{40}{12}-\frac{9}{12}-\frac{44}{12}\\=\frac{40-9-44}{12}\\=\frac{-13}{12}\)
2. \(+\left(\frac{8}{-3}\right) -\left(\frac{10}{2}\right) -\left(\frac{-7}{-5}\right)\\= \frac{-8}{3}- \frac{10}{2}-\frac{7}{5}\\=\frac{-8}{3}-\frac{5}{1}-\frac{7}{5}\\=\frac{-40}{15}-\frac{75}{15}-\frac{21}{15}\\=\frac{-40-75-21}{15}\\=\frac{-136}{15}\)
3. \(+\left(\frac{-5}{-8}\right) -\left(\frac{7}{8}\right) -\left(\frac{-10}{4}\right)\\= \frac{5}{8}- \frac{7}{8}+\frac{10}{4}\\=\frac{5}{8}-\frac{7}{8}+\frac{5}{2}\\=\frac{5-7+5}{8}\\=\frac{3}{8}\)
4. \(+\left(\frac{4}{-9}\right) -\left(\frac{9}{-3}\right) -\left(\frac{-4}{-7}\right)\\= \frac{-4}{9}+ \frac{9}{3}-\frac{4}{7}\\=\frac{-4}{9}+\frac{3}{1}-\frac{4}{7}\\=\frac{-28}{63}+\frac{189}{63}-\frac{36}{63}\\=\frac{-28+189-36}{63}\\=\frac{125}{63}\)
5. \(+\left(\frac{10}{-9}\right) +\left(\frac{-8}{6}\right) +\left(\frac{-2}{-6}\right)\\= \frac{-10}{9}- \frac{8}{6}+\frac{2}{6}\\=\frac{-10}{9}-\frac{4}{3}+\frac{1}{3}\\=\frac{-10-4+1}{9}\\=\frac{-13}{9}\)
6. \(+\left(\frac{5}{6}\right) -\left(\frac{9}{10}\right) +\left(\frac{5}{-4}\right)\\= \frac{5}{6}- \frac{9}{10}-\frac{5}{4}\\=\frac{50}{60}-\frac{54}{60}-\frac{75}{60}\\=\frac{50-54-75}{60}\\=\frac{-79}{60}\)
7. \(-\left(\frac{-4}{-3}\right) -\left(\frac{8}{5}\right) -\left(\frac{-3}{-10}\right)\\= \frac{-4}{3}- \frac{8}{5}-\frac{3}{10}\\=\frac{-40}{30}-\frac{48}{30}-\frac{9}{30}\\=\frac{-40-48-9}{30}\\=\frac{-97}{30}\)
8. \(-\left(\frac{5}{2}\right) -\left(\frac{-10}{-6}\right) +\left(\frac{10}{2}\right)\\= \frac{-5}{2}- \frac{10}{6}+\frac{10}{2}\\=\frac{-5}{2}-\frac{5}{3}+\frac{5}{1}\\=\frac{-15}{6}-\frac{10}{6}+\frac{30}{6}\\=\frac{-15-10+30}{6}\\=\frac{5}{6}\)
9. \(+\left(\frac{-7}{-3}\right) +\left(\frac{8}{-5}\right) -\left(\frac{-9}{10}\right)\\= \frac{7}{3}- \frac{8}{5}+\frac{9}{10}\\=\frac{70}{30}-\frac{48}{30}+\frac{27}{30}\\=\frac{70-48+27}{30}\\=\frac{49}{30}\)
10. \(+\left(\frac{8}{7}\right) -\left(\frac{-10}{-6}\right) +\left(\frac{4}{-8}\right)\\= \frac{8}{7}- \frac{10}{6}-\frac{4}{8}\\=\frac{8}{7}-\frac{5}{3}-\frac{1}{2}\\=\frac{48}{42}-\frac{70}{42}-\frac{21}{42}\\=\frac{48-70-21}{42}\\=\frac{-43}{42}\)
11. \(-\left(\frac{-4}{3}\right) -\left(\frac{9}{10}\right) -\left(\frac{9}{-5}\right)\\= \frac{4}{3}- \frac{9}{10}+\frac{9}{5}\\=\frac{40}{30}-\frac{27}{30}+\frac{54}{30}\\=\frac{40-27+54}{30}\\=\frac{67}{30}\)
12. \(+\left(\frac{-9}{5}\right) -\left(\frac{2}{-6}\right) -\left(\frac{-5}{-5}\right)\\= \frac{-9}{5}+ \frac{2}{6}-\frac{5}{5}\\=\frac{-9}{5}+\frac{1}{3}-\frac{1}{1}\\=\frac{-27}{15}+\frac{5}{15}-\frac{15}{15}\\=\frac{-27+5-15}{15}\\=\frac{-37}{15}\)