Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{-4}{-9}\right) -\left(\frac{9}{-8}\right) +\left(\frac{-11}{5}\right)\\= \frac{-4}{9}+ \frac{9}{8}-\frac{11}{5}\\=\frac{-160}{360}+\frac{405}{360}-\frac{792}{360}\\=\frac{-160+405-792}{360}\\=\frac{-547}{360}\)
2. \(-\left(\frac{-9}{-4}\right) -\left(\frac{10}{4}\right) -\left(\frac{-11}{7}\right)\\= \frac{-9}{4}- \frac{10}{4}+\frac{11}{7}\\=\frac{-9}{4}-\frac{5}{2}+\frac{11}{7}\\=\frac{-63}{28}-\frac{70}{28}+\frac{44}{28}\\=\frac{-63-70+44}{28}\\=\frac{-89}{28}\)
3. \(+\left(\frac{4}{9}\right) +\left(\frac{8}{2}\right) +\left(\frac{-10}{-5}\right)\\= \frac{4}{9}+ \frac{8}{2}+\frac{10}{5}\\=\frac{4}{9}+\frac{4}{1}+\frac{2}{1}\\=\frac{4+4+2}{9}\\=\frac{10}{9}\)
4. \(-\left(\frac{-3}{-2}\right) +\left(\frac{5}{8}\right) +\left(\frac{-5}{8}\right)\\= \frac{-3}{2}+ \frac{5}{8}-\frac{5}{8}\\=\frac{-12}{8}+\frac{5}{8}-\frac{5}{8}\\=\frac{-12+5-5}{8}\\=\frac{-12}{8}\\=\frac{-3}{2}\)
5. \(-\left(\frac{-9}{2}\right) -\left(\frac{-10}{8}\right) +\left(\frac{-12}{-3}\right)\\= \frac{9}{2}+ \frac{10}{8}+\frac{12}{3}\\=\frac{9}{2}+\frac{5}{4}+\frac{4}{1}\\=\frac{18}{4}+\frac{5}{4}+\frac{16}{4}\\=\frac{18+5+16}{4}\\=\frac{39}{4}\)
6. \(-\left(\frac{7}{-5}\right) +\left(\frac{2}{-9}\right) -\left(\frac{-5}{4}\right)\\= \frac{7}{5}- \frac{2}{9}+\frac{5}{4}\\=\frac{252}{180}-\frac{40}{180}+\frac{225}{180}\\=\frac{252-40+225}{180}\\=\frac{437}{180}\)
7. \(+\left(\frac{-7}{-8}\right) -\left(\frac{5}{7}\right) +\left(\frac{2}{11}\right)\\= \frac{7}{8}- \frac{5}{7}+\frac{2}{11}\\=\frac{539}{616}-\frac{440}{616}+\frac{112}{616}\\=\frac{539-440+112}{616}\\=\frac{211}{616}\)
8. \(-\left(\frac{-7}{8}\right) +\left(\frac{-10}{-5}\right) +\left(\frac{-2}{-5}\right)\\= \frac{7}{8}+ \frac{10}{5}+\frac{2}{5}\\=\frac{7}{8}+\frac{2}{1}+\frac{2}{5}\\=\frac{35}{40}+\frac{80}{40}+\frac{16}{40}\\=\frac{35+80+16}{40}\\=\frac{131}{40}\)
9. \(-\left(\frac{-3}{2}\right) +\left(\frac{-6}{-6}\right) -\left(\frac{5}{-2}\right)\\= \frac{3}{2}+ \frac{6}{6}+\frac{5}{2}\\=\frac{3}{2}+\frac{1}{1}+\frac{5}{2}\\=\frac{3+1+5}{2}\\=\frac{9}{2}\)
10. \(-\left(\frac{9}{-2}\right) -\left(\frac{2}{-6}\right) -\left(\frac{2}{-7}\right)\\= \frac{9}{2}+ \frac{2}{6}+\frac{2}{7}\\=\frac{9}{2}+\frac{1}{3}+\frac{2}{7}\\=\frac{189}{42}+\frac{14}{42}+\frac{12}{42}\\=\frac{189+14+12}{42}\\=\frac{215}{42}\)
11. \(-\left(\frac{8}{3}\right) -\left(\frac{6}{2}\right) -\left(\frac{-11}{4}\right)\\= \frac{-8}{3}- \frac{6}{2}+\frac{11}{4}\\=\frac{-8}{3}-\frac{3}{1}+\frac{11}{4}\\=\frac{-32}{12}-\frac{36}{12}+\frac{33}{12}\\=\frac{-32-36+33}{12}\\=\frac{-35}{12}\)
12. \(-\left(\frac{7}{-2}\right) -\left(\frac{5}{-4}\right) +\left(\frac{5}{-9}\right)\\= \frac{7}{2}+ \frac{5}{4}-\frac{5}{9}\\=\frac{126}{36}+\frac{45}{36}-\frac{20}{36}\\=\frac{126+45-20}{36}\\=\frac{151}{36}\)