Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{5}{8}\right) -\left(\frac{8}{-6}\right) -\left(\frac{-5}{-8}\right)\\= \frac{5}{8}+ \frac{8}{6}-\frac{5}{8}\\=\frac{5}{8}+\frac{4}{3}-\frac{5}{8}\\=\frac{15}{24}+\frac{32}{24}-\frac{15}{24}\\=\frac{15+32-15}{24}\\=\frac{32}{24}\\=\frac{4}{3}\)
2. \(-\left(\frac{-6}{5}\right) -\left(\frac{5}{-9}\right) -\left(\frac{5}{8}\right)\\= \frac{6}{5}+ \frac{5}{9}-\frac{5}{8}\\=\frac{432}{360}+\frac{200}{360}-\frac{225}{360}\\=\frac{432+200-225}{360}\\=\frac{407}{360}\)
3. \(+\left(\frac{3}{2}\right) +\left(\frac{2}{-2}\right) -\left(\frac{10}{-3}\right)\\= \frac{3}{2}- \frac{2}{2}+\frac{10}{3}\\=\frac{3}{2}-\frac{1}{1}+\frac{10}{3}\\=\frac{9}{6}-\frac{6}{6}+\frac{20}{6}\\=\frac{9-6+20}{6}\\=\frac{23}{6}\)
4. \(-\left(\frac{-10}{7}\right) -\left(\frac{-7}{9}\right) -\left(\frac{-9}{-12}\right)\\= \frac{10}{7}+ \frac{7}{9}-\frac{9}{12}\\=\frac{10}{7}+\frac{7}{9}-\frac{3}{4}\\=\frac{360}{252}+\frac{196}{252}-\frac{189}{252}\\=\frac{360+196-189}{252}\\=\frac{367}{252}\)
5. \(+\left(\frac{-9}{2}\right) -\left(\frac{5}{6}\right) +\left(\frac{10}{-3}\right)\\= \frac{-9}{2}- \frac{5}{6}-\frac{10}{3}\\=\frac{-27}{6}-\frac{5}{6}-\frac{20}{6}\\=\frac{-27-5-20}{6}\\=\frac{-52}{6}\\=\frac{-26}{3}\)
6. \(-\left(\frac{-3}{2}\right) +\left(\frac{-7}{8}\right) +\left(\frac{7}{-10}\right)\\= \frac{3}{2}- \frac{7}{8}-\frac{7}{10}\\=\frac{60}{40}-\frac{35}{40}-\frac{28}{40}\\=\frac{60-35-28}{40}\\=\frac{-3}{40}\)
7. \(+\left(\frac{-3}{8}\right) -\left(\frac{-3}{-7}\right) +\left(\frac{-2}{8}\right)\\= \frac{-3}{8}- \frac{3}{7}-\frac{2}{8}\\=\frac{-3}{8}-\frac{3}{7}-\frac{1}{4}\\=\frac{-21}{56}-\frac{24}{56}-\frac{14}{56}\\=\frac{-21-24-14}{56}\\=\frac{-59}{56}\)
8. \(+\left(\frac{8}{3}\right) -\left(\frac{-8}{4}\right) -\left(\frac{5}{-5}\right)\\= \frac{8}{3}+ \frac{8}{4}+\frac{5}{5}\\=\frac{8}{3}+\frac{2}{1}+\frac{1}{1}\\=\frac{8+2+1}{3}\\=\frac{11}{3}\)
9. \(-\left(\frac{-7}{-3}\right) +\left(\frac{10}{4}\right) -\left(\frac{2}{12}\right)\\= \frac{-7}{3}+ \frac{10}{4}-\frac{2}{12}\\=\frac{-7}{3}+\frac{5}{2}-\frac{1}{6}\\=\frac{-14}{6}+\frac{15}{6}-\frac{1}{6}\\=\frac{-14+15-1}{6}\\=\frac{0}{6}\\=\frac{0}{1}\)
10. \(+\left(\frac{-2}{9}\right) +\left(\frac{-4}{-2}\right) +\left(\frac{-3}{3}\right)\\= \frac{-2}{9}+ \frac{4}{2}-\frac{3}{3}\\=\frac{-2}{9}+\frac{2}{1}-\frac{1}{1}\\=\frac{-2+2-1}{9}\\=\frac{-1}{9}\)
11. \(-\left(\frac{-4}{-5}\right) +\left(\frac{-2}{7}\right) +\left(\frac{-10}{-6}\right)\\= \frac{-4}{5}- \frac{2}{7}+\frac{10}{6}\\=\frac{-4}{5}-\frac{2}{7}+\frac{5}{3}\\=\frac{-84}{105}-\frac{30}{105}+\frac{175}{105}\\=\frac{-84-30+175}{105}\\=\frac{61}{105}\)
12. \(+\left(\frac{-10}{3}\right) -\left(\frac{4}{-8}\right) -\left(\frac{-7}{-3}\right)\\= \frac{-10}{3}+ \frac{4}{8}-\frac{7}{3}\\=\frac{-10}{3}+\frac{1}{2}-\frac{7}{3}\\=\frac{-20}{6}+\frac{3}{6}-\frac{14}{6}\\=\frac{-20+3-14}{6}\\=\frac{-31}{6}\)