Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{-5}{4}\right) -\left(\frac{-5}{8}\right) -\left(\frac{6}{-2}\right)\\= \frac{5}{4}+ \frac{5}{8}+\frac{6}{2}\\=\frac{5}{4}+\frac{5}{8}+\frac{3}{1}\\=\frac{10}{8}+\frac{5}{8}+\frac{24}{8}\\=\frac{10+5+24}{8}\\=\frac{39}{8}\)
2. \(-\left(\frac{-3}{2}\right) -\left(\frac{9}{-2}\right) -\left(\frac{8}{-6}\right)\\= \frac{3}{2}+ \frac{9}{2}+\frac{8}{6}\\=\frac{3}{2}+\frac{9}{2}+\frac{4}{3}\\=\frac{9}{6}+\frac{27}{6}+\frac{8}{6}\\=\frac{9+27+8}{6}\\=\frac{44}{6}\\=\frac{22}{3}\)
3. \(+\left(\frac{6}{5}\right) +\left(\frac{-10}{8}\right) -\left(\frac{-8}{-5}\right)\\= \frac{6}{5}- \frac{10}{8}-\frac{8}{5}\\=\frac{6}{5}-\frac{5}{4}-\frac{8}{5}\\=\frac{24}{20}-\frac{25}{20}-\frac{32}{20}\\=\frac{24-25-32}{20}\\=\frac{-33}{20}\)
4. \(+\left(\frac{-7}{-8}\right) -\left(\frac{2}{-7}\right) +\left(\frac{9}{-6}\right)\\= \frac{7}{8}+ \frac{2}{7}-\frac{9}{6}\\=\frac{7}{8}+\frac{2}{7}-\frac{3}{2}\\=\frac{49}{56}+\frac{16}{56}-\frac{84}{56}\\=\frac{49+16-84}{56}\\=\frac{-19}{56}\)
5. \(+\left(\frac{5}{-7}\right) +\left(\frac{-7}{7}\right) -\left(\frac{-10}{-6}\right)\\= \frac{-5}{7}- \frac{7}{7}-\frac{10}{6}\\=\frac{-5}{7}-\frac{1}{1}-\frac{5}{3}\\=\frac{-15}{21}-\frac{21}{21}-\frac{35}{21}\\=\frac{-15-21-35}{21}\\=\frac{-71}{21}\)
6. \(+\left(\frac{-8}{3}\right) +\left(\frac{3}{-6}\right) -\left(\frac{9}{11}\right)\\= \frac{-8}{3}- \frac{3}{6}-\frac{9}{11}\\=\frac{-8}{3}-\frac{1}{2}-\frac{9}{11}\\=\frac{-176}{66}-\frac{33}{66}-\frac{54}{66}\\=\frac{-176-33-54}{66}\\=\frac{-263}{66}\)
7. \(-\left(\frac{-8}{7}\right) +\left(\frac{-4}{-7}\right) +\left(\frac{-7}{-6}\right)\\= \frac{8}{7}+ \frac{4}{7}+\frac{7}{6}\\=\frac{48}{42}+\frac{24}{42}+\frac{49}{42}\\=\frac{48+24+49}{42}\\=\frac{121}{42}\)
8. \(+\left(\frac{2}{5}\right) -\left(\frac{4}{10}\right) -\left(\frac{5}{-5}\right)\\= \frac{2}{5}- \frac{4}{10}+\frac{5}{5}\\=\frac{2}{5}-\frac{2}{5}+\frac{1}{1}\\=\frac{2-2+1}{5}\\=\frac{1}{5}\)
9. \(-\left(\frac{6}{5}\right) -\left(\frac{10}{4}\right) +\left(\frac{2}{4}\right)\\= \frac{-6}{5}- \frac{10}{4}+\frac{2}{4}\\=\frac{-6}{5}-\frac{5}{2}+\frac{1}{2}\\=\frac{-12}{10}-\frac{25}{10}+\frac{5}{10}\\=\frac{-12-25+5}{10}\\=\frac{-32}{10}\\=\frac{-16}{5}\)
10. \(+\left(\frac{4}{-7}\right) +\left(\frac{-8}{-9}\right) +\left(\frac{8}{-6}\right)\\= \frac{-4}{7}+ \frac{8}{9}-\frac{8}{6}\\=\frac{-4}{7}+\frac{8}{9}-\frac{4}{3}\\=\frac{-36}{63}+\frac{56}{63}-\frac{84}{63}\\=\frac{-36+56-84}{63}\\=\frac{-64}{63}\)
11. \(+\left(\frac{9}{4}\right) -\left(\frac{10}{6}\right) +\left(\frac{12}{8}\right)\\= \frac{9}{4}- \frac{10}{6}+\frac{12}{8}\\=\frac{9}{4}-\frac{5}{3}+\frac{3}{2}\\=\frac{27}{12}-\frac{20}{12}+\frac{18}{12}\\=\frac{27-20+18}{12}\\=\frac{25}{12}\)
12. \(+\left(\frac{5}{6}\right) +\left(\frac{-7}{8}\right) -\left(\frac{-5}{4}\right)\\= \frac{5}{6}- \frac{7}{8}+\frac{5}{4}\\=\frac{20}{24}-\frac{21}{24}+\frac{30}{24}\\=\frac{20-21+30}{24}\\=\frac{29}{24}\)