Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{-9}{-4}\right) -\left(\frac{-5}{-5}\right) +\left(\frac{5}{4}\right)\\= \frac{9}{4}- \frac{5}{5}+\frac{5}{4}\\=\frac{9}{4}-\frac{1}{1}+\frac{5}{4}\\=\frac{9-1+5}{4}\\=\frac{13}{4}\)
2. \(-\left(\frac{-9}{4}\right) +\left(\frac{5}{7}\right) +\left(\frac{11}{-10}\right)\\= \frac{9}{4}+ \frac{5}{7}-\frac{11}{10}\\=\frac{315}{140}+\frac{100}{140}-\frac{154}{140}\\=\frac{315+100-154}{140}\\=\frac{261}{140}\)
3. \(-\left(\frac{10}{-7}\right) +\left(\frac{-3}{-8}\right) +\left(\frac{-10}{10}\right)\\= \frac{10}{7}+ \frac{3}{8}-\frac{10}{10}\\=\frac{10}{7}+\frac{3}{8}-\frac{1}{1}\\=\frac{80}{56}+\frac{21}{56}-\frac{56}{56}\\=\frac{80+21-56}{56}\\=\frac{45}{56}\)
4. \(-\left(\frac{8}{5}\right) -\left(\frac{-5}{6}\right) +\left(\frac{-7}{11}\right)\\= \frac{-8}{5}+ \frac{5}{6}-\frac{7}{11}\\=\frac{-528}{330}+\frac{275}{330}-\frac{210}{330}\\=\frac{-528+275-210}{330}\\=\frac{-463}{330}\)
5. \(+\left(\frac{-3}{-5}\right) -\left(\frac{3}{-9}\right) -\left(\frac{8}{7}\right)\\= \frac{3}{5}+ \frac{3}{9}-\frac{8}{7}\\=\frac{3}{5}+\frac{1}{3}-\frac{8}{7}\\=\frac{63}{105}+\frac{35}{105}-\frac{120}{105}\\=\frac{63+35-120}{105}\\=\frac{-22}{105}\)
6. \(+\left(\frac{9}{-2}\right) -\left(\frac{9}{10}\right) +\left(\frac{-5}{-4}\right)\\= \frac{-9}{2}- \frac{9}{10}+\frac{5}{4}\\=\frac{-90}{20}-\frac{18}{20}+\frac{25}{20}\\=\frac{-90-18+25}{20}\\=\frac{-83}{20}\)
7. \(+\left(\frac{8}{-3}\right) -\left(\frac{-8}{5}\right) -\left(\frac{10}{-9}\right)\\= \frac{-8}{3}+ \frac{8}{5}+\frac{10}{9}\\=\frac{-120}{45}+\frac{72}{45}+\frac{50}{45}\\=\frac{-120+72+50}{45}\\=\frac{2}{45}\)
8. \(-\left(\frac{7}{-8}\right) -\left(\frac{-7}{5}\right) +\left(\frac{-10}{3}\right)\\= \frac{7}{8}+ \frac{7}{5}-\frac{10}{3}\\=\frac{105}{120}+\frac{168}{120}-\frac{400}{120}\\=\frac{105+168-400}{120}\\=\frac{-127}{120}\)
9. \(-\left(\frac{-5}{-6}\right) -\left(\frac{-7}{2}\right) -\left(\frac{-12}{12}\right)\\= \frac{-5}{6}+ \frac{7}{2}+\frac{12}{12}\\=\frac{-5}{6}+\frac{7}{2}+\frac{1}{1}\\=\frac{-5+7+1}{6}\\=\frac{3}{6}\\=\frac{1}{2}\)
10. \(-\left(\frac{10}{7}\right) +\left(\frac{-3}{-7}\right) -\left(\frac{-11}{7}\right)\\= \frac{-10}{7}+ \frac{3}{7}+\frac{11}{7}\\=\frac{-10+3+11}{7}\\=\frac{4}{7}\)
11. \(+\left(\frac{-4}{9}\right) +\left(\frac{8}{-2}\right) +\left(\frac{8}{8}\right)\\= \frac{-4}{9}- \frac{8}{2}+\frac{8}{8}\\=\frac{-4}{9}-\frac{4}{1}+\frac{1}{1}\\=\frac{-4-4+1}{9}\\=\frac{-7}{9}\)
12. \(+\left(\frac{4}{7}\right) -\left(\frac{10}{9}\right) +\left(\frac{8}{-9}\right)\\= \frac{4}{7}- \frac{10}{9}-\frac{8}{9}\\=\frac{36}{63}-\frac{70}{63}-\frac{56}{63}\\=\frac{36-70-56}{63}\\=\frac{-90}{63}\\=\frac{-10}{7}\)