Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{7}\right) -\left(\frac{5}{6}\right) -\left(\frac{-9}{8}\right)\\= \frac{9}{7}- \frac{5}{6}+\frac{9}{8}\\=\frac{216}{168}-\frac{140}{168}+\frac{189}{168}\\=\frac{216-140+189}{168}\\=\frac{265}{168}\)
2. \(+\left(\frac{10}{9}\right) -\left(\frac{6}{3}\right) +\left(\frac{-3}{-3}\right)\\= \frac{10}{9}- \frac{6}{3}+\frac{3}{3}\\=\frac{10}{9}-\frac{2}{1}+\frac{1}{1}\\=\frac{10-2+1}{9}\\=\frac{9}{9}\\=\frac{1}{1}\)
3. \(-\left(\frac{-4}{-7}\right) +\left(\frac{5}{2}\right) +\left(\frac{-8}{8}\right)\\= \frac{-4}{7}+ \frac{5}{2}-\frac{8}{8}\\=\frac{-4}{7}+\frac{5}{2}-\frac{1}{1}\\=\frac{-8}{14}+\frac{35}{14}-\frac{14}{14}\\=\frac{-8+35-14}{14}\\=\frac{13}{14}\)
4. \(-\left(\frac{-9}{7}\right) -\left(\frac{9}{-4}\right) +\left(\frac{-5}{-8}\right)\\= \frac{9}{7}+ \frac{9}{4}+\frac{5}{8}\\=\frac{72}{56}+\frac{126}{56}+\frac{35}{56}\\=\frac{72+126+35}{56}\\=\frac{233}{56}\)
5. \(+\left(\frac{7}{-2}\right) -\left(\frac{-6}{4}\right) -\left(\frac{3}{-3}\right)\\= \frac{-7}{2}+ \frac{6}{4}+\frac{3}{3}\\=\frac{-7}{2}+\frac{3}{2}+\frac{1}{1}\\=\frac{-7+3+1}{2}\\=\frac{-3}{2}\)
6. \(+\left(\frac{-8}{-7}\right) +\left(\frac{-3}{4}\right) -\left(\frac{12}{-5}\right)\\= \frac{8}{7}- \frac{3}{4}+\frac{12}{5}\\=\frac{160}{140}-\frac{105}{140}+\frac{336}{140}\\=\frac{160-105+336}{140}\\=\frac{391}{140}\)
7. \(+\left(\frac{-8}{9}\right) -\left(\frac{-6}{-8}\right) -\left(\frac{-5}{-4}\right)\\= \frac{-8}{9}- \frac{6}{8}-\frac{5}{4}\\=\frac{-8}{9}-\frac{3}{4}-\frac{5}{4}\\=\frac{-32}{36}-\frac{27}{36}-\frac{45}{36}\\=\frac{-32-27-45}{36}\\=\frac{-104}{36}\\=\frac{-26}{9}\)
8. \(-\left(\frac{8}{9}\right) -\left(\frac{5}{3}\right) -\left(\frac{11}{10}\right)\\= \frac{-8}{9}- \frac{5}{3}-\frac{11}{10}\\=\frac{-80}{90}-\frac{150}{90}-\frac{99}{90}\\=\frac{-80-150-99}{90}\\=\frac{-329}{90}\)
9. \(-\left(\frac{10}{-7}\right) +\left(\frac{-5}{7}\right) -\left(\frac{-3}{-9}\right)\\= \frac{10}{7}- \frac{5}{7}-\frac{3}{9}\\=\frac{10}{7}-\frac{5}{7}-\frac{1}{3}\\=\frac{30}{21}-\frac{15}{21}-\frac{7}{21}\\=\frac{30-15-7}{21}\\=\frac{8}{21}\)
10. \(+\left(\frac{-10}{7}\right) +\left(\frac{3}{-8}\right) -\left(\frac{11}{-12}\right)\\= \frac{-10}{7}- \frac{3}{8}+\frac{11}{12}\\=\frac{-240}{168}-\frac{63}{168}+\frac{154}{168}\\=\frac{-240-63+154}{168}\\=\frac{-149}{168}\)
11. \(-\left(\frac{3}{2}\right) -\left(\frac{-8}{-6}\right) +\left(\frac{-3}{6}\right)\\= \frac{-3}{2}- \frac{8}{6}-\frac{3}{6}\\=\frac{-3}{2}-\frac{4}{3}-\frac{1}{2}\\=\frac{-9}{6}-\frac{8}{6}-\frac{3}{6}\\=\frac{-9-8-3}{6}\\=\frac{-20}{6}\\=\frac{-10}{3}\)
12. \(+\left(\frac{-8}{-3}\right) +\left(\frac{7}{7}\right) -\left(\frac{-5}{8}\right)\\= \frac{8}{3}+ \frac{7}{7}+\frac{5}{8}\\=\frac{8}{3}+\frac{1}{1}+\frac{5}{8}\\=\frac{64}{24}+\frac{24}{24}+\frac{15}{24}\\=\frac{64+24+15}{24}\\=\frac{103}{24}\)