Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{5}{6}\right) -\left(\frac{9}{10}\right) +\left(\frac{5}{7}\right)\\= \frac{5}{6}- \frac{9}{10}+\frac{5}{7}\\=\frac{175}{210}-\frac{189}{210}+\frac{150}{210}\\=\frac{175-189+150}{210}\\=\frac{136}{210}\\=\frac{68}{105}\)
2. \(-\left(\frac{-4}{9}\right) +\left(\frac{-3}{8}\right) +\left(\frac{-10}{-9}\right)\\= \frac{4}{9}- \frac{3}{8}+\frac{10}{9}\\=\frac{32}{72}-\frac{27}{72}+\frac{80}{72}\\=\frac{32-27+80}{72}\\=\frac{85}{72}\)
3. \(+\left(\frac{5}{9}\right) -\left(\frac{-9}{2}\right) -\left(\frac{8}{-9}\right)\\= \frac{5}{9}+ \frac{9}{2}+\frac{8}{9}\\=\frac{10}{18}+\frac{81}{18}+\frac{16}{18}\\=\frac{10+81+16}{18}\\=\frac{107}{18}\)
4. \(-\left(\frac{-9}{-7}\right) -\left(\frac{-9}{-3}\right) +\left(\frac{7}{-8}\right)\\= \frac{-9}{7}- \frac{9}{3}-\frac{7}{8}\\=\frac{-9}{7}-\frac{3}{1}-\frac{7}{8}\\=\frac{-72}{56}-\frac{168}{56}-\frac{49}{56}\\=\frac{-72-168-49}{56}\\=\frac{-289}{56}\)
5. \(+\left(\frac{8}{3}\right) +\left(\frac{-7}{4}\right) +\left(\frac{-12}{-11}\right)\\= \frac{8}{3}- \frac{7}{4}+\frac{12}{11}\\=\frac{352}{132}-\frac{231}{132}+\frac{144}{132}\\=\frac{352-231+144}{132}\\=\frac{265}{132}\)
6. \(-\left(\frac{10}{-3}\right) +\left(\frac{10}{-3}\right) +\left(\frac{4}{-5}\right)\\= \frac{10}{3}- \frac{10}{3}-\frac{4}{5}\\=\frac{50}{15}-\frac{50}{15}-\frac{12}{15}\\=\frac{50-50-12}{15}\\=\frac{-12}{15}\\=\frac{-4}{5}\)
7. \(-\left(\frac{-5}{6}\right) +\left(\frac{2}{-3}\right) +\left(\frac{10}{8}\right)\\= \frac{5}{6}- \frac{2}{3}+\frac{10}{8}\\=\frac{5}{6}-\frac{2}{3}+\frac{5}{4}\\=\frac{10}{12}-\frac{8}{12}+\frac{15}{12}\\=\frac{10-8+15}{12}\\=\frac{17}{12}\)
8. \(+\left(\frac{6}{-5}\right) +\left(\frac{9}{-4}\right) -\left(\frac{-11}{7}\right)\\= \frac{-6}{5}- \frac{9}{4}+\frac{11}{7}\\=\frac{-168}{140}-\frac{315}{140}+\frac{220}{140}\\=\frac{-168-315+220}{140}\\=\frac{-263}{140}\)
9. \(-\left(\frac{9}{-8}\right) -\left(\frac{-6}{-6}\right) -\left(\frac{2}{-7}\right)\\= \frac{9}{8}- \frac{6}{6}+\frac{2}{7}\\=\frac{9}{8}-\frac{1}{1}+\frac{2}{7}\\=\frac{63}{56}-\frac{56}{56}+\frac{16}{56}\\=\frac{63-56+16}{56}\\=\frac{23}{56}\)
10. \(-\left(\frac{10}{7}\right) +\left(\frac{10}{10}\right) -\left(\frac{4}{6}\right)\\= \frac{-10}{7}+ \frac{10}{10}-\frac{4}{6}\\=\frac{-10}{7}+\frac{1}{1}-\frac{2}{3}\\=\frac{-30}{21}+\frac{21}{21}-\frac{14}{21}\\=\frac{-30+21-14}{21}\\=\frac{-23}{21}\)
11. \(-\left(\frac{-10}{-9}\right) -\left(\frac{3}{-3}\right) +\left(\frac{10}{-7}\right)\\= \frac{-10}{9}+ \frac{3}{3}-\frac{10}{7}\\=\frac{-10}{9}+\frac{1}{1}-\frac{10}{7}\\=\frac{-70}{63}+\frac{63}{63}-\frac{90}{63}\\=\frac{-70+63-90}{63}\\=\frac{-97}{63}\)
12. \(-\left(\frac{-6}{5}\right) -\left(\frac{7}{4}\right) -\left(\frac{12}{3}\right)\\= \frac{6}{5}- \frac{7}{4}-\frac{12}{3}\\=\frac{6}{5}-\frac{7}{4}-\frac{4}{1}\\=\frac{24}{20}-\frac{35}{20}-\frac{80}{20}\\=\frac{24-35-80}{20}\\=\frac{-91}{20}\)