Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{3}{-8}\right) -\left(\frac{3}{-7}\right) -\left(\frac{8}{6}\right)\\= \frac{-3}{8}+ \frac{3}{7}-\frac{8}{6}\\=\frac{-3}{8}+\frac{3}{7}-\frac{4}{3}\\=\frac{-63}{168}+\frac{72}{168}-\frac{224}{168}\\=\frac{-63+72-224}{168}\\=\frac{-215}{168}\)
2. \(-\left(\frac{-7}{-3}\right) +\left(\frac{-2}{-9}\right) +\left(\frac{-6}{8}\right)\\= \frac{-7}{3}+ \frac{2}{9}-\frac{6}{8}\\=\frac{-7}{3}+\frac{2}{9}-\frac{3}{4}\\=\frac{-84}{36}+\frac{8}{36}-\frac{27}{36}\\=\frac{-84+8-27}{36}\\=\frac{-103}{36}\)
3. \(+\left(\frac{-5}{6}\right) -\left(\frac{-2}{-6}\right) -\left(\frac{11}{-12}\right)\\= \frac{-5}{6}- \frac{2}{6}+\frac{11}{12}\\=\frac{-5}{6}-\frac{1}{3}+\frac{11}{12}\\=\frac{-10}{12}-\frac{4}{12}+\frac{11}{12}\\=\frac{-10-4+11}{12}\\=\frac{-3}{12}\\=\frac{-1}{4}\)
4. \(-\left(\frac{5}{-2}\right) +\left(\frac{9}{10}\right) -\left(\frac{-12}{-11}\right)\\= \frac{5}{2}+ \frac{9}{10}-\frac{12}{11}\\=\frac{275}{110}+\frac{99}{110}-\frac{120}{110}\\=\frac{275+99-120}{110}\\=\frac{254}{110}\\=\frac{127}{55}\)
5. \(-\left(\frac{-7}{-2}\right) +\left(\frac{-4}{-2}\right) -\left(\frac{-8}{-12}\right)\\= \frac{-7}{2}+ \frac{4}{2}-\frac{8}{12}\\=\frac{-7}{2}+\frac{2}{1}-\frac{2}{3}\\=\frac{-21}{6}+\frac{12}{6}-\frac{4}{6}\\=\frac{-21+12-4}{6}\\=\frac{-13}{6}\)
6. \(+\left(\frac{-5}{-2}\right) -\left(\frac{-4}{3}\right) -\left(\frac{-5}{-5}\right)\\= \frac{5}{2}+ \frac{4}{3}-\frac{5}{5}\\=\frac{5}{2}+\frac{4}{3}-\frac{1}{1}\\=\frac{15}{6}+\frac{8}{6}-\frac{6}{6}\\=\frac{15+8-6}{6}\\=\frac{17}{6}\)
7. \(+\left(\frac{-4}{-7}\right) -\left(\frac{5}{8}\right) -\left(\frac{8}{6}\right)\\= \frac{4}{7}- \frac{5}{8}-\frac{8}{6}\\=\frac{4}{7}-\frac{5}{8}-\frac{4}{3}\\=\frac{96}{168}-\frac{105}{168}-\frac{224}{168}\\=\frac{96-105-224}{168}\\=\frac{-233}{168}\)
8. \(-\left(\frac{-5}{8}\right) -\left(\frac{-10}{-7}\right) -\left(\frac{10}{11}\right)\\= \frac{5}{8}- \frac{10}{7}-\frac{10}{11}\\=\frac{385}{616}-\frac{880}{616}-\frac{560}{616}\\=\frac{385-880-560}{616}\\=\frac{-1055}{616}\)
9. \(+\left(\frac{3}{-2}\right) +\left(\frac{6}{-2}\right) +\left(\frac{3}{9}\right)\\= \frac{-3}{2}- \frac{6}{2}+\frac{3}{9}\\=\frac{-3}{2}-\frac{3}{1}+\frac{1}{3}\\=\frac{-9}{6}-\frac{18}{6}+\frac{2}{6}\\=\frac{-9-18+2}{6}\\=\frac{-25}{6}\)
10. \(-\left(\frac{10}{-3}\right) +\left(\frac{7}{-6}\right) -\left(\frac{3}{3}\right)\\= \frac{10}{3}- \frac{7}{6}-\frac{3}{3}\\=\frac{10}{3}-\frac{7}{6}-\frac{1}{1}\\=\frac{20}{6}-\frac{7}{6}-\frac{6}{6}\\=\frac{20-7-6}{6}\\=\frac{7}{6}\)
11. \(+\left(\frac{9}{-7}\right) -\left(\frac{9}{-4}\right) +\left(\frac{9}{11}\right)\\= \frac{-9}{7}+ \frac{9}{4}+\frac{9}{11}\\=\frac{-396}{308}+\frac{693}{308}+\frac{252}{308}\\=\frac{-396+693+252}{308}\\=\frac{549}{308}\)
12. \(+\left(\frac{-8}{3}\right) +\left(\frac{-2}{-8}\right) -\left(\frac{12}{-3}\right)\\= \frac{-8}{3}+ \frac{2}{8}+\frac{12}{3}\\=\frac{-8}{3}+\frac{1}{4}+\frac{4}{1}\\=\frac{-32}{12}+\frac{3}{12}+\frac{48}{12}\\=\frac{-32+3+48}{12}\\=\frac{19}{12}\)