Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{10}{7}\right) -\left(\frac{-9}{-8}\right) +\left(\frac{11}{9}\right)\\= \frac{10}{7}- \frac{9}{8}+\frac{11}{9}\\=\frac{720}{504}-\frac{567}{504}+\frac{616}{504}\\=\frac{720-567+616}{504}\\=\frac{769}{504}\)
2. \(+\left(\frac{4}{9}\right) +\left(\frac{-9}{9}\right) -\left(\frac{-3}{-6}\right)\\= \frac{4}{9}- \frac{9}{9}-\frac{3}{6}\\=\frac{4}{9}-\frac{1}{1}-\frac{1}{2}\\=\frac{8}{18}-\frac{18}{18}-\frac{9}{18}\\=\frac{8-18-9}{18}\\=\frac{-19}{18}\)
3. \(+\left(\frac{-2}{5}\right) -\left(\frac{-3}{9}\right) -\left(\frac{-10}{-12}\right)\\= \frac{-2}{5}+ \frac{3}{9}-\frac{10}{12}\\=\frac{-2}{5}+\frac{1}{3}-\frac{5}{6}\\=\frac{-12}{30}+\frac{10}{30}-\frac{25}{30}\\=\frac{-12+10-25}{30}\\=\frac{-27}{30}\\=\frac{-9}{10}\)
4. \(+\left(\frac{6}{-5}\right) +\left(\frac{2}{5}\right) +\left(\frac{-4}{-10}\right)\\= \frac{-6}{5}+ \frac{2}{5}+\frac{4}{10}\\=\frac{-6}{5}+\frac{2}{5}+\frac{2}{5}\\=\frac{-6+2+2}{5}\\=\frac{-2}{5}\)
5. \(+\left(\frac{-4}{9}\right) -\left(\frac{-7}{-2}\right) -\left(\frac{-9}{-3}\right)\\= \frac{-4}{9}- \frac{7}{2}-\frac{9}{3}\\=\frac{-4}{9}-\frac{7}{2}-\frac{3}{1}\\=\frac{-8}{18}-\frac{63}{18}-\frac{54}{18}\\=\frac{-8-63-54}{18}\\=\frac{-125}{18}\)
6. \(+\left(\frac{-6}{-5}\right) +\left(\frac{-2}{-7}\right) -\left(\frac{-2}{8}\right)\\= \frac{6}{5}+ \frac{2}{7}+\frac{2}{8}\\=\frac{6}{5}+\frac{2}{7}+\frac{1}{4}\\=\frac{168}{140}+\frac{40}{140}+\frac{35}{140}\\=\frac{168+40+35}{140}\\=\frac{243}{140}\)
7. \(-\left(\frac{-9}{2}\right) -\left(\frac{-7}{-6}\right) +\left(\frac{-9}{-3}\right)\\= \frac{9}{2}- \frac{7}{6}+\frac{9}{3}\\=\frac{9}{2}-\frac{7}{6}+\frac{3}{1}\\=\frac{27}{6}-\frac{7}{6}+\frac{18}{6}\\=\frac{27-7+18}{6}\\=\frac{38}{6}\\=\frac{19}{3}\)
8. \(+\left(\frac{8}{-3}\right) +\left(\frac{8}{-6}\right) -\left(\frac{-5}{-6}\right)\\= \frac{-8}{3}- \frac{8}{6}-\frac{5}{6}\\=\frac{-8}{3}-\frac{4}{3}-\frac{5}{6}\\=\frac{-16}{6}-\frac{8}{6}-\frac{5}{6}\\=\frac{-16-8-5}{6}\\=\frac{-29}{6}\)
9. \(+\left(\frac{3}{8}\right) -\left(\frac{8}{-4}\right) +\left(\frac{-9}{-8}\right)\\= \frac{3}{8}+ \frac{8}{4}+\frac{9}{8}\\=\frac{3}{8}+\frac{2}{1}+\frac{9}{8}\\=\frac{3+2+9}{8}\\=\frac{14}{8}\\=\frac{7}{4}\)
10. \(-\left(\frac{-3}{2}\right) -\left(\frac{10}{-8}\right) -\left(\frac{11}{-7}\right)\\= \frac{3}{2}+ \frac{10}{8}+\frac{11}{7}\\=\frac{3}{2}+\frac{5}{4}+\frac{11}{7}\\=\frac{42}{28}+\frac{35}{28}+\frac{44}{28}\\=\frac{42+35+44}{28}\\=\frac{121}{28}\)
11. \(-\left(\frac{-7}{2}\right) -\left(\frac{8}{-9}\right) +\left(\frac{3}{7}\right)\\= \frac{7}{2}+ \frac{8}{9}+\frac{3}{7}\\=\frac{441}{126}+\frac{112}{126}+\frac{54}{126}\\=\frac{441+112+54}{126}\\=\frac{607}{126}\)
12. \(-\left(\frac{7}{-5}\right) -\left(\frac{-5}{5}\right) -\left(\frac{4}{-5}\right)\\= \frac{7}{5}+ \frac{5}{5}+\frac{4}{5}\\=\frac{7}{5}+\frac{1}{1}+\frac{4}{5}\\=\frac{7+1+4}{5}\\=\frac{12}{5}\)