Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{4}{5}\right) -\left(\frac{8}{-4}\right) -\left(\frac{6}{6}\right)\\= \frac{4}{5}+ \frac{8}{4}-\frac{6}{6}\\=\frac{4}{5}+\frac{2}{1}-\frac{1}{1}\\=\frac{4+2-1}{5}\\=\frac{5}{5}\\=\frac{1}{1}\)
2. \(+\left(\frac{6}{-7}\right) +\left(\frac{-10}{2}\right) -\left(\frac{2}{9}\right)\\= \frac{-6}{7}- \frac{10}{2}-\frac{2}{9}\\=\frac{-6}{7}-\frac{5}{1}-\frac{2}{9}\\=\frac{-54}{63}-\frac{315}{63}-\frac{14}{63}\\=\frac{-54-315-14}{63}\\=\frac{-383}{63}\)
3. \(-\left(\frac{9}{-2}\right) -\left(\frac{-5}{-6}\right) -\left(\frac{2}{-12}\right)\\= \frac{9}{2}- \frac{5}{6}+\frac{2}{12}\\=\frac{9}{2}-\frac{5}{6}+\frac{1}{6}\\=\frac{27}{6}-\frac{5}{6}+\frac{1}{6}\\=\frac{27-5+1}{6}\\=\frac{23}{6}\)
4. \(-\left(\frac{-4}{-5}\right) -\left(\frac{-8}{-7}\right) -\left(\frac{5}{-8}\right)\\= \frac{-4}{5}- \frac{8}{7}+\frac{5}{8}\\=\frac{-224}{280}-\frac{320}{280}+\frac{175}{280}\\=\frac{-224-320+175}{280}\\=\frac{-369}{280}\)
5. \(-\left(\frac{-5}{9}\right) -\left(\frac{-6}{6}\right) -\left(\frac{2}{-11}\right)\\= \frac{5}{9}+ \frac{6}{6}+\frac{2}{11}\\=\frac{5}{9}+\frac{1}{1}+\frac{2}{11}\\=\frac{55}{99}+\frac{99}{99}+\frac{18}{99}\\=\frac{55+99+18}{99}\\=\frac{172}{99}\)
6. \(+\left(\frac{7}{-6}\right) +\left(\frac{9}{-6}\right) -\left(\frac{-10}{11}\right)\\= \frac{-7}{6}- \frac{9}{6}+\frac{10}{11}\\=\frac{-7}{6}-\frac{3}{2}+\frac{10}{11}\\=\frac{-77}{66}-\frac{99}{66}+\frac{60}{66}\\=\frac{-77-99+60}{66}\\=\frac{-116}{66}\\=\frac{-58}{33}\)
7. \(-\left(\frac{-7}{-2}\right) +\left(\frac{-2}{-3}\right) +\left(\frac{3}{2}\right)\\= \frac{-7}{2}+ \frac{2}{3}+\frac{3}{2}\\=\frac{-21}{6}+\frac{4}{6}+\frac{9}{6}\\=\frac{-21+4+9}{6}\\=\frac{-8}{6}\\=\frac{-4}{3}\)
8. \(-\left(\frac{6}{5}\right) -\left(\frac{4}{8}\right) +\left(\frac{-5}{-7}\right)\\= \frac{-6}{5}- \frac{4}{8}+\frac{5}{7}\\=\frac{-6}{5}-\frac{1}{2}+\frac{5}{7}\\=\frac{-84}{70}-\frac{35}{70}+\frac{50}{70}\\=\frac{-84-35+50}{70}\\=\frac{-69}{70}\)
9. \(+\left(\frac{-6}{-5}\right) +\left(\frac{-3}{-10}\right) +\left(\frac{10}{-4}\right)\\= \frac{6}{5}+ \frac{3}{10}-\frac{10}{4}\\=\frac{6}{5}+\frac{3}{10}-\frac{5}{2}\\=\frac{12}{10}+\frac{3}{10}-\frac{25}{10}\\=\frac{12+3-25}{10}\\=\frac{-10}{10}\\=\frac{-1}{1}\)
10. \(+\left(\frac{7}{-8}\right) -\left(\frac{-3}{-9}\right) -\left(\frac{-8}{4}\right)\\= \frac{-7}{8}- \frac{3}{9}+\frac{8}{4}\\=\frac{-7}{8}-\frac{1}{3}+\frac{2}{1}\\=\frac{-21}{24}-\frac{8}{24}+\frac{48}{24}\\=\frac{-21-8+48}{24}\\=\frac{19}{24}\)
11. \(+\left(\frac{-7}{2}\right) +\left(\frac{3}{-6}\right) +\left(\frac{-10}{-9}\right)\\= \frac{-7}{2}- \frac{3}{6}+\frac{10}{9}\\=\frac{-7}{2}-\frac{1}{2}+\frac{10}{9}\\=\frac{-63}{18}-\frac{9}{18}+\frac{20}{18}\\=\frac{-63-9+20}{18}\\=\frac{-52}{18}\\=\frac{-26}{9}\)
12. \(+\left(\frac{4}{7}\right) +\left(\frac{2}{-7}\right) -\left(\frac{3}{7}\right)\\= \frac{4}{7}- \frac{2}{7}-\frac{3}{7}\\=\frac{4-2-3}{7}\\=\frac{-1}{7}\)