Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{9}{-2}\right) -\left(\frac{7}{-7}\right) +\left(\frac{9}{2}\right)\\= \frac{9}{2}+ \frac{7}{7}+\frac{9}{2}\\=\frac{9}{2}+\frac{1}{1}+\frac{9}{2}\\=\frac{9+1+9}{2}\\=\frac{19}{2}\)
2. \(+\left(\frac{-5}{6}\right) -\left(\frac{4}{6}\right) -\left(\frac{2}{4}\right)\\= \frac{-5}{6}- \frac{4}{6}-\frac{2}{4}\\=\frac{-5}{6}-\frac{2}{3}-\frac{1}{2}\\=\frac{-5-2-1}{6}\\=\frac{-8}{6}\\=\frac{-4}{3}\)
3. \(+\left(\frac{-2}{-3}\right) +\left(\frac{8}{-6}\right) +\left(\frac{6}{-11}\right)\\= \frac{2}{3}- \frac{8}{6}-\frac{6}{11}\\=\frac{2}{3}-\frac{4}{3}-\frac{6}{11}\\=\frac{22}{33}-\frac{44}{33}-\frac{18}{33}\\=\frac{22-44-18}{33}\\=\frac{-40}{33}\)
4. \(-\left(\frac{5}{-4}\right) +\left(\frac{-3}{-8}\right) -\left(\frac{5}{-8}\right)\\= \frac{5}{4}+ \frac{3}{8}+\frac{5}{8}\\=\frac{10}{8}+\frac{3}{8}+\frac{5}{8}\\=\frac{10+3+5}{8}\\=\frac{18}{8}\\=\frac{9}{4}\)
5. \(+\left(\frac{3}{-7}\right) +\left(\frac{-4}{10}\right) +\left(\frac{-2}{-3}\right)\\= \frac{-3}{7}- \frac{4}{10}+\frac{2}{3}\\=\frac{-3}{7}-\frac{2}{5}+\frac{2}{3}\\=\frac{-45}{105}-\frac{42}{105}+\frac{70}{105}\\=\frac{-45-42+70}{105}\\=\frac{-17}{105}\)
6. \(-\left(\frac{-3}{7}\right) +\left(\frac{-10}{-9}\right) -\left(\frac{-2}{-9}\right)\\= \frac{3}{7}+ \frac{10}{9}-\frac{2}{9}\\=\frac{27}{63}+\frac{70}{63}-\frac{14}{63}\\=\frac{27+70-14}{63}\\=\frac{83}{63}\)
7. \(-\left(\frac{-9}{2}\right) -\left(\frac{-4}{-6}\right) -\left(\frac{-4}{-2}\right)\\= \frac{9}{2}- \frac{4}{6}-\frac{4}{2}\\=\frac{9}{2}-\frac{2}{3}-\frac{2}{1}\\=\frac{27}{6}-\frac{4}{6}-\frac{12}{6}\\=\frac{27-4-12}{6}\\=\frac{11}{6}\)
8. \(+\left(\frac{2}{9}\right) +\left(\frac{-6}{8}\right) -\left(\frac{-6}{10}\right)\\= \frac{2}{9}- \frac{6}{8}+\frac{6}{10}\\=\frac{2}{9}-\frac{3}{4}+\frac{3}{5}\\=\frac{40}{180}-\frac{135}{180}+\frac{108}{180}\\=\frac{40-135+108}{180}\\=\frac{13}{180}\)
9. \(-\left(\frac{5}{6}\right) -\left(\frac{-3}{-10}\right) -\left(\frac{-10}{3}\right)\\= \frac{-5}{6}- \frac{3}{10}+\frac{10}{3}\\=\frac{-25}{30}-\frac{9}{30}+\frac{100}{30}\\=\frac{-25-9+100}{30}\\=\frac{66}{30}\\=\frac{11}{5}\)
10. \(+\left(\frac{-2}{7}\right) +\left(\frac{2}{-2}\right) +\left(\frac{6}{-6}\right)\\= \frac{-2}{7}- \frac{2}{2}-\frac{6}{6}\\=\frac{-2}{7}-\frac{1}{1}-\frac{1}{1}\\=\frac{-2-1-1}{7}\\=\frac{-4}{7}\)
11. \(-\left(\frac{-3}{-4}\right) +\left(\frac{-10}{-7}\right) -\left(\frac{12}{-11}\right)\\= \frac{-3}{4}+ \frac{10}{7}+\frac{12}{11}\\=\frac{-231}{308}+\frac{440}{308}+\frac{336}{308}\\=\frac{-231+440+336}{308}\\=\frac{545}{308}\)
12. \(+\left(\frac{-4}{9}\right) +\left(\frac{-2}{-7}\right) -\left(\frac{2}{-6}\right)\\= \frac{-4}{9}+ \frac{2}{7}+\frac{2}{6}\\=\frac{-4}{9}+\frac{2}{7}+\frac{1}{3}\\=\frac{-28}{63}+\frac{18}{63}+\frac{21}{63}\\=\frac{-28+18+21}{63}\\=\frac{11}{63}\)