Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{10}{3}\right) +\left(\frac{10}{-10}\right) +\left(\frac{-3}{-6}\right)\\= \frac{-10}{3}- \frac{10}{10}+\frac{3}{6}\\=\frac{-10}{3}-\frac{1}{1}+\frac{1}{2}\\=\frac{-20}{6}-\frac{6}{6}+\frac{3}{6}\\=\frac{-20-6+3}{6}\\=\frac{-23}{6}\)
2. \(+\left(\frac{9}{-8}\right) -\left(\frac{-6}{6}\right) +\left(\frac{-4}{-2}\right)\\= \frac{-9}{8}+ \frac{6}{6}+\frac{4}{2}\\=\frac{-9}{8}+\frac{1}{1}+\frac{2}{1}\\=\frac{-9+1+2}{8}\\=\frac{-6}{8}\\=\frac{-3}{4}\)
3. \(+\left(\frac{5}{6}\right) -\left(\frac{4}{9}\right) +\left(\frac{-6}{11}\right)\\= \frac{5}{6}- \frac{4}{9}-\frac{6}{11}\\=\frac{165}{198}-\frac{88}{198}-\frac{108}{198}\\=\frac{165-88-108}{198}\\=\frac{-31}{198}\)
4. \(-\left(\frac{-10}{7}\right) -\left(\frac{-10}{-6}\right) +\left(\frac{2}{4}\right)\\= \frac{10}{7}- \frac{10}{6}+\frac{2}{4}\\=\frac{10}{7}-\frac{5}{3}+\frac{1}{2}\\=\frac{60}{42}-\frac{70}{42}+\frac{21}{42}\\=\frac{60-70+21}{42}\\=\frac{11}{42}\)
5. \(-\left(\frac{7}{-6}\right) +\left(\frac{6}{-8}\right) -\left(\frac{-6}{8}\right)\\= \frac{7}{6}- \frac{6}{8}+\frac{6}{8}\\=\frac{7}{6}-\frac{3}{4}+\frac{3}{4}\\=\frac{14}{12}-\frac{9}{12}+\frac{9}{12}\\=\frac{14-9+9}{12}\\=\frac{14}{12}\\=\frac{7}{6}\)
6. \(-\left(\frac{-8}{3}\right) -\left(\frac{-4}{8}\right) -\left(\frac{-6}{-10}\right)\\= \frac{8}{3}+ \frac{4}{8}-\frac{6}{10}\\=\frac{8}{3}+\frac{1}{2}-\frac{3}{5}\\=\frac{80}{30}+\frac{15}{30}-\frac{18}{30}\\=\frac{80+15-18}{30}\\=\frac{77}{30}\)
7. \(+\left(\frac{9}{7}\right) +\left(\frac{9}{-6}\right) +\left(\frac{2}{-7}\right)\\= \frac{9}{7}- \frac{9}{6}-\frac{2}{7}\\=\frac{9}{7}-\frac{3}{2}-\frac{2}{7}\\=\frac{18}{14}-\frac{21}{14}-\frac{4}{14}\\=\frac{18-21-4}{14}\\=\frac{-7}{14}\\=\frac{-1}{2}\)
8. \(+\left(\frac{-3}{-4}\right) +\left(\frac{-2}{2}\right) +\left(\frac{-10}{-10}\right)\\= \frac{3}{4}- \frac{2}{2}+\frac{10}{10}\\=\frac{3}{4}-\frac{1}{1}+\frac{1}{1}\\=\frac{3-1+1}{4}\\=\frac{3}{4}\)
9. \(+\left(\frac{8}{-7}\right) +\left(\frac{-7}{4}\right) -\left(\frac{5}{11}\right)\\= \frac{-8}{7}- \frac{7}{4}-\frac{5}{11}\\=\frac{-352}{308}-\frac{539}{308}-\frac{140}{308}\\=\frac{-352-539-140}{308}\\=\frac{-1031}{308}\)
10. \(-\left(\frac{5}{4}\right) +\left(\frac{-7}{-3}\right) -\left(\frac{-4}{-2}\right)\\= \frac{-5}{4}+ \frac{7}{3}-\frac{4}{2}\\=\frac{-5}{4}+\frac{7}{3}-\frac{2}{1}\\=\frac{-15}{12}+\frac{28}{12}-\frac{24}{12}\\=\frac{-15+28-24}{12}\\=\frac{-11}{12}\)
11. \(-\left(\frac{-10}{9}\right) +\left(\frac{7}{6}\right) +\left(\frac{-5}{9}\right)\\= \frac{10}{9}+ \frac{7}{6}-\frac{5}{9}\\=\frac{20}{18}+\frac{21}{18}-\frac{10}{18}\\=\frac{20+21-10}{18}\\=\frac{31}{18}\)
12. \(-\left(\frac{-7}{-8}\right) -\left(\frac{7}{-5}\right) +\left(\frac{-10}{-10}\right)\\= \frac{-7}{8}+ \frac{7}{5}+\frac{10}{10}\\=\frac{-7}{8}+\frac{7}{5}+\frac{1}{1}\\=\frac{-35}{40}+\frac{56}{40}+\frac{40}{40}\\=\frac{-35+56+40}{40}\\=\frac{61}{40}\)