Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{10}{-3}\right) -\left(\frac{-4}{-7}\right) -\left(\frac{-4}{-6}\right)\\= \frac{10}{3}- \frac{4}{7}-\frac{4}{6}\\=\frac{10}{3}-\frac{4}{7}-\frac{2}{3}\\=\frac{70}{21}-\frac{12}{21}-\frac{14}{21}\\=\frac{70-12-14}{21}\\=\frac{44}{21}\)
2. \(-\left(\frac{7}{6}\right) +\left(\frac{2}{7}\right) +\left(\frac{-8}{6}\right)\\= \frac{-7}{6}+ \frac{2}{7}-\frac{8}{6}\\=\frac{-7}{6}+\frac{2}{7}-\frac{4}{3}\\=\frac{-49}{42}+\frac{12}{42}-\frac{56}{42}\\=\frac{-49+12-56}{42}\\=\frac{-93}{42}\\=\frac{-31}{14}\)
3. \(+\left(\frac{3}{-2}\right) -\left(\frac{-9}{6}\right) +\left(\frac{10}{-9}\right)\\= \frac{-3}{2}+ \frac{9}{6}-\frac{10}{9}\\=\frac{-3}{2}+\frac{3}{2}-\frac{10}{9}\\=\frac{-27}{18}+\frac{27}{18}-\frac{20}{18}\\=\frac{-27+27-20}{18}\\=\frac{-20}{18}\\=\frac{-10}{9}\)
4. \(-\left(\frac{-10}{-7}\right) -\left(\frac{2}{9}\right) -\left(\frac{3}{10}\right)\\= \frac{-10}{7}- \frac{2}{9}-\frac{3}{10}\\=\frac{-900}{630}-\frac{140}{630}-\frac{189}{630}\\=\frac{-900-140-189}{630}\\=\frac{-1229}{630}\)
5. \(-\left(\frac{7}{9}\right) -\left(\frac{-3}{5}\right) -\left(\frac{8}{-5}\right)\\= \frac{-7}{9}+ \frac{3}{5}+\frac{8}{5}\\=\frac{-35}{45}+\frac{27}{45}+\frac{72}{45}\\=\frac{-35+27+72}{45}\\=\frac{64}{45}\)
6. \(-\left(\frac{-9}{5}\right) +\left(\frac{-10}{-2}\right) -\left(\frac{-12}{-2}\right)\\= \frac{9}{5}+ \frac{10}{2}-\frac{12}{2}\\=\frac{9}{5}+\frac{5}{1}-\frac{6}{1}\\=\frac{9+5-6}{5}\\=\frac{8}{5}\)
7. \(+\left(\frac{-6}{5}\right) -\left(\frac{-4}{-5}\right) +\left(\frac{5}{8}\right)\\= \frac{-6}{5}- \frac{4}{5}+\frac{5}{8}\\=\frac{-48}{40}-\frac{32}{40}+\frac{25}{40}\\=\frac{-48-32+25}{40}\\=\frac{-55}{40}\\=\frac{-11}{8}\)
8. \(+\left(\frac{-6}{7}\right) +\left(\frac{-9}{9}\right) +\left(\frac{-4}{5}\right)\\= \frac{-6}{7}- \frac{9}{9}-\frac{4}{5}\\=\frac{-6}{7}-\frac{1}{1}-\frac{4}{5}\\=\frac{-30}{35}-\frac{35}{35}-\frac{28}{35}\\=\frac{-30-35-28}{35}\\=\frac{-93}{35}\)
9. \(-\left(\frac{-4}{9}\right) -\left(\frac{4}{9}\right) -\left(\frac{-11}{-11}\right)\\= \frac{4}{9}- \frac{4}{9}-\frac{11}{11}\\=\frac{4}{9}-\frac{4}{9}-\frac{1}{1}\\=\frac{4-4-1}{9}\\=\frac{-1}{9}\)
10. \(+\left(\frac{-10}{9}\right) -\left(\frac{-5}{9}\right) +\left(\frac{3}{-7}\right)\\= \frac{-10}{9}+ \frac{5}{9}-\frac{3}{7}\\=\frac{-70}{63}+\frac{35}{63}-\frac{27}{63}\\=\frac{-70+35-27}{63}\\=\frac{-62}{63}\)
11. \(-\left(\frac{8}{-9}\right) +\left(\frac{-6}{-8}\right) +\left(\frac{11}{10}\right)\\= \frac{8}{9}+ \frac{6}{8}+\frac{11}{10}\\=\frac{8}{9}+\frac{3}{4}+\frac{11}{10}\\=\frac{160}{180}+\frac{135}{180}+\frac{198}{180}\\=\frac{160+135+198}{180}\\=\frac{493}{180}\)
12. \(+\left(\frac{9}{10}\right) +\left(\frac{4}{-2}\right) +\left(\frac{9}{-2}\right)\\= \frac{9}{10}- \frac{4}{2}-\frac{9}{2}\\=\frac{9}{10}-\frac{2}{1}-\frac{9}{2}\\=\frac{9-2-9}{10}\\=\frac{-2}{10}\\=\frac{-1}{5}\)