Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{5}{-9}\right) +\left(\frac{-9}{5}\right) +\left(\frac{-9}{9}\right)\\= \frac{5}{9}- \frac{9}{5}-\frac{9}{9}\\=\frac{5}{9}-\frac{9}{5}-\frac{1}{1}\\=\frac{25}{45}-\frac{81}{45}-\frac{45}{45}\\=\frac{25-81-45}{45}\\=\frac{-101}{45}\)
2. \(-\left(\frac{6}{5}\right) -\left(\frac{-9}{-8}\right) +\left(\frac{-12}{8}\right)\\= \frac{-6}{5}- \frac{9}{8}-\frac{12}{8}\\=\frac{-6}{5}-\frac{9}{8}-\frac{3}{2}\\=\frac{-48}{40}-\frac{45}{40}-\frac{60}{40}\\=\frac{-48-45-60}{40}\\=\frac{-153}{40}\)
3. \(+\left(\frac{-2}{7}\right) -\left(\frac{10}{-4}\right) +\left(\frac{6}{-6}\right)\\= \frac{-2}{7}+ \frac{10}{4}-\frac{6}{6}\\=\frac{-2}{7}+\frac{5}{2}-\frac{1}{1}\\=\frac{-4}{14}+\frac{35}{14}-\frac{14}{14}\\=\frac{-4+35-14}{14}\\=\frac{17}{14}\)
4. \(-\left(\frac{4}{3}\right) -\left(\frac{-9}{-8}\right) -\left(\frac{-6}{-9}\right)\\= \frac{-4}{3}- \frac{9}{8}-\frac{6}{9}\\=\frac{-4}{3}-\frac{9}{8}-\frac{2}{3}\\=\frac{-32}{24}-\frac{27}{24}-\frac{16}{24}\\=\frac{-32-27-16}{24}\\=\frac{-75}{24}\\=\frac{-25}{8}\)
5. \(-\left(\frac{7}{-5}\right) +\left(\frac{-8}{-7}\right) +\left(\frac{3}{6}\right)\\= \frac{7}{5}+ \frac{8}{7}+\frac{3}{6}\\=\frac{7}{5}+\frac{8}{7}+\frac{1}{2}\\=\frac{98}{70}+\frac{80}{70}+\frac{35}{70}\\=\frac{98+80+35}{70}\\=\frac{213}{70}\)
6. \(-\left(\frac{2}{-5}\right) +\left(\frac{-4}{-7}\right) -\left(\frac{-10}{2}\right)\\= \frac{2}{5}+ \frac{4}{7}+\frac{10}{2}\\=\frac{2}{5}+\frac{4}{7}+\frac{5}{1}\\=\frac{14}{35}+\frac{20}{35}+\frac{175}{35}\\=\frac{14+20+175}{35}\\=\frac{209}{35}\)
7. \(+\left(\frac{-8}{-3}\right) -\left(\frac{-9}{2}\right) +\left(\frac{-4}{-5}\right)\\= \frac{8}{3}+ \frac{9}{2}+\frac{4}{5}\\=\frac{80}{30}+\frac{135}{30}+\frac{24}{30}\\=\frac{80+135+24}{30}\\=\frac{239}{30}\)
8. \(+\left(\frac{9}{-2}\right) -\left(\frac{-9}{9}\right) +\left(\frac{-11}{6}\right)\\= \frac{-9}{2}+ \frac{9}{9}-\frac{11}{6}\\=\frac{-9}{2}+\frac{1}{1}-\frac{11}{6}\\=\frac{-27}{6}+\frac{6}{6}-\frac{11}{6}\\=\frac{-27+6-11}{6}\\=\frac{-32}{6}\\=\frac{-16}{3}\)
9. \(+\left(\frac{-8}{-9}\right) -\left(\frac{7}{8}\right) -\left(\frac{-8}{-10}\right)\\= \frac{8}{9}- \frac{7}{8}-\frac{8}{10}\\=\frac{8}{9}-\frac{7}{8}-\frac{4}{5}\\=\frac{320}{360}-\frac{315}{360}-\frac{288}{360}\\=\frac{320-315-288}{360}\\=\frac{-283}{360}\)
10. \(+\left(\frac{-7}{3}\right) -\left(\frac{-10}{10}\right) -\left(\frac{12}{6}\right)\\= \frac{-7}{3}+ \frac{10}{10}-\frac{12}{6}\\=\frac{-7}{3}+\frac{1}{1}-\frac{2}{1}\\=\frac{-7+1-2}{3}\\=\frac{-8}{3}\)
11. \(-\left(\frac{8}{5}\right) -\left(\frac{9}{-5}\right) -\left(\frac{4}{-11}\right)\\= \frac{-8}{5}+ \frac{9}{5}+\frac{4}{11}\\=\frac{-88}{55}+\frac{99}{55}+\frac{20}{55}\\=\frac{-88+99+20}{55}\\=\frac{31}{55}\)
12. \(-\left(\frac{4}{-7}\right) -\left(\frac{-8}{-3}\right) +\left(\frac{9}{2}\right)\\= \frac{4}{7}- \frac{8}{3}+\frac{9}{2}\\=\frac{24}{42}-\frac{112}{42}+\frac{189}{42}\\=\frac{24-112+189}{42}\\=\frac{101}{42}\)