Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{5}{-4}\right) -\left(\frac{4}{2}\right) -\left(\frac{-2}{6}\right)\\= \frac{-5}{4}- \frac{4}{2}+\frac{2}{6}\\=\frac{-5}{4}-\frac{2}{1}+\frac{1}{3}\\=\frac{-15}{12}-\frac{24}{12}+\frac{4}{12}\\=\frac{-15-24+4}{12}\\=\frac{-35}{12}\)
2. \(-\left(\frac{-5}{-6}\right) +\left(\frac{-3}{8}\right) +\left(\frac{-4}{-11}\right)\\= \frac{-5}{6}- \frac{3}{8}+\frac{4}{11}\\=\frac{-220}{264}-\frac{99}{264}+\frac{96}{264}\\=\frac{-220-99+96}{264}\\=\frac{-223}{264}\)
3. \(+\left(\frac{5}{8}\right) +\left(\frac{6}{-5}\right) +\left(\frac{-2}{-12}\right)\\= \frac{5}{8}- \frac{6}{5}+\frac{2}{12}\\=\frac{5}{8}-\frac{6}{5}+\frac{1}{6}\\=\frac{75}{120}-\frac{144}{120}+\frac{20}{120}\\=\frac{75-144+20}{120}\\=\frac{-49}{120}\)
4. \(-\left(\frac{-7}{-8}\right) -\left(\frac{8}{3}\right) +\left(\frac{7}{7}\right)\\= \frac{-7}{8}- \frac{8}{3}+\frac{7}{7}\\=\frac{-7}{8}-\frac{8}{3}+\frac{1}{1}\\=\frac{-21}{24}-\frac{64}{24}+\frac{24}{24}\\=\frac{-21-64+24}{24}\\=\frac{-61}{24}\)
5. \(-\left(\frac{-10}{-9}\right) -\left(\frac{-5}{-2}\right) +\left(\frac{-4}{4}\right)\\= \frac{-10}{9}- \frac{5}{2}-\frac{4}{4}\\=\frac{-10}{9}-\frac{5}{2}-\frac{1}{1}\\=\frac{-20}{18}-\frac{45}{18}-\frac{18}{18}\\=\frac{-20-45-18}{18}\\=\frac{-83}{18}\)
6. \(-\left(\frac{10}{-3}\right) -\left(\frac{3}{-7}\right) +\left(\frac{-9}{7}\right)\\= \frac{10}{3}+ \frac{3}{7}-\frac{9}{7}\\=\frac{70}{21}+\frac{9}{21}-\frac{27}{21}\\=\frac{70+9-27}{21}\\=\frac{52}{21}\)
7. \(-\left(\frac{6}{7}\right) -\left(\frac{4}{-2}\right) -\left(\frac{10}{-5}\right)\\= \frac{-6}{7}+ \frac{4}{2}+\frac{10}{5}\\=\frac{-6}{7}+\frac{2}{1}+\frac{2}{1}\\=\frac{-6+2+2}{7}\\=\frac{-2}{7}\)
8. \(-\left(\frac{-4}{-5}\right) +\left(\frac{2}{9}\right) +\left(\frac{-3}{4}\right)\\= \frac{-4}{5}+ \frac{2}{9}-\frac{3}{4}\\=\frac{-144}{180}+\frac{40}{180}-\frac{135}{180}\\=\frac{-144+40-135}{180}\\=\frac{-239}{180}\)
9. \(-\left(\frac{-5}{-9}\right) -\left(\frac{9}{-4}\right) -\left(\frac{3}{10}\right)\\= \frac{-5}{9}+ \frac{9}{4}-\frac{3}{10}\\=\frac{-100}{180}+\frac{405}{180}-\frac{54}{180}\\=\frac{-100+405-54}{180}\\=\frac{251}{180}\)
10. \(+\left(\frac{-2}{-3}\right) +\left(\frac{7}{2}\right) +\left(\frac{-5}{12}\right)\\= \frac{2}{3}+ \frac{7}{2}-\frac{5}{12}\\=\frac{8}{12}+\frac{42}{12}-\frac{5}{12}\\=\frac{8+42-5}{12}\\=\frac{45}{12}\\=\frac{15}{4}\)
11. \(+\left(\frac{-9}{7}\right) -\left(\frac{-7}{-6}\right) +\left(\frac{-4}{9}\right)\\= \frac{-9}{7}- \frac{7}{6}-\frac{4}{9}\\=\frac{-162}{126}-\frac{147}{126}-\frac{56}{126}\\=\frac{-162-147-56}{126}\\=\frac{-365}{126}\)
12. \(+\left(\frac{4}{-3}\right) +\left(\frac{-6}{-9}\right) -\left(\frac{3}{-7}\right)\\= \frac{-4}{3}+ \frac{6}{9}+\frac{3}{7}\\=\frac{-4}{3}+\frac{2}{3}+\frac{3}{7}\\=\frac{-28}{21}+\frac{14}{21}+\frac{9}{21}\\=\frac{-28+14+9}{21}\\=\frac{-5}{21}\)