Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{-7}\right) +\left(\frac{-5}{5}\right) +\left(\frac{8}{-3}\right)\\= \frac{10}{7}- \frac{5}{5}-\frac{8}{3}\\=\frac{10}{7}-\frac{1}{1}-\frac{8}{3}\\=\frac{30}{21}-\frac{21}{21}-\frac{56}{21}\\=\frac{30-21-56}{21}\\=\frac{-47}{21}\)
2. \(-\left(\frac{10}{7}\right) +\left(\frac{4}{5}\right) -\left(\frac{10}{-6}\right)\\= \frac{-10}{7}+ \frac{4}{5}+\frac{10}{6}\\=\frac{-10}{7}+\frac{4}{5}+\frac{5}{3}\\=\frac{-150}{105}+\frac{84}{105}+\frac{175}{105}\\=\frac{-150+84+175}{105}\\=\frac{109}{105}\)
3. \(+\left(\frac{9}{-2}\right) -\left(\frac{4}{6}\right) -\left(\frac{8}{12}\right)\\= \frac{-9}{2}- \frac{4}{6}-\frac{8}{12}\\=\frac{-9}{2}-\frac{2}{3}-\frac{2}{3}\\=\frac{-27}{6}-\frac{4}{6}-\frac{4}{6}\\=\frac{-27-4-4}{6}\\=\frac{-35}{6}\)
4. \(-\left(\frac{4}{-7}\right) +\left(\frac{-3}{8}\right) -\left(\frac{-7}{8}\right)\\= \frac{4}{7}- \frac{3}{8}+\frac{7}{8}\\=\frac{32}{56}-\frac{21}{56}+\frac{49}{56}\\=\frac{32-21+49}{56}\\=\frac{60}{56}\\=\frac{15}{14}\)
5. \(-\left(\frac{-10}{-3}\right) +\left(\frac{10}{5}\right) +\left(\frac{-11}{9}\right)\\= \frac{-10}{3}+ \frac{10}{5}-\frac{11}{9}\\=\frac{-10}{3}+\frac{2}{1}-\frac{11}{9}\\=\frac{-30}{9}+\frac{18}{9}-\frac{11}{9}\\=\frac{-30+18-11}{9}\\=\frac{-23}{9}\)
6. \(+\left(\frac{-8}{-9}\right) +\left(\frac{6}{8}\right) -\left(\frac{12}{8}\right)\\= \frac{8}{9}+ \frac{6}{8}-\frac{12}{8}\\=\frac{8}{9}+\frac{3}{4}-\frac{3}{2}\\=\frac{32}{36}+\frac{27}{36}-\frac{54}{36}\\=\frac{32+27-54}{36}\\=\frac{5}{36}\)
7. \(-\left(\frac{2}{-9}\right) -\left(\frac{-8}{-7}\right) +\left(\frac{8}{11}\right)\\= \frac{2}{9}- \frac{8}{7}+\frac{8}{11}\\=\frac{154}{693}-\frac{792}{693}+\frac{504}{693}\\=\frac{154-792+504}{693}\\=\frac{-134}{693}\)
8. \(-\left(\frac{-7}{-8}\right) -\left(\frac{-5}{-9}\right) +\left(\frac{-9}{-9}\right)\\= \frac{-7}{8}- \frac{5}{9}+\frac{9}{9}\\=\frac{-7}{8}-\frac{5}{9}+\frac{1}{1}\\=\frac{-63}{72}-\frac{40}{72}+\frac{72}{72}\\=\frac{-63-40+72}{72}\\=\frac{-31}{72}\)
9. \(-\left(\frac{7}{8}\right) -\left(\frac{-2}{-3}\right) -\left(\frac{-2}{-8}\right)\\= \frac{-7}{8}- \frac{2}{3}-\frac{2}{8}\\=\frac{-7}{8}-\frac{2}{3}-\frac{1}{4}\\=\frac{-21}{24}-\frac{16}{24}-\frac{6}{24}\\=\frac{-21-16-6}{24}\\=\frac{-43}{24}\)
10. \(+\left(\frac{4}{3}\right) -\left(\frac{6}{-8}\right) +\left(\frac{6}{-5}\right)\\= \frac{4}{3}+ \frac{6}{8}-\frac{6}{5}\\=\frac{4}{3}+\frac{3}{4}-\frac{6}{5}\\=\frac{80}{60}+\frac{45}{60}-\frac{72}{60}\\=\frac{80+45-72}{60}\\=\frac{53}{60}\)
11. \(+\left(\frac{5}{8}\right) +\left(\frac{5}{6}\right) -\left(\frac{4}{10}\right)\\= \frac{5}{8}+ \frac{5}{6}-\frac{4}{10}\\=\frac{5}{8}+\frac{5}{6}-\frac{2}{5}\\=\frac{75}{120}+\frac{100}{120}-\frac{48}{120}\\=\frac{75+100-48}{120}\\=\frac{127}{120}\)
12. \(-\left(\frac{6}{-5}\right) -\left(\frac{-2}{9}\right) -\left(\frac{2}{-6}\right)\\= \frac{6}{5}+ \frac{2}{9}+\frac{2}{6}\\=\frac{6}{5}+\frac{2}{9}+\frac{1}{3}\\=\frac{54}{45}+\frac{10}{45}+\frac{15}{45}\\=\frac{54+10+15}{45}\\=\frac{79}{45}\)