Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{8}{-9}\right) -\left(\frac{-4}{-5}\right) +\left(\frac{-8}{-11}\right)\\= \frac{-8}{9}- \frac{4}{5}+\frac{8}{11}\\=\frac{-440}{495}-\frac{396}{495}+\frac{360}{495}\\=\frac{-440-396+360}{495}\\=\frac{-476}{495}\)
2. \(+\left(\frac{4}{-7}\right) +\left(\frac{-4}{-9}\right) -\left(\frac{6}{11}\right)\\= \frac{-4}{7}+ \frac{4}{9}-\frac{6}{11}\\=\frac{-396}{693}+\frac{308}{693}-\frac{378}{693}\\=\frac{-396+308-378}{693}\\=\frac{-466}{693}\)
3. \(-\left(\frac{-9}{-5}\right) -\left(\frac{-3}{-3}\right) +\left(\frac{-7}{10}\right)\\= \frac{-9}{5}- \frac{3}{3}-\frac{7}{10}\\=\frac{-9}{5}-\frac{1}{1}-\frac{7}{10}\\=\frac{-18}{10}-\frac{10}{10}-\frac{7}{10}\\=\frac{-18-10-7}{10}\\=\frac{-35}{10}\\=\frac{-7}{2}\)
4. \(-\left(\frac{-2}{-3}\right) -\left(\frac{7}{4}\right) +\left(\frac{-7}{6}\right)\\= \frac{-2}{3}- \frac{7}{4}-\frac{7}{6}\\=\frac{-8}{12}-\frac{21}{12}-\frac{14}{12}\\=\frac{-8-21-14}{12}\\=\frac{-43}{12}\)
5. \(+\left(\frac{-3}{5}\right) -\left(\frac{-6}{6}\right) -\left(\frac{-4}{3}\right)\\= \frac{-3}{5}+ \frac{6}{6}+\frac{4}{3}\\=\frac{-3}{5}+\frac{1}{1}+\frac{4}{3}\\=\frac{-9}{15}+\frac{15}{15}+\frac{20}{15}\\=\frac{-9+15+20}{15}\\=\frac{26}{15}\)
6. \(+\left(\frac{4}{9}\right) -\left(\frac{-8}{-9}\right) -\left(\frac{3}{12}\right)\\= \frac{4}{9}- \frac{8}{9}-\frac{3}{12}\\=\frac{4}{9}-\frac{8}{9}-\frac{1}{4}\\=\frac{16}{36}-\frac{32}{36}-\frac{9}{36}\\=\frac{16-32-9}{36}\\=\frac{-25}{36}\)
7. \(+\left(\frac{5}{-8}\right) -\left(\frac{-5}{8}\right) +\left(\frac{10}{10}\right)\\= \frac{-5}{8}+ \frac{5}{8}+\frac{10}{10}\\=\frac{-5}{8}+\frac{5}{8}+\frac{1}{1}\\=\frac{-5+5+1}{8}\\=\frac{1}{8}\)
8. \(-\left(\frac{10}{9}\right) -\left(\frac{-6}{10}\right) +\left(\frac{6}{-9}\right)\\= \frac{-10}{9}+ \frac{6}{10}-\frac{6}{9}\\=\frac{-10}{9}+\frac{3}{5}-\frac{2}{3}\\=\frac{-50}{45}+\frac{27}{45}-\frac{30}{45}\\=\frac{-50+27-30}{45}\\=\frac{-53}{45}\)
9. \(+\left(\frac{-6}{-5}\right) -\left(\frac{7}{4}\right) +\left(\frac{-8}{-5}\right)\\= \frac{6}{5}- \frac{7}{4}+\frac{8}{5}\\=\frac{24}{20}-\frac{35}{20}+\frac{32}{20}\\=\frac{24-35+32}{20}\\=\frac{21}{20}\)
10. \(+\left(\frac{3}{-7}\right) -\left(\frac{-3}{-10}\right) +\left(\frac{-10}{-4}\right)\\= \frac{-3}{7}- \frac{3}{10}+\frac{10}{4}\\=\frac{-3}{7}-\frac{3}{10}+\frac{5}{2}\\=\frac{-30}{70}-\frac{21}{70}+\frac{175}{70}\\=\frac{-30-21+175}{70}\\=\frac{124}{70}\\=\frac{62}{35}\)
11. \(-\left(\frac{9}{4}\right) -\left(\frac{8}{-4}\right) +\left(\frac{3}{-4}\right)\\= \frac{-9}{4}+ \frac{8}{4}-\frac{3}{4}\\=\frac{-9}{4}+\frac{2}{1}-\frac{3}{4}\\=\frac{-9+2-3}{4}\\=\frac{-10}{4}\\=\frac{-5}{2}\)
12. \(+\left(\frac{-7}{-2}\right) +\left(\frac{-4}{5}\right) -\left(\frac{3}{-7}\right)\\= \frac{7}{2}- \frac{4}{5}+\frac{3}{7}\\=\frac{245}{70}-\frac{56}{70}+\frac{30}{70}\\=\frac{245-56+30}{70}\\=\frac{219}{70}\)