Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-7}{8}\right) -\left(\frac{-4}{-9}\right) -\left(\frac{3}{7}\right)\\= \frac{7}{8}- \frac{4}{9}-\frac{3}{7}\\=\frac{441}{504}-\frac{224}{504}-\frac{216}{504}\\=\frac{441-224-216}{504}\\=\frac{1}{504}\)
2. \(-\left(\frac{-6}{-5}\right) -\left(\frac{10}{9}\right) -\left(\frac{8}{-7}\right)\\= \frac{-6}{5}- \frac{10}{9}+\frac{8}{7}\\=\frac{-378}{315}-\frac{350}{315}+\frac{360}{315}\\=\frac{-378-350+360}{315}\\=\frac{-368}{315}\)
3. \(-\left(\frac{-4}{5}\right) +\left(\frac{-9}{8}\right) +\left(\frac{-6}{8}\right)\\= \frac{4}{5}- \frac{9}{8}-\frac{6}{8}\\=\frac{4}{5}-\frac{9}{8}-\frac{3}{4}\\=\frac{32}{40}-\frac{45}{40}-\frac{30}{40}\\=\frac{32-45-30}{40}\\=\frac{-43}{40}\)
4. \(-\left(\frac{6}{5}\right) -\left(\frac{10}{2}\right) -\left(\frac{11}{9}\right)\\= \frac{-6}{5}- \frac{10}{2}-\frac{11}{9}\\=\frac{-6}{5}-\frac{5}{1}-\frac{11}{9}\\=\frac{-54}{45}-\frac{225}{45}-\frac{55}{45}\\=\frac{-54-225-55}{45}\\=\frac{-334}{45}\)
5. \(-\left(\frac{4}{-3}\right) -\left(\frac{-9}{10}\right) +\left(\frac{2}{-3}\right)\\= \frac{4}{3}+ \frac{9}{10}-\frac{2}{3}\\=\frac{40}{30}+\frac{27}{30}-\frac{20}{30}\\=\frac{40+27-20}{30}\\=\frac{47}{30}\)
6. \(-\left(\frac{-7}{-9}\right) +\left(\frac{-5}{4}\right) +\left(\frac{5}{-3}\right)\\= \frac{-7}{9}- \frac{5}{4}-\frac{5}{3}\\=\frac{-28}{36}-\frac{45}{36}-\frac{60}{36}\\=\frac{-28-45-60}{36}\\=\frac{-133}{36}\)
7. \(+\left(\frac{-7}{5}\right) +\left(\frac{5}{-9}\right) -\left(\frac{7}{9}\right)\\= \frac{-7}{5}- \frac{5}{9}-\frac{7}{9}\\=\frac{-63}{45}-\frac{25}{45}-\frac{35}{45}\\=\frac{-63-25-35}{45}\\=\frac{-123}{45}\\=\frac{-41}{15}\)
8. \(+\left(\frac{-10}{-9}\right) +\left(\frac{4}{7}\right) -\left(\frac{2}{3}\right)\\= \frac{10}{9}+ \frac{4}{7}-\frac{2}{3}\\=\frac{70}{63}+\frac{36}{63}-\frac{42}{63}\\=\frac{70+36-42}{63}\\=\frac{64}{63}\)
9. \(+\left(\frac{8}{-9}\right) -\left(\frac{-5}{-3}\right) +\left(\frac{-2}{-11}\right)\\= \frac{-8}{9}- \frac{5}{3}+\frac{2}{11}\\=\frac{-88}{99}-\frac{165}{99}+\frac{18}{99}\\=\frac{-88-165+18}{99}\\=\frac{-235}{99}\)
10. \(-\left(\frac{2}{7}\right) -\left(\frac{-10}{5}\right) -\left(\frac{-9}{4}\right)\\= \frac{-2}{7}+ \frac{10}{5}+\frac{9}{4}\\=\frac{-2}{7}+\frac{2}{1}+\frac{9}{4}\\=\frac{-8}{28}+\frac{56}{28}+\frac{63}{28}\\=\frac{-8+56+63}{28}\\=\frac{111}{28}\)
11. \(+\left(\frac{-2}{5}\right) -\left(\frac{-4}{-3}\right) -\left(\frac{-5}{-11}\right)\\= \frac{-2}{5}- \frac{4}{3}-\frac{5}{11}\\=\frac{-66}{165}-\frac{220}{165}-\frac{75}{165}\\=\frac{-66-220-75}{165}\\=\frac{-361}{165}\)
12. \(-\left(\frac{-8}{3}\right) -\left(\frac{3}{2}\right) +\left(\frac{10}{-3}\right)\\= \frac{8}{3}- \frac{3}{2}-\frac{10}{3}\\=\frac{16}{6}-\frac{9}{6}-\frac{20}{6}\\=\frac{16-9-20}{6}\\=\frac{-13}{6}\)