Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-3}{5}\right) +\left(\frac{5}{-6}\right) +\left(\frac{9}{-12}\right)\\= \frac{-3}{5}- \frac{5}{6}-\frac{9}{12}\\=\frac{-3}{5}-\frac{5}{6}-\frac{3}{4}\\=\frac{-36}{60}-\frac{50}{60}-\frac{45}{60}\\=\frac{-36-50-45}{60}\\=\frac{-131}{60}\)
2. \(+\left(\frac{-7}{-3}\right) -\left(\frac{-5}{-10}\right) +\left(\frac{-6}{-6}\right)\\= \frac{7}{3}- \frac{5}{10}+\frac{6}{6}\\=\frac{7}{3}-\frac{1}{2}+\frac{1}{1}\\=\frac{14}{6}-\frac{3}{6}+\frac{6}{6}\\=\frac{14-3+6}{6}\\=\frac{17}{6}\)
3. \(+\left(\frac{7}{6}\right) -\left(\frac{-6}{5}\right) -\left(\frac{9}{10}\right)\\= \frac{7}{6}+ \frac{6}{5}-\frac{9}{10}\\=\frac{35}{30}+\frac{36}{30}-\frac{27}{30}\\=\frac{35+36-27}{30}\\=\frac{44}{30}\\=\frac{22}{15}\)
4. \(+\left(\frac{-7}{2}\right) -\left(\frac{4}{2}\right) -\left(\frac{7}{-5}\right)\\= \frac{-7}{2}- \frac{4}{2}+\frac{7}{5}\\=\frac{-7}{2}-\frac{2}{1}+\frac{7}{5}\\=\frac{-35}{10}-\frac{20}{10}+\frac{14}{10}\\=\frac{-35-20+14}{10}\\=\frac{-41}{10}\)
5. \(-\left(\frac{8}{-5}\right) -\left(\frac{-10}{6}\right) +\left(\frac{12}{-6}\right)\\= \frac{8}{5}+ \frac{10}{6}-\frac{12}{6}\\=\frac{8}{5}+\frac{5}{3}-\frac{2}{1}\\=\frac{24}{15}+\frac{25}{15}-\frac{30}{15}\\=\frac{24+25-30}{15}\\=\frac{19}{15}\)
6. \(-\left(\frac{8}{3}\right) +\left(\frac{8}{3}\right) +\left(\frac{10}{5}\right)\\= \frac{-8}{3}+ \frac{8}{3}+\frac{10}{5}\\=\frac{-8}{3}+\frac{8}{3}+\frac{2}{1}\\=\frac{-8+8+2}{3}\\=\frac{2}{3}\)
7. \(+\left(\frac{-7}{4}\right) +\left(\frac{2}{2}\right) -\left(\frac{-2}{-7}\right)\\= \frac{-7}{4}+ \frac{2}{2}-\frac{2}{7}\\=\frac{-7}{4}+\frac{1}{1}-\frac{2}{7}\\=\frac{-49}{28}+\frac{28}{28}-\frac{8}{28}\\=\frac{-49+28-8}{28}\\=\frac{-29}{28}\)
8. \(-\left(\frac{-2}{-5}\right) +\left(\frac{3}{3}\right) +\left(\frac{-6}{-11}\right)\\= \frac{-2}{5}+ \frac{3}{3}+\frac{6}{11}\\=\frac{-2}{5}+\frac{1}{1}+\frac{6}{11}\\=\frac{-22}{55}+\frac{55}{55}+\frac{30}{55}\\=\frac{-22+55+30}{55}\\=\frac{63}{55}\)
9. \(+\left(\frac{10}{-9}\right) +\left(\frac{9}{5}\right) -\left(\frac{-2}{-3}\right)\\= \frac{-10}{9}+ \frac{9}{5}-\frac{2}{3}\\=\frac{-50}{45}+\frac{81}{45}-\frac{30}{45}\\=\frac{-50+81-30}{45}\\=\frac{1}{45}\)
10. \(+\left(\frac{-3}{2}\right) -\left(\frac{8}{5}\right) +\left(\frac{-10}{-5}\right)\\= \frac{-3}{2}- \frac{8}{5}+\frac{10}{5}\\=\frac{-3}{2}-\frac{8}{5}+\frac{2}{1}\\=\frac{-15}{10}-\frac{16}{10}+\frac{20}{10}\\=\frac{-15-16+20}{10}\\=\frac{-11}{10}\)
11. \(+\left(\frac{8}{9}\right) -\left(\frac{-3}{-3}\right) -\left(\frac{-5}{-6}\right)\\= \frac{8}{9}- \frac{3}{3}-\frac{5}{6}\\=\frac{8}{9}-\frac{1}{1}-\frac{5}{6}\\=\frac{16}{18}-\frac{18}{18}-\frac{15}{18}\\=\frac{16-18-15}{18}\\=\frac{-17}{18}\)
12. \(+\left(\frac{8}{-5}\right) +\left(\frac{8}{9}\right) +\left(\frac{-8}{-7}\right)\\= \frac{-8}{5}+ \frac{8}{9}+\frac{8}{7}\\=\frac{-504}{315}+\frac{280}{315}+\frac{360}{315}\\=\frac{-504+280+360}{315}\\=\frac{136}{315}\)