Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-5}{2}\right) +\left(\frac{-8}{-8}\right) -\left(\frac{10}{-10}\right)\\= \frac{-5}{2}+ \frac{8}{8}+\frac{10}{10}\\=\frac{-5}{2}+\frac{1}{1}+\frac{1}{1}\\=\frac{-5+1+1}{2}\\=\frac{-3}{2}\)
2. \(+\left(\frac{-9}{5}\right) -\left(\frac{4}{5}\right) -\left(\frac{-10}{2}\right)\\= \frac{-9}{5}- \frac{4}{5}+\frac{10}{2}\\=\frac{-9}{5}-\frac{4}{5}+\frac{5}{1}\\=\frac{-9-4+5}{5}\\=\frac{-8}{5}\)
3. \(-\left(\frac{4}{-7}\right) +\left(\frac{-10}{-7}\right) +\left(\frac{11}{7}\right)\\= \frac{4}{7}+ \frac{10}{7}+\frac{11}{7}\\=\frac{4+10+11}{7}\\=\frac{25}{7}\)
4. \(+\left(\frac{6}{5}\right) -\left(\frac{8}{4}\right) -\left(\frac{12}{-5}\right)\\= \frac{6}{5}- \frac{8}{4}+\frac{12}{5}\\=\frac{6}{5}-\frac{2}{1}+\frac{12}{5}\\=\frac{6-2+12}{5}\\=\frac{16}{5}\)
5. \(-\left(\frac{-8}{9}\right) -\left(\frac{-2}{-5}\right) -\left(\frac{-6}{9}\right)\\= \frac{8}{9}- \frac{2}{5}+\frac{6}{9}\\=\frac{8}{9}-\frac{2}{5}+\frac{2}{3}\\=\frac{40}{45}-\frac{18}{45}+\frac{30}{45}\\=\frac{40-18+30}{45}\\=\frac{52}{45}\)
6. \(+\left(\frac{2}{7}\right) -\left(\frac{-4}{2}\right) +\left(\frac{10}{-4}\right)\\= \frac{2}{7}+ \frac{4}{2}-\frac{10}{4}\\=\frac{2}{7}+\frac{2}{1}-\frac{5}{2}\\=\frac{4}{14}+\frac{28}{14}-\frac{35}{14}\\=\frac{4+28-35}{14}\\=\frac{-3}{14}\)
7. \(-\left(\frac{10}{3}\right) +\left(\frac{-4}{3}\right) +\left(\frac{6}{-9}\right)\\= \frac{-10}{3}- \frac{4}{3}-\frac{6}{9}\\=\frac{-10}{3}-\frac{4}{3}-\frac{2}{3}\\=\frac{-10-4-2}{3}\\=\frac{-16}{3}\)
8. \(-\left(\frac{-4}{3}\right) -\left(\frac{-9}{-7}\right) -\left(\frac{-9}{-8}\right)\\= \frac{4}{3}- \frac{9}{7}-\frac{9}{8}\\=\frac{224}{168}-\frac{216}{168}-\frac{189}{168}\\=\frac{224-216-189}{168}\\=\frac{-181}{168}\)
9. \(+\left(\frac{-8}{5}\right) -\left(\frac{-2}{10}\right) -\left(\frac{-2}{11}\right)\\= \frac{-8}{5}+ \frac{2}{10}+\frac{2}{11}\\=\frac{-8}{5}+\frac{1}{5}+\frac{2}{11}\\=\frac{-88}{55}+\frac{11}{55}+\frac{10}{55}\\=\frac{-88+11+10}{55}\\=\frac{-67}{55}\)
10. \(+\left(\frac{-2}{7}\right) -\left(\frac{-9}{-3}\right) +\left(\frac{-9}{3}\right)\\= \frac{-2}{7}- \frac{9}{3}-\frac{9}{3}\\=\frac{-2}{7}-\frac{3}{1}-\frac{3}{1}\\=\frac{-2-3-3}{7}\\=\frac{-8}{7}\)
11. \(-\left(\frac{2}{-5}\right) +\left(\frac{-5}{4}\right) -\left(\frac{-7}{5}\right)\\= \frac{2}{5}- \frac{5}{4}+\frac{7}{5}\\=\frac{8}{20}-\frac{25}{20}+\frac{28}{20}\\=\frac{8-25+28}{20}\\=\frac{11}{20}\)
12. \(-\left(\frac{5}{9}\right) +\left(\frac{-4}{-7}\right) -\left(\frac{-3}{3}\right)\\= \frac{-5}{9}+ \frac{4}{7}+\frac{3}{3}\\=\frac{-5}{9}+\frac{4}{7}+\frac{1}{1}\\=\frac{-35}{63}+\frac{36}{63}+\frac{63}{63}\\=\frac{-35+36+63}{63}\\=\frac{64}{63}\)