Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{2}{-3}\right) +\left(\frac{-8}{4}\right) -\left(\frac{-8}{8}\right)\\= \frac{-2}{3}- \frac{8}{4}+\frac{8}{8}\\=\frac{-2}{3}-\frac{2}{1}+\frac{1}{1}\\=\frac{-2-2+1}{3}\\=\frac{-3}{3}\\=\frac{-1}{1}\)
2. \(+\left(\frac{8}{9}\right) +\left(\frac{-10}{4}\right) -\left(\frac{2}{10}\right)\\= \frac{8}{9}- \frac{10}{4}-\frac{2}{10}\\=\frac{8}{9}-\frac{5}{2}-\frac{1}{5}\\=\frac{80}{90}-\frac{225}{90}-\frac{18}{90}\\=\frac{80-225-18}{90}\\=\frac{-163}{90}\)
3. \(+\left(\frac{7}{-3}\right) -\left(\frac{4}{-9}\right) +\left(\frac{-2}{6}\right)\\= \frac{-7}{3}+ \frac{4}{9}-\frac{2}{6}\\=\frac{-7}{3}+\frac{4}{9}-\frac{1}{3}\\=\frac{-21}{9}+\frac{4}{9}-\frac{3}{9}\\=\frac{-21+4-3}{9}\\=\frac{-20}{9}\)
4. \(-\left(\frac{4}{9}\right) -\left(\frac{-5}{6}\right) +\left(\frac{-7}{-12}\right)\\= \frac{-4}{9}+ \frac{5}{6}+\frac{7}{12}\\=\frac{-16}{36}+\frac{30}{36}+\frac{21}{36}\\=\frac{-16+30+21}{36}\\=\frac{35}{36}\)
5. \(-\left(\frac{8}{-3}\right) -\left(\frac{-5}{8}\right) -\left(\frac{-10}{-6}\right)\\= \frac{8}{3}+ \frac{5}{8}-\frac{10}{6}\\=\frac{8}{3}+\frac{5}{8}-\frac{5}{3}\\=\frac{64}{24}+\frac{15}{24}-\frac{40}{24}\\=\frac{64+15-40}{24}\\=\frac{39}{24}\\=\frac{13}{8}\)
6. \(+\left(\frac{10}{-3}\right) -\left(\frac{4}{2}\right) -\left(\frac{-11}{6}\right)\\= \frac{-10}{3}- \frac{4}{2}+\frac{11}{6}\\=\frac{-10}{3}-\frac{2}{1}+\frac{11}{6}\\=\frac{-20}{6}-\frac{12}{6}+\frac{11}{6}\\=\frac{-20-12+11}{6}\\=\frac{-21}{6}\\=\frac{-7}{2}\)
7. \(+\left(\frac{8}{-3}\right) +\left(\frac{2}{9}\right) -\left(\frac{-6}{-10}\right)\\= \frac{-8}{3}+ \frac{2}{9}-\frac{6}{10}\\=\frac{-8}{3}+\frac{2}{9}-\frac{3}{5}\\=\frac{-120}{45}+\frac{10}{45}-\frac{27}{45}\\=\frac{-120+10-27}{45}\\=\frac{-137}{45}\)
8. \(+\left(\frac{2}{3}\right) -\left(\frac{2}{-5}\right) +\left(\frac{-4}{12}\right)\\= \frac{2}{3}+ \frac{2}{5}-\frac{4}{12}\\=\frac{2}{3}+\frac{2}{5}-\frac{1}{3}\\=\frac{10}{15}+\frac{6}{15}-\frac{5}{15}\\=\frac{10+6-5}{15}\\=\frac{11}{15}\)
9. \(-\left(\frac{6}{-5}\right) +\left(\frac{10}{-5}\right) +\left(\frac{8}{3}\right)\\= \frac{6}{5}- \frac{10}{5}+\frac{8}{3}\\=\frac{6}{5}-\frac{2}{1}+\frac{8}{3}\\=\frac{18}{15}-\frac{30}{15}+\frac{40}{15}\\=\frac{18-30+40}{15}\\=\frac{28}{15}\)
10. \(+\left(\frac{9}{8}\right) +\left(\frac{4}{-2}\right) +\left(\frac{2}{-8}\right)\\= \frac{9}{8}- \frac{4}{2}-\frac{2}{8}\\=\frac{9}{8}-\frac{2}{1}-\frac{1}{4}\\=\frac{9-2-1}{8}\\=\frac{6}{8}\\=\frac{3}{4}\)
11. \(+\left(\frac{4}{-3}\right) -\left(\frac{-2}{-3}\right) -\left(\frac{-12}{-2}\right)\\= \frac{-4}{3}- \frac{2}{3}-\frac{12}{2}\\=\frac{-4}{3}-\frac{2}{3}-\frac{6}{1}\\=\frac{-4-2-6}{3}\\=\frac{-12}{3}\\=\frac{-4}{1}\)
12. \(+\left(\frac{5}{8}\right) -\left(\frac{9}{2}\right) -\left(\frac{-4}{11}\right)\\= \frac{5}{8}- \frac{9}{2}+\frac{4}{11}\\=\frac{55}{88}-\frac{396}{88}+\frac{32}{88}\\=\frac{55-396+32}{88}\\=\frac{-309}{88}\)