Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{6}{5}\right) +\left(\frac{-8}{8}\right) -\left(\frac{4}{-10}\right)\\= \frac{6}{5}- \frac{8}{8}+\frac{4}{10}\\=\frac{6}{5}-\frac{1}{1}+\frac{2}{5}\\=\frac{6-1+2}{5}\\=\frac{7}{5}\)
2. \(-\left(\frac{-5}{-6}\right) +\left(\frac{9}{-6}\right) -\left(\frac{10}{12}\right)\\= \frac{-5}{6}- \frac{9}{6}-\frac{10}{12}\\=\frac{-5}{6}-\frac{3}{2}-\frac{5}{6}\\=\frac{-5-3-5}{6}\\=\frac{-13}{6}\)
3. \(+\left(\frac{6}{-7}\right) +\left(\frac{10}{6}\right) +\left(\frac{-11}{-12}\right)\\= \frac{-6}{7}+ \frac{10}{6}+\frac{11}{12}\\=\frac{-6}{7}+\frac{5}{3}+\frac{11}{12}\\=\frac{-72}{84}+\frac{140}{84}+\frac{77}{84}\\=\frac{-72+140+77}{84}\\=\frac{145}{84}\)
4. \(+\left(\frac{8}{9}\right) -\left(\frac{-5}{-10}\right) +\left(\frac{8}{10}\right)\\= \frac{8}{9}- \frac{5}{10}+\frac{8}{10}\\=\frac{8}{9}-\frac{1}{2}+\frac{4}{5}\\=\frac{80}{90}-\frac{45}{90}+\frac{72}{90}\\=\frac{80-45+72}{90}\\=\frac{107}{90}\)
5. \(+\left(\frac{-6}{-5}\right) +\left(\frac{-8}{2}\right) +\left(\frac{-7}{-8}\right)\\= \frac{6}{5}- \frac{8}{2}+\frac{7}{8}\\=\frac{6}{5}-\frac{4}{1}+\frac{7}{8}\\=\frac{48}{40}-\frac{160}{40}+\frac{35}{40}\\=\frac{48-160+35}{40}\\=\frac{-77}{40}\)
6. \(-\left(\frac{8}{-7}\right) +\left(\frac{10}{10}\right) -\left(\frac{4}{-10}\right)\\= \frac{8}{7}+ \frac{10}{10}+\frac{4}{10}\\=\frac{8}{7}+\frac{1}{1}+\frac{2}{5}\\=\frac{40}{35}+\frac{35}{35}+\frac{14}{35}\\=\frac{40+35+14}{35}\\=\frac{89}{35}\)
7. \(-\left(\frac{5}{-3}\right) -\left(\frac{5}{8}\right) -\left(\frac{-9}{-8}\right)\\= \frac{5}{3}- \frac{5}{8}-\frac{9}{8}\\=\frac{40}{24}-\frac{15}{24}-\frac{27}{24}\\=\frac{40-15-27}{24}\\=\frac{-2}{24}\\=\frac{-1}{12}\)
8. \(+\left(\frac{-8}{-9}\right) -\left(\frac{-4}{-3}\right) -\left(\frac{-4}{-4}\right)\\= \frac{8}{9}- \frac{4}{3}-\frac{4}{4}\\=\frac{8}{9}-\frac{4}{3}-\frac{1}{1}\\=\frac{8-4-1}{9}\\=\frac{3}{9}\\=\frac{1}{3}\)
9. \(+\left(\frac{-4}{-9}\right) +\left(\frac{-4}{8}\right) +\left(\frac{9}{-6}\right)\\= \frac{4}{9}- \frac{4}{8}-\frac{9}{6}\\=\frac{4}{9}-\frac{1}{2}-\frac{3}{2}\\=\frac{8}{18}-\frac{9}{18}-\frac{27}{18}\\=\frac{8-9-27}{18}\\=\frac{-28}{18}\\=\frac{-14}{9}\)
10. \(+\left(\frac{-6}{5}\right) -\left(\frac{-5}{7}\right) -\left(\frac{8}{2}\right)\\= \frac{-6}{5}+ \frac{5}{7}-\frac{8}{2}\\=\frac{-6}{5}+\frac{5}{7}-\frac{4}{1}\\=\frac{-42}{35}+\frac{25}{35}-\frac{140}{35}\\=\frac{-42+25-140}{35}\\=\frac{-157}{35}\)
11. \(+\left(\frac{2}{9}\right) -\left(\frac{-6}{-5}\right) -\left(\frac{10}{5}\right)\\= \frac{2}{9}- \frac{6}{5}-\frac{10}{5}\\=\frac{2}{9}-\frac{6}{5}-\frac{2}{1}\\=\frac{10}{45}-\frac{54}{45}-\frac{90}{45}\\=\frac{10-54-90}{45}\\=\frac{-134}{45}\)
12. \(+\left(\frac{-5}{7}\right) -\left(\frac{-6}{6}\right) +\left(\frac{-7}{9}\right)\\= \frac{-5}{7}+ \frac{6}{6}-\frac{7}{9}\\=\frac{-5}{7}+\frac{1}{1}-\frac{7}{9}\\=\frac{-45}{63}+\frac{63}{63}-\frac{49}{63}\\=\frac{-45+63-49}{63}\\=\frac{-31}{63}\)