Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-2}{9}\right) +\left(\frac{-5}{10}\right) -\left(\frac{-9}{6}\right)\\= \frac{2}{9}- \frac{5}{10}+\frac{9}{6}\\=\frac{2}{9}-\frac{1}{2}+\frac{3}{2}\\=\frac{4}{18}-\frac{9}{18}+\frac{27}{18}\\=\frac{4-9+27}{18}\\=\frac{22}{18}\\=\frac{11}{9}\)
2. \(+\left(\frac{6}{5}\right) +\left(\frac{-8}{-8}\right) +\left(\frac{-8}{10}\right)\\= \frac{6}{5}+ \frac{8}{8}-\frac{8}{10}\\=\frac{6}{5}+\frac{1}{1}-\frac{4}{5}\\=\frac{6+1-4}{5}\\=\frac{3}{5}\)
3. \(-\left(\frac{-6}{5}\right) -\left(\frac{2}{8}\right) +\left(\frac{7}{-6}\right)\\= \frac{6}{5}- \frac{2}{8}-\frac{7}{6}\\=\frac{6}{5}-\frac{1}{4}-\frac{7}{6}\\=\frac{72}{60}-\frac{15}{60}-\frac{70}{60}\\=\frac{72-15-70}{60}\\=\frac{-13}{60}\)
4. \(-\left(\frac{8}{-3}\right) +\left(\frac{10}{-9}\right) -\left(\frac{8}{10}\right)\\= \frac{8}{3}- \frac{10}{9}-\frac{8}{10}\\=\frac{8}{3}-\frac{10}{9}-\frac{4}{5}\\=\frac{120}{45}-\frac{50}{45}-\frac{36}{45}\\=\frac{120-50-36}{45}\\=\frac{34}{45}\)
5. \(+\left(\frac{3}{-4}\right) +\left(\frac{-2}{10}\right) +\left(\frac{6}{-7}\right)\\= \frac{-3}{4}- \frac{2}{10}-\frac{6}{7}\\=\frac{-3}{4}-\frac{1}{5}-\frac{6}{7}\\=\frac{-105}{140}-\frac{28}{140}-\frac{120}{140}\\=\frac{-105-28-120}{140}\\=\frac{-253}{140}\)
6. \(+\left(\frac{6}{5}\right) -\left(\frac{3}{5}\right) +\left(\frac{10}{2}\right)\\= \frac{6}{5}- \frac{3}{5}+\frac{10}{2}\\=\frac{6}{5}-\frac{3}{5}+\frac{5}{1}\\=\frac{6-3+5}{5}\\=\frac{8}{5}\)
7. \(-\left(\frac{3}{-8}\right) -\left(\frac{4}{-10}\right) +\left(\frac{-7}{8}\right)\\= \frac{3}{8}+ \frac{4}{10}-\frac{7}{8}\\=\frac{3}{8}+\frac{2}{5}-\frac{7}{8}\\=\frac{15}{40}+\frac{16}{40}-\frac{35}{40}\\=\frac{15+16-35}{40}\\=\frac{-4}{40}\\=\frac{-1}{10}\)
8. \(-\left(\frac{6}{5}\right) -\left(\frac{7}{-5}\right) +\left(\frac{7}{5}\right)\\= \frac{-6}{5}+ \frac{7}{5}+\frac{7}{5}\\=\frac{-6+7+7}{5}\\=\frac{8}{5}\)
9. \(-\left(\frac{2}{-9}\right) +\left(\frac{6}{5}\right) -\left(\frac{-2}{11}\right)\\= \frac{2}{9}+ \frac{6}{5}+\frac{2}{11}\\=\frac{110}{495}+\frac{594}{495}+\frac{90}{495}\\=\frac{110+594+90}{495}\\=\frac{794}{495}\)
10. \(+\left(\frac{-7}{4}\right) +\left(\frac{-9}{5}\right) -\left(\frac{2}{-2}\right)\\= \frac{-7}{4}- \frac{9}{5}+\frac{2}{2}\\=\frac{-7}{4}-\frac{9}{5}+\frac{1}{1}\\=\frac{-35}{20}-\frac{36}{20}+\frac{20}{20}\\=\frac{-35-36+20}{20}\\=\frac{-51}{20}\)
11. \(-\left(\frac{4}{3}\right) -\left(\frac{9}{-5}\right) -\left(\frac{-7}{3}\right)\\= \frac{-4}{3}+ \frac{9}{5}+\frac{7}{3}\\=\frac{-20}{15}+\frac{27}{15}+\frac{35}{15}\\=\frac{-20+27+35}{15}\\=\frac{42}{15}\\=\frac{14}{5}\)
12. \(-\left(\frac{9}{-2}\right) -\left(\frac{-2}{-4}\right) -\left(\frac{-6}{-6}\right)\\= \frac{9}{2}- \frac{2}{4}-\frac{6}{6}\\=\frac{9}{2}-\frac{1}{2}-\frac{1}{1}\\=\frac{9-1-1}{2}\\=\frac{7}{2}\)