Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{10}{-7}\right) -\left(\frac{-5}{9}\right) -\left(\frac{2}{-2}\right)\\= \frac{10}{7}+ \frac{5}{9}+\frac{2}{2}\\=\frac{10}{7}+\frac{5}{9}+\frac{1}{1}\\=\frac{90}{63}+\frac{35}{63}+\frac{63}{63}\\=\frac{90+35+63}{63}\\=\frac{188}{63}\)
2. \(-\left(\frac{-7}{-2}\right) +\left(\frac{-10}{6}\right) +\left(\frac{2}{6}\right)\\= \frac{-7}{2}- \frac{10}{6}+\frac{2}{6}\\=\frac{-7}{2}-\frac{5}{3}+\frac{1}{3}\\=\frac{-21}{6}-\frac{10}{6}+\frac{2}{6}\\=\frac{-21-10+2}{6}\\=\frac{-29}{6}\)
3. \(+\left(\frac{2}{-7}\right) -\left(\frac{3}{-9}\right) +\left(\frac{-5}{10}\right)\\= \frac{-2}{7}+ \frac{3}{9}-\frac{5}{10}\\=\frac{-2}{7}+\frac{1}{3}-\frac{1}{2}\\=\frac{-12}{42}+\frac{14}{42}-\frac{21}{42}\\=\frac{-12+14-21}{42}\\=\frac{-19}{42}\)
4. \(-\left(\frac{5}{-2}\right) +\left(\frac{5}{8}\right) -\left(\frac{5}{7}\right)\\= \frac{5}{2}+ \frac{5}{8}-\frac{5}{7}\\=\frac{140}{56}+\frac{35}{56}-\frac{40}{56}\\=\frac{140+35-40}{56}\\=\frac{135}{56}\)
5. \(+\left(\frac{-6}{-5}\right) -\left(\frac{8}{-6}\right) -\left(\frac{5}{10}\right)\\= \frac{6}{5}+ \frac{8}{6}-\frac{5}{10}\\=\frac{6}{5}+\frac{4}{3}-\frac{1}{2}\\=\frac{36}{30}+\frac{40}{30}-\frac{15}{30}\\=\frac{36+40-15}{30}\\=\frac{61}{30}\)
6. \(-\left(\frac{-9}{-7}\right) +\left(\frac{-8}{-8}\right) -\left(\frac{-5}{6}\right)\\= \frac{-9}{7}+ \frac{8}{8}+\frac{5}{6}\\=\frac{-9}{7}+\frac{1}{1}+\frac{5}{6}\\=\frac{-54}{42}+\frac{42}{42}+\frac{35}{42}\\=\frac{-54+42+35}{42}\\=\frac{23}{42}\)
7. \(-\left(\frac{10}{9}\right) -\left(\frac{4}{9}\right) -\left(\frac{11}{-5}\right)\\= \frac{-10}{9}- \frac{4}{9}+\frac{11}{5}\\=\frac{-50}{45}-\frac{20}{45}+\frac{99}{45}\\=\frac{-50-20+99}{45}\\=\frac{29}{45}\)
8. \(-\left(\frac{10}{9}\right) -\left(\frac{-7}{5}\right) +\left(\frac{-8}{-12}\right)\\= \frac{-10}{9}+ \frac{7}{5}+\frac{8}{12}\\=\frac{-10}{9}+\frac{7}{5}+\frac{2}{3}\\=\frac{-50}{45}+\frac{63}{45}+\frac{30}{45}\\=\frac{-50+63+30}{45}\\=\frac{43}{45}\)
9. \(-\left(\frac{3}{-7}\right) +\left(\frac{5}{2}\right) -\left(\frac{-9}{-12}\right)\\= \frac{3}{7}+ \frac{5}{2}-\frac{9}{12}\\=\frac{3}{7}+\frac{5}{2}-\frac{3}{4}\\=\frac{12}{28}+\frac{70}{28}-\frac{21}{28}\\=\frac{12+70-21}{28}\\=\frac{61}{28}\)
10. \(-\left(\frac{-9}{2}\right) +\left(\frac{6}{-9}\right) -\left(\frac{6}{-9}\right)\\= \frac{9}{2}- \frac{6}{9}+\frac{6}{9}\\=\frac{9}{2}-\frac{2}{3}+\frac{2}{3}\\=\frac{27}{6}-\frac{4}{6}+\frac{4}{6}\\=\frac{27-4+4}{6}\\=\frac{27}{6}\\=\frac{9}{2}\)
11. \(-\left(\frac{-2}{3}\right) +\left(\frac{-2}{5}\right) +\left(\frac{-9}{11}\right)\\= \frac{2}{3}- \frac{2}{5}-\frac{9}{11}\\=\frac{110}{165}-\frac{66}{165}-\frac{135}{165}\\=\frac{110-66-135}{165}\\=\frac{-91}{165}\)
12. \(-\left(\frac{-10}{-7}\right) +\left(\frac{-10}{3}\right) -\left(\frac{-2}{8}\right)\\= \frac{-10}{7}- \frac{10}{3}+\frac{2}{8}\\=\frac{-10}{7}-\frac{10}{3}+\frac{1}{4}\\=\frac{-120}{84}-\frac{280}{84}+\frac{21}{84}\\=\frac{-120-280+21}{84}\\=\frac{-379}{84}\)