Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{3}\right) +\left(\frac{5}{-5}\right) -\left(\frac{6}{11}\right)\\= \frac{-10}{3}- \frac{5}{5}-\frac{6}{11}\\=\frac{-10}{3}-\frac{1}{1}-\frac{6}{11}\\=\frac{-110}{33}-\frac{33}{33}-\frac{18}{33}\\=\frac{-110-33-18}{33}\\=\frac{-161}{33}\)
2. \(-\left(\frac{-9}{4}\right) -\left(\frac{-5}{5}\right) +\left(\frac{2}{6}\right)\\= \frac{9}{4}+ \frac{5}{5}+\frac{2}{6}\\=\frac{9}{4}+\frac{1}{1}+\frac{1}{3}\\=\frac{27}{12}+\frac{12}{12}+\frac{4}{12}\\=\frac{27+12+4}{12}\\=\frac{43}{12}\)
3. \(-\left(\frac{6}{-7}\right) -\left(\frac{-8}{-9}\right) +\left(\frac{-6}{5}\right)\\= \frac{6}{7}- \frac{8}{9}-\frac{6}{5}\\=\frac{270}{315}-\frac{280}{315}-\frac{378}{315}\\=\frac{270-280-378}{315}\\=\frac{-388}{315}\)
4. \(-\left(\frac{6}{-5}\right) -\left(\frac{-9}{-10}\right) -\left(\frac{-4}{-2}\right)\\= \frac{6}{5}- \frac{9}{10}-\frac{4}{2}\\=\frac{6}{5}-\frac{9}{10}-\frac{2}{1}\\=\frac{12}{10}-\frac{9}{10}-\frac{20}{10}\\=\frac{12-9-20}{10}\\=\frac{-17}{10}\)
5. \(-\left(\frac{-7}{-2}\right) -\left(\frac{5}{3}\right) -\left(\frac{-12}{9}\right)\\= \frac{-7}{2}- \frac{5}{3}+\frac{12}{9}\\=\frac{-7}{2}-\frac{5}{3}+\frac{4}{3}\\=\frac{-21}{6}-\frac{10}{6}+\frac{8}{6}\\=\frac{-21-10+8}{6}\\=\frac{-23}{6}\)
6. \(-\left(\frac{-9}{7}\right) -\left(\frac{-10}{-10}\right) -\left(\frac{12}{-10}\right)\\= \frac{9}{7}- \frac{10}{10}+\frac{12}{10}\\=\frac{9}{7}-\frac{1}{1}+\frac{6}{5}\\=\frac{45}{35}-\frac{35}{35}+\frac{42}{35}\\=\frac{45-35+42}{35}\\=\frac{52}{35}\)
7. \(-\left(\frac{3}{2}\right) +\left(\frac{-8}{-2}\right) +\left(\frac{8}{-8}\right)\\= \frac{-3}{2}+ \frac{8}{2}-\frac{8}{8}\\=\frac{-3}{2}+\frac{4}{1}-\frac{1}{1}\\=\frac{-3+4-1}{2}\\=\frac{0}{2}\\=\frac{0}{1}\)
8. \(+\left(\frac{5}{-8}\right) -\left(\frac{-10}{-7}\right) -\left(\frac{-10}{6}\right)\\= \frac{-5}{8}- \frac{10}{7}+\frac{10}{6}\\=\frac{-5}{8}-\frac{10}{7}+\frac{5}{3}\\=\frac{-105}{168}-\frac{240}{168}+\frac{280}{168}\\=\frac{-105-240+280}{168}\\=\frac{-65}{168}\)
9. \(-\left(\frac{-4}{9}\right) -\left(\frac{-2}{-10}\right) +\left(\frac{-4}{-2}\right)\\= \frac{4}{9}- \frac{2}{10}+\frac{4}{2}\\=\frac{4}{9}-\frac{1}{5}+\frac{2}{1}\\=\frac{20}{45}-\frac{9}{45}+\frac{90}{45}\\=\frac{20-9+90}{45}\\=\frac{101}{45}\)
10. \(-\left(\frac{9}{-5}\right) -\left(\frac{4}{2}\right) -\left(\frac{9}{3}\right)\\= \frac{9}{5}- \frac{4}{2}-\frac{9}{3}\\=\frac{9}{5}-\frac{2}{1}-\frac{3}{1}\\=\frac{9-2-3}{5}\\=\frac{4}{5}\)
11. \(+\left(\frac{9}{-2}\right) -\left(\frac{-4}{-9}\right) -\left(\frac{8}{11}\right)\\= \frac{-9}{2}- \frac{4}{9}-\frac{8}{11}\\=\frac{-891}{198}-\frac{88}{198}-\frac{144}{198}\\=\frac{-891-88-144}{198}\\=\frac{-1123}{198}\)
12. \(+\left(\frac{2}{3}\right) -\left(\frac{6}{4}\right) -\left(\frac{-11}{-6}\right)\\= \frac{2}{3}- \frac{6}{4}-\frac{11}{6}\\=\frac{2}{3}-\frac{3}{2}-\frac{11}{6}\\=\frac{4}{6}-\frac{9}{6}-\frac{11}{6}\\=\frac{4-9-11}{6}\\=\frac{-16}{6}\\=\frac{-8}{3}\)