Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-8}{-9}\right) -\left(\frac{10}{8}\right) -\left(\frac{-12}{-5}\right)\\= \frac{-8}{9}- \frac{10}{8}-\frac{12}{5}\\=\frac{-8}{9}-\frac{5}{4}-\frac{12}{5}\\=\frac{-160}{180}-\frac{225}{180}-\frac{432}{180}\\=\frac{-160-225-432}{180}\\=\frac{-817}{180}\)
2. \(+\left(\frac{-2}{5}\right) +\left(\frac{-10}{5}\right) -\left(\frac{-6}{6}\right)\\= \frac{-2}{5}- \frac{10}{5}+\frac{6}{6}\\=\frac{-2}{5}-\frac{2}{1}+\frac{1}{1}\\=\frac{-2-2+1}{5}\\=\frac{-3}{5}\)
3. \(+\left(\frac{-5}{-6}\right) -\left(\frac{3}{-5}\right) -\left(\frac{-4}{-12}\right)\\= \frac{5}{6}+ \frac{3}{5}-\frac{4}{12}\\=\frac{5}{6}+\frac{3}{5}-\frac{1}{3}\\=\frac{25}{30}+\frac{18}{30}-\frac{10}{30}\\=\frac{25+18-10}{30}\\=\frac{33}{30}\\=\frac{11}{10}\)
4. \(-\left(\frac{8}{-9}\right) -\left(\frac{3}{3}\right) +\left(\frac{4}{-2}\right)\\= \frac{8}{9}- \frac{3}{3}-\frac{4}{2}\\=\frac{8}{9}-\frac{1}{1}-\frac{2}{1}\\=\frac{8-1-2}{9}\\=\frac{5}{9}\)
5. \(-\left(\frac{-5}{-7}\right) -\left(\frac{-3}{-3}\right) +\left(\frac{7}{2}\right)\\= \frac{-5}{7}- \frac{3}{3}+\frac{7}{2}\\=\frac{-5}{7}-\frac{1}{1}+\frac{7}{2}\\=\frac{-10}{14}-\frac{14}{14}+\frac{49}{14}\\=\frac{-10-14+49}{14}\\=\frac{25}{14}\)
6. \(-\left(\frac{-3}{2}\right) +\left(\frac{4}{-10}\right) +\left(\frac{-5}{-12}\right)\\= \frac{3}{2}- \frac{4}{10}+\frac{5}{12}\\=\frac{3}{2}-\frac{2}{5}+\frac{5}{12}\\=\frac{90}{60}-\frac{24}{60}+\frac{25}{60}\\=\frac{90-24+25}{60}\\=\frac{91}{60}\)
7. \(+\left(\frac{-10}{7}\right) -\left(\frac{-2}{-3}\right) -\left(\frac{-12}{6}\right)\\= \frac{-10}{7}- \frac{2}{3}+\frac{12}{6}\\=\frac{-10}{7}-\frac{2}{3}+\frac{2}{1}\\=\frac{-30}{21}-\frac{14}{21}+\frac{42}{21}\\=\frac{-30-14+42}{21}\\=\frac{-2}{21}\)
8. \(-\left(\frac{-2}{-5}\right) +\left(\frac{-2}{-5}\right) -\left(\frac{5}{11}\right)\\= \frac{-2}{5}+ \frac{2}{5}-\frac{5}{11}\\=\frac{-22}{55}+\frac{22}{55}-\frac{25}{55}\\=\frac{-22+22-25}{55}\\=\frac{-25}{55}\\=\frac{-5}{11}\)
9. \(+\left(\frac{-8}{3}\right) -\left(\frac{-2}{10}\right) -\left(\frac{-8}{-3}\right)\\= \frac{-8}{3}+ \frac{2}{10}-\frac{8}{3}\\=\frac{-8}{3}+\frac{1}{5}-\frac{8}{3}\\=\frac{-40}{15}+\frac{3}{15}-\frac{40}{15}\\=\frac{-40+3-40}{15}\\=\frac{-77}{15}\)
10. \(-\left(\frac{-9}{-8}\right) -\left(\frac{-2}{-10}\right) +\left(\frac{12}{10}\right)\\= \frac{-9}{8}- \frac{2}{10}+\frac{12}{10}\\=\frac{-9}{8}-\frac{1}{5}+\frac{6}{5}\\=\frac{-45}{40}-\frac{8}{40}+\frac{48}{40}\\=\frac{-45-8+48}{40}\\=\frac{-5}{40}\\=\frac{-1}{8}\)
11. \(+\left(\frac{-3}{-7}\right) +\left(\frac{2}{-2}\right) -\left(\frac{4}{4}\right)\\= \frac{3}{7}- \frac{2}{2}-\frac{4}{4}\\=\frac{3}{7}-\frac{1}{1}-\frac{1}{1}\\=\frac{3-1-1}{7}\\=\frac{1}{7}\)
12. \(+\left(\frac{8}{9}\right) +\left(\frac{-6}{-10}\right) -\left(\frac{5}{3}\right)\\= \frac{8}{9}+ \frac{6}{10}-\frac{5}{3}\\=\frac{8}{9}+\frac{3}{5}-\frac{5}{3}\\=\frac{40}{45}+\frac{27}{45}-\frac{75}{45}\\=\frac{40+27-75}{45}\\=\frac{-8}{45}\)