Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{7}{-3}\right) -\left(\frac{10}{5}\right) -\left(\frac{-4}{-4}\right)\\= \frac{7}{3}- \frac{10}{5}-\frac{4}{4}\\=\frac{7}{3}-\frac{2}{1}-\frac{1}{1}\\=\frac{7-2-1}{3}\\=\frac{4}{3}\)
2. \(+\left(\frac{-5}{2}\right) -\left(\frac{-2}{8}\right) -\left(\frac{-4}{4}\right)\\= \frac{-5}{2}+ \frac{2}{8}+\frac{4}{4}\\=\frac{-5}{2}+\frac{1}{4}+\frac{1}{1}\\=\frac{-10}{4}+\frac{1}{4}+\frac{4}{4}\\=\frac{-10+1+4}{4}\\=\frac{-5}{4}\)
3. \(+\left(\frac{6}{5}\right) -\left(\frac{7}{3}\right) +\left(\frac{-7}{8}\right)\\= \frac{6}{5}- \frac{7}{3}-\frac{7}{8}\\=\frac{144}{120}-\frac{280}{120}-\frac{105}{120}\\=\frac{144-280-105}{120}\\=\frac{-241}{120}\)
4. \(+\left(\frac{-3}{-5}\right) -\left(\frac{-4}{-9}\right) -\left(\frac{7}{5}\right)\\= \frac{3}{5}- \frac{4}{9}-\frac{7}{5}\\=\frac{27}{45}-\frac{20}{45}-\frac{63}{45}\\=\frac{27-20-63}{45}\\=\frac{-56}{45}\)
5. \(+\left(\frac{-4}{-9}\right) -\left(\frac{-6}{10}\right) +\left(\frac{10}{-8}\right)\\= \frac{4}{9}+ \frac{6}{10}-\frac{10}{8}\\=\frac{4}{9}+\frac{3}{5}-\frac{5}{4}\\=\frac{80}{180}+\frac{108}{180}-\frac{225}{180}\\=\frac{80+108-225}{180}\\=\frac{-37}{180}\)
6. \(-\left(\frac{10}{7}\right) +\left(\frac{-2}{-9}\right) -\left(\frac{-5}{10}\right)\\= \frac{-10}{7}+ \frac{2}{9}+\frac{5}{10}\\=\frac{-10}{7}+\frac{2}{9}+\frac{1}{2}\\=\frac{-180}{126}+\frac{28}{126}+\frac{63}{126}\\=\frac{-180+28+63}{126}\\=\frac{-89}{126}\)
7. \(-\left(\frac{-3}{-8}\right) -\left(\frac{7}{7}\right) +\left(\frac{9}{11}\right)\\= \frac{-3}{8}- \frac{7}{7}+\frac{9}{11}\\=\frac{-3}{8}-\frac{1}{1}+\frac{9}{11}\\=\frac{-33}{88}-\frac{88}{88}+\frac{72}{88}\\=\frac{-33-88+72}{88}\\=\frac{-49}{88}\)
8. \(-\left(\frac{-5}{8}\right) +\left(\frac{-4}{-7}\right) -\left(\frac{-3}{-7}\right)\\= \frac{5}{8}+ \frac{4}{7}-\frac{3}{7}\\=\frac{35}{56}+\frac{32}{56}-\frac{24}{56}\\=\frac{35+32-24}{56}\\=\frac{43}{56}\)
9. \(-\left(\frac{-9}{-5}\right) +\left(\frac{-6}{3}\right) -\left(\frac{10}{5}\right)\\= \frac{-9}{5}- \frac{6}{3}-\frac{10}{5}\\=\frac{-9}{5}-\frac{2}{1}-\frac{2}{1}\\=\frac{-9-2-2}{5}\\=\frac{-13}{5}\)
10. \(+\left(\frac{10}{-7}\right) +\left(\frac{-5}{-10}\right) -\left(\frac{-4}{4}\right)\\= \frac{-10}{7}+ \frac{5}{10}+\frac{4}{4}\\=\frac{-10}{7}+\frac{1}{2}+\frac{1}{1}\\=\frac{-20}{14}+\frac{7}{14}+\frac{14}{14}\\=\frac{-20+7+14}{14}\\=\frac{1}{14}\)
11. \(-\left(\frac{6}{5}\right) -\left(\frac{9}{-9}\right) -\left(\frac{9}{-9}\right)\\= \frac{-6}{5}+ \frac{9}{9}+\frac{9}{9}\\=\frac{-6}{5}+\frac{1}{1}+\frac{1}{1}\\=\frac{-6+1+1}{5}\\=\frac{-4}{5}\)
12. \(+\left(\frac{8}{5}\right) +\left(\frac{6}{5}\right) +\left(\frac{6}{-9}\right)\\= \frac{8}{5}+ \frac{6}{5}-\frac{6}{9}\\=\frac{8}{5}+\frac{6}{5}-\frac{2}{3}\\=\frac{24}{15}+\frac{18}{15}-\frac{10}{15}\\=\frac{24+18-10}{15}\\=\frac{32}{15}\)