Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{9}{8}\right) -\left(\frac{5}{-10}\right) +\left(\frac{-5}{-4}\right)\\= \frac{-9}{8}+ \frac{5}{10}+\frac{5}{4}\\=\frac{-9}{8}+\frac{1}{2}+\frac{5}{4}\\=\frac{-9+1+5}{8}\\=\frac{-3}{8}\)
2. \(+\left(\frac{-7}{8}\right) +\left(\frac{4}{7}\right) +\left(\frac{4}{12}\right)\\= \frac{-7}{8}+ \frac{4}{7}+\frac{4}{12}\\=\frac{-7}{8}+\frac{4}{7}+\frac{1}{3}\\=\frac{-147}{168}+\frac{96}{168}+\frac{56}{168}\\=\frac{-147+96+56}{168}\\=\frac{5}{168}\)
3. \(+\left(\frac{-10}{7}\right) +\left(\frac{-4}{-7}\right) -\left(\frac{-11}{7}\right)\\= \frac{-10}{7}+ \frac{4}{7}+\frac{11}{7}\\=\frac{-10+4+11}{7}\\=\frac{5}{7}\)
4. \(-\left(\frac{7}{-6}\right) -\left(\frac{-9}{-2}\right) +\left(\frac{-11}{12}\right)\\= \frac{7}{6}- \frac{9}{2}-\frac{11}{12}\\=\frac{14}{12}-\frac{54}{12}-\frac{11}{12}\\=\frac{14-54-11}{12}\\=\frac{-51}{12}\\=\frac{-17}{4}\)
5. \(-\left(\frac{-2}{9}\right) +\left(\frac{-4}{7}\right) -\left(\frac{-12}{-10}\right)\\= \frac{2}{9}- \frac{4}{7}-\frac{12}{10}\\=\frac{2}{9}-\frac{4}{7}-\frac{6}{5}\\=\frac{70}{315}-\frac{180}{315}-\frac{378}{315}\\=\frac{70-180-378}{315}\\=\frac{-488}{315}\)
6. \(-\left(\frac{2}{-3}\right) -\left(\frac{-3}{-3}\right) +\left(\frac{-9}{-8}\right)\\= \frac{2}{3}- \frac{3}{3}+\frac{9}{8}\\=\frac{2}{3}-\frac{1}{1}+\frac{9}{8}\\=\frac{16}{24}-\frac{24}{24}+\frac{27}{24}\\=\frac{16-24+27}{24}\\=\frac{19}{24}\)
7. \(-\left(\frac{3}{-4}\right) -\left(\frac{-6}{5}\right) +\left(\frac{-4}{-11}\right)\\= \frac{3}{4}+ \frac{6}{5}+\frac{4}{11}\\=\frac{165}{220}+\frac{264}{220}+\frac{80}{220}\\=\frac{165+264+80}{220}\\=\frac{509}{220}\)
8. \(+\left(\frac{6}{5}\right) -\left(\frac{-10}{4}\right) -\left(\frac{-8}{-10}\right)\\= \frac{6}{5}+ \frac{10}{4}-\frac{8}{10}\\=\frac{6}{5}+\frac{5}{2}-\frac{4}{5}\\=\frac{12}{10}+\frac{25}{10}-\frac{8}{10}\\=\frac{12+25-8}{10}\\=\frac{29}{10}\)
9. \(-\left(\frac{10}{-9}\right) +\left(\frac{-8}{-5}\right) -\left(\frac{6}{-9}\right)\\= \frac{10}{9}+ \frac{8}{5}+\frac{6}{9}\\=\frac{10}{9}+\frac{8}{5}+\frac{2}{3}\\=\frac{50}{45}+\frac{72}{45}+\frac{30}{45}\\=\frac{50+72+30}{45}\\=\frac{152}{45}\)
10. \(+\left(\frac{-4}{3}\right) +\left(\frac{6}{7}\right) -\left(\frac{9}{7}\right)\\= \frac{-4}{3}+ \frac{6}{7}-\frac{9}{7}\\=\frac{-28}{21}+\frac{18}{21}-\frac{27}{21}\\=\frac{-28+18-27}{21}\\=\frac{-37}{21}\)
11. \(-\left(\frac{-6}{-5}\right) +\left(\frac{-6}{4}\right) -\left(\frac{-7}{-4}\right)\\= \frac{-6}{5}- \frac{6}{4}-\frac{7}{4}\\=\frac{-6}{5}-\frac{3}{2}-\frac{7}{4}\\=\frac{-24}{20}-\frac{30}{20}-\frac{35}{20}\\=\frac{-24-30-35}{20}\\=\frac{-89}{20}\)
12. \(-\left(\frac{2}{-9}\right) +\left(\frac{-2}{8}\right) +\left(\frac{10}{5}\right)\\= \frac{2}{9}- \frac{2}{8}+\frac{10}{5}\\=\frac{2}{9}-\frac{1}{4}+\frac{2}{1}\\=\frac{8}{36}-\frac{9}{36}+\frac{72}{36}\\=\frac{8-9+72}{36}\\=\frac{71}{36}\)