Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{7}{8}\right) -\left(\frac{9}{9}\right) -\left(\frac{-2}{9}\right)\\= \frac{-7}{8}- \frac{9}{9}+\frac{2}{9}\\=\frac{-7}{8}-\frac{1}{1}+\frac{2}{9}\\=\frac{-63}{72}-\frac{72}{72}+\frac{16}{72}\\=\frac{-63-72+16}{72}\\=\frac{-119}{72}\)
2. \(-\left(\frac{-8}{7}\right) +\left(\frac{-10}{10}\right) +\left(\frac{11}{-5}\right)\\= \frac{8}{7}- \frac{10}{10}-\frac{11}{5}\\=\frac{8}{7}-\frac{1}{1}-\frac{11}{5}\\=\frac{40}{35}-\frac{35}{35}-\frac{77}{35}\\=\frac{40-35-77}{35}\\=\frac{-72}{35}\)
3. \(-\left(\frac{-10}{-9}\right) +\left(\frac{-8}{9}\right) +\left(\frac{-9}{-6}\right)\\= \frac{-10}{9}- \frac{8}{9}+\frac{9}{6}\\=\frac{-10}{9}-\frac{8}{9}+\frac{3}{2}\\=\frac{-20}{18}-\frac{16}{18}+\frac{27}{18}\\=\frac{-20-16+27}{18}\\=\frac{-9}{18}\\=\frac{-1}{2}\)
4. \(-\left(\frac{5}{9}\right) -\left(\frac{2}{7}\right) -\left(\frac{-8}{-7}\right)\\= \frac{-5}{9}- \frac{2}{7}-\frac{8}{7}\\=\frac{-35}{63}-\frac{18}{63}-\frac{72}{63}\\=\frac{-35-18-72}{63}\\=\frac{-125}{63}\)
5. \(+\left(\frac{10}{-7}\right) -\left(\frac{3}{-7}\right) -\left(\frac{-12}{-4}\right)\\= \frac{-10}{7}+ \frac{3}{7}-\frac{12}{4}\\=\frac{-10}{7}+\frac{3}{7}-\frac{3}{1}\\=\frac{-10+3-3}{7}\\=\frac{-10}{7}\)
6. \(-\left(\frac{2}{3}\right) +\left(\frac{-9}{5}\right) -\left(\frac{-8}{9}\right)\\= \frac{-2}{3}- \frac{9}{5}+\frac{8}{9}\\=\frac{-30}{45}-\frac{81}{45}+\frac{40}{45}\\=\frac{-30-81+40}{45}\\=\frac{-71}{45}\)
7. \(+\left(\frac{-9}{-2}\right) -\left(\frac{8}{-6}\right) +\left(\frac{-8}{10}\right)\\= \frac{9}{2}+ \frac{8}{6}-\frac{8}{10}\\=\frac{9}{2}+\frac{4}{3}-\frac{4}{5}\\=\frac{135}{30}+\frac{40}{30}-\frac{24}{30}\\=\frac{135+40-24}{30}\\=\frac{151}{30}\)
8. \(+\left(\frac{5}{9}\right) -\left(\frac{-4}{-9}\right) +\left(\frac{6}{6}\right)\\= \frac{5}{9}- \frac{4}{9}+\frac{6}{6}\\=\frac{5}{9}-\frac{4}{9}+\frac{1}{1}\\=\frac{5-4+1}{9}\\=\frac{2}{9}\)
9. \(-\left(\frac{8}{9}\right) +\left(\frac{2}{5}\right) -\left(\frac{10}{-7}\right)\\= \frac{-8}{9}+ \frac{2}{5}+\frac{10}{7}\\=\frac{-280}{315}+\frac{126}{315}+\frac{450}{315}\\=\frac{-280+126+450}{315}\\=\frac{296}{315}\)
10. \(-\left(\frac{-8}{5}\right) +\left(\frac{7}{5}\right) +\left(\frac{10}{-5}\right)\\= \frac{8}{5}+ \frac{7}{5}-\frac{10}{5}\\=\frac{8}{5}+\frac{7}{5}-\frac{2}{1}\\=\frac{8+7-2}{5}\\=\frac{13}{5}\)
11. \(+\left(\frac{4}{-3}\right) -\left(\frac{-5}{-6}\right) +\left(\frac{-4}{-2}\right)\\= \frac{-4}{3}- \frac{5}{6}+\frac{4}{2}\\=\frac{-4}{3}-\frac{5}{6}+\frac{2}{1}\\=\frac{-8}{6}-\frac{5}{6}+\frac{12}{6}\\=\frac{-8-5+12}{6}\\=\frac{-1}{6}\)
12. \(+\left(\frac{4}{9}\right) -\left(\frac{-6}{3}\right) +\left(\frac{8}{-3}\right)\\= \frac{4}{9}+ \frac{6}{3}-\frac{8}{3}\\=\frac{4}{9}+\frac{2}{1}-\frac{8}{3}\\=\frac{4+2-8}{9}\\=\frac{-2}{9}\)