Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-6}{-5}\right) -\left(\frac{-8}{-7}\right) -\left(\frac{-10}{-3}\right)\\= \frac{-6}{5}- \frac{8}{7}-\frac{10}{3}\\=\frac{-126}{105}-\frac{120}{105}-\frac{350}{105}\\=\frac{-126-120-350}{105}\\=\frac{-596}{105}\)
2. \(+\left(\frac{10}{-7}\right) -\left(\frac{-4}{-4}\right) +\left(\frac{-6}{6}\right)\\= \frac{-10}{7}- \frac{4}{4}-\frac{6}{6}\\=\frac{-10}{7}-\frac{1}{1}-\frac{1}{1}\\=\frac{-10-1-1}{7}\\=\frac{-12}{7}\)
3. \(-\left(\frac{-7}{-4}\right) +\left(\frac{-8}{-9}\right) -\left(\frac{-2}{7}\right)\\= \frac{-7}{4}+ \frac{8}{9}+\frac{2}{7}\\=\frac{-441}{252}+\frac{224}{252}+\frac{72}{252}\\=\frac{-441+224+72}{252}\\=\frac{-145}{252}\)
4. \(-\left(\frac{-10}{-3}\right) +\left(\frac{6}{-2}\right) +\left(\frac{6}{-12}\right)\\= \frac{-10}{3}- \frac{6}{2}-\frac{6}{12}\\=\frac{-10}{3}-\frac{3}{1}-\frac{1}{2}\\=\frac{-20}{6}-\frac{18}{6}-\frac{3}{6}\\=\frac{-20-18-3}{6}\\=\frac{-41}{6}\)
5. \(+\left(\frac{10}{7}\right) -\left(\frac{-6}{-7}\right) -\left(\frac{6}{12}\right)\\= \frac{10}{7}- \frac{6}{7}-\frac{6}{12}\\=\frac{10}{7}-\frac{6}{7}-\frac{1}{2}\\=\frac{20}{14}-\frac{12}{14}-\frac{7}{14}\\=\frac{20-12-7}{14}\\=\frac{1}{14}\)
6. \(-\left(\frac{-4}{-3}\right) +\left(\frac{9}{-3}\right) -\left(\frac{-7}{11}\right)\\= \frac{-4}{3}- \frac{9}{3}+\frac{7}{11}\\=\frac{-4}{3}-\frac{3}{1}+\frac{7}{11}\\=\frac{-44}{33}-\frac{99}{33}+\frac{21}{33}\\=\frac{-44-99+21}{33}\\=\frac{-122}{33}\)
7. \(+\left(\frac{4}{5}\right) -\left(\frac{-9}{6}\right) +\left(\frac{-4}{-6}\right)\\= \frac{4}{5}+ \frac{9}{6}+\frac{4}{6}\\=\frac{4}{5}+\frac{3}{2}+\frac{2}{3}\\=\frac{24}{30}+\frac{45}{30}+\frac{20}{30}\\=\frac{24+45+20}{30}\\=\frac{89}{30}\)
8. \(+\left(\frac{9}{8}\right) +\left(\frac{6}{2}\right) +\left(\frac{2}{10}\right)\\= \frac{9}{8}+ \frac{6}{2}+\frac{2}{10}\\=\frac{9}{8}+\frac{3}{1}+\frac{1}{5}\\=\frac{45}{40}+\frac{120}{40}+\frac{8}{40}\\=\frac{45+120+8}{40}\\=\frac{173}{40}\)
9. \(+\left(\frac{-8}{-5}\right) +\left(\frac{-5}{9}\right) -\left(\frac{10}{-2}\right)\\= \frac{8}{5}- \frac{5}{9}+\frac{10}{2}\\=\frac{8}{5}-\frac{5}{9}+\frac{5}{1}\\=\frac{72}{45}-\frac{25}{45}+\frac{225}{45}\\=\frac{72-25+225}{45}\\=\frac{272}{45}\)
10. \(-\left(\frac{-6}{-7}\right) +\left(\frac{8}{7}\right) -\left(\frac{5}{-7}\right)\\= \frac{-6}{7}+ \frac{8}{7}+\frac{5}{7}\\=\frac{-6+8+5}{7}\\=\frac{7}{7}\\=\frac{1}{1}\)
11. \(+\left(\frac{-5}{7}\right) -\left(\frac{5}{4}\right) -\left(\frac{-9}{2}\right)\\= \frac{-5}{7}- \frac{5}{4}+\frac{9}{2}\\=\frac{-20}{28}-\frac{35}{28}+\frac{126}{28}\\=\frac{-20-35+126}{28}\\=\frac{71}{28}\)
12. \(-\left(\frac{5}{-4}\right) +\left(\frac{-5}{-8}\right) -\left(\frac{-5}{8}\right)\\= \frac{5}{4}+ \frac{5}{8}+\frac{5}{8}\\=\frac{10}{8}+\frac{5}{8}+\frac{5}{8}\\=\frac{10+5+5}{8}\\=\frac{20}{8}\\=\frac{5}{2}\)