Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{10}{-7}\right) -\left(\frac{-4}{5}\right) -\left(\frac{-8}{-11}\right)\\= \frac{10}{7}+ \frac{4}{5}-\frac{8}{11}\\=\frac{550}{385}+\frac{308}{385}-\frac{280}{385}\\=\frac{550+308-280}{385}\\=\frac{578}{385}\)
2. \(-\left(\frac{-7}{-9}\right) +\left(\frac{-3}{7}\right) -\left(\frac{-12}{11}\right)\\= \frac{-7}{9}- \frac{3}{7}+\frac{12}{11}\\=\frac{-539}{693}-\frac{297}{693}+\frac{756}{693}\\=\frac{-539-297+756}{693}\\=\frac{-80}{693}\)
3. \(-\left(\frac{-4}{-7}\right) +\left(\frac{4}{-2}\right) -\left(\frac{2}{11}\right)\\= \frac{-4}{7}- \frac{4}{2}-\frac{2}{11}\\=\frac{-4}{7}-\frac{2}{1}-\frac{2}{11}\\=\frac{-44}{77}-\frac{154}{77}-\frac{14}{77}\\=\frac{-44-154-14}{77}\\=\frac{-212}{77}\)
4. \(-\left(\frac{-5}{2}\right) +\left(\frac{-7}{5}\right) -\left(\frac{-8}{2}\right)\\= \frac{5}{2}- \frac{7}{5}+\frac{8}{2}\\=\frac{5}{2}-\frac{7}{5}+\frac{4}{1}\\=\frac{25}{10}-\frac{14}{10}+\frac{40}{10}\\=\frac{25-14+40}{10}\\=\frac{51}{10}\)
5. \(-\left(\frac{-2}{5}\right) -\left(\frac{-10}{3}\right) +\left(\frac{-2}{9}\right)\\= \frac{2}{5}+ \frac{10}{3}-\frac{2}{9}\\=\frac{18}{45}+\frac{150}{45}-\frac{10}{45}\\=\frac{18+150-10}{45}\\=\frac{158}{45}\)
6. \(-\left(\frac{-7}{4}\right) +\left(\frac{5}{-8}\right) -\left(\frac{9}{6}\right)\\= \frac{7}{4}- \frac{5}{8}-\frac{9}{6}\\=\frac{7}{4}-\frac{5}{8}-\frac{3}{2}\\=\frac{14}{8}-\frac{5}{8}-\frac{12}{8}\\=\frac{14-5-12}{8}\\=\frac{-3}{8}\)
7. \(-\left(\frac{-2}{-7}\right) +\left(\frac{-8}{8}\right) -\left(\frac{-7}{2}\right)\\= \frac{-2}{7}- \frac{8}{8}+\frac{7}{2}\\=\frac{-2}{7}-\frac{1}{1}+\frac{7}{2}\\=\frac{-4}{14}-\frac{14}{14}+\frac{49}{14}\\=\frac{-4-14+49}{14}\\=\frac{31}{14}\)
8. \(-\left(\frac{-10}{-3}\right) +\left(\frac{-6}{7}\right) -\left(\frac{7}{-11}\right)\\= \frac{-10}{3}- \frac{6}{7}+\frac{7}{11}\\=\frac{-770}{231}-\frac{198}{231}+\frac{147}{231}\\=\frac{-770-198+147}{231}\\=\frac{-821}{231}\)
9. \(-\left(\frac{-3}{5}\right) -\left(\frac{9}{8}\right) +\left(\frac{-12}{-5}\right)\\= \frac{3}{5}- \frac{9}{8}+\frac{12}{5}\\=\frac{24}{40}-\frac{45}{40}+\frac{96}{40}\\=\frac{24-45+96}{40}\\=\frac{75}{40}\\=\frac{15}{8}\)
10. \(+\left(\frac{-10}{-3}\right) -\left(\frac{10}{-9}\right) +\left(\frac{10}{2}\right)\\= \frac{10}{3}+ \frac{10}{9}+\frac{10}{2}\\=\frac{10}{3}+\frac{10}{9}+\frac{5}{1}\\=\frac{30}{9}+\frac{10}{9}+\frac{45}{9}\\=\frac{30+10+45}{9}\\=\frac{85}{9}\)
11. \(-\left(\frac{5}{-6}\right) +\left(\frac{6}{-7}\right) +\left(\frac{3}{-3}\right)\\= \frac{5}{6}- \frac{6}{7}-\frac{3}{3}\\=\frac{5}{6}-\frac{6}{7}-\frac{1}{1}\\=\frac{35}{42}-\frac{36}{42}-\frac{42}{42}\\=\frac{35-36-42}{42}\\=\frac{-43}{42}\)
12. \(+\left(\frac{-9}{7}\right) -\left(\frac{-7}{-10}\right) +\left(\frac{-2}{-10}\right)\\= \frac{-9}{7}- \frac{7}{10}+\frac{2}{10}\\=\frac{-9}{7}-\frac{7}{10}+\frac{1}{5}\\=\frac{-90}{70}-\frac{49}{70}+\frac{14}{70}\\=\frac{-90-49+14}{70}\\=\frac{-125}{70}\\=\frac{-25}{14}\)