Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-8}{7}\right) -\left(\frac{-5}{7}\right) +\left(\frac{-10}{-11}\right)\\= \frac{-8}{7}+ \frac{5}{7}+\frac{10}{11}\\=\frac{-88}{77}+\frac{55}{77}+\frac{70}{77}\\=\frac{-88+55+70}{77}\\=\frac{37}{77}\)
2. \(-\left(\frac{-10}{7}\right) +\left(\frac{7}{5}\right) -\left(\frac{-5}{9}\right)\\= \frac{10}{7}+ \frac{7}{5}+\frac{5}{9}\\=\frac{450}{315}+\frac{441}{315}+\frac{175}{315}\\=\frac{450+441+175}{315}\\=\frac{1066}{315}\)
3. \(-\left(\frac{10}{3}\right) -\left(\frac{-2}{-8}\right) +\left(\frac{2}{-2}\right)\\= \frac{-10}{3}- \frac{2}{8}-\frac{2}{2}\\=\frac{-10}{3}-\frac{1}{4}-\frac{1}{1}\\=\frac{-40}{12}-\frac{3}{12}-\frac{12}{12}\\=\frac{-40-3-12}{12}\\=\frac{-55}{12}\)
4. \(-\left(\frac{2}{-9}\right) -\left(\frac{3}{9}\right) +\left(\frac{4}{7}\right)\\= \frac{2}{9}- \frac{3}{9}+\frac{4}{7}\\=\frac{2}{9}-\frac{1}{3}+\frac{4}{7}\\=\frac{14}{63}-\frac{21}{63}+\frac{36}{63}\\=\frac{14-21+36}{63}\\=\frac{29}{63}\)
5. \(-\left(\frac{-4}{-5}\right) -\left(\frac{4}{6}\right) +\left(\frac{8}{-11}\right)\\= \frac{-4}{5}- \frac{4}{6}-\frac{8}{11}\\=\frac{-4}{5}-\frac{2}{3}-\frac{8}{11}\\=\frac{-132}{165}-\frac{110}{165}-\frac{120}{165}\\=\frac{-132-110-120}{165}\\=\frac{-362}{165}\)
6. \(-\left(\frac{6}{5}\right) -\left(\frac{2}{6}\right) -\left(\frac{12}{-6}\right)\\= \frac{-6}{5}- \frac{2}{6}+\frac{12}{6}\\=\frac{-6}{5}-\frac{1}{3}+\frac{2}{1}\\=\frac{-18}{15}-\frac{5}{15}+\frac{30}{15}\\=\frac{-18-5+30}{15}\\=\frac{7}{15}\)
7. \(+\left(\frac{6}{-5}\right) +\left(\frac{3}{7}\right) -\left(\frac{4}{12}\right)\\= \frac{-6}{5}+ \frac{3}{7}-\frac{4}{12}\\=\frac{-6}{5}+\frac{3}{7}-\frac{1}{3}\\=\frac{-126}{105}+\frac{45}{105}-\frac{35}{105}\\=\frac{-126+45-35}{105}\\=\frac{-116}{105}\)
8. \(-\left(\frac{-9}{4}\right) -\left(\frac{-9}{-9}\right) -\left(\frac{-3}{11}\right)\\= \frac{9}{4}- \frac{9}{9}+\frac{3}{11}\\=\frac{9}{4}-\frac{1}{1}+\frac{3}{11}\\=\frac{99}{44}-\frac{44}{44}+\frac{12}{44}\\=\frac{99-44+12}{44}\\=\frac{67}{44}\)
9. \(-\left(\frac{-6}{-5}\right) -\left(\frac{10}{10}\right) -\left(\frac{9}{2}\right)\\= \frac{-6}{5}- \frac{10}{10}-\frac{9}{2}\\=\frac{-6}{5}-\frac{1}{1}-\frac{9}{2}\\=\frac{-12}{10}-\frac{10}{10}-\frac{45}{10}\\=\frac{-12-10-45}{10}\\=\frac{-67}{10}\)
10. \(-\left(\frac{-3}{-2}\right) +\left(\frac{10}{-4}\right) -\left(\frac{12}{-6}\right)\\= \frac{-3}{2}- \frac{10}{4}+\frac{12}{6}\\=\frac{-3}{2}-\frac{5}{2}+\frac{2}{1}\\=\frac{-3-5+2}{2}\\=\frac{-6}{2}\\=\frac{-3}{1}\)
11. \(-\left(\frac{-6}{5}\right) -\left(\frac{-7}{7}\right) -\left(\frac{-5}{9}\right)\\= \frac{6}{5}+ \frac{7}{7}+\frac{5}{9}\\=\frac{6}{5}+\frac{1}{1}+\frac{5}{9}\\=\frac{54}{45}+\frac{45}{45}+\frac{25}{45}\\=\frac{54+45+25}{45}\\=\frac{124}{45}\)
12. \(-\left(\frac{2}{-9}\right) +\left(\frac{4}{5}\right) +\left(\frac{-4}{-10}\right)\\= \frac{2}{9}+ \frac{4}{5}+\frac{4}{10}\\=\frac{2}{9}+\frac{4}{5}+\frac{2}{5}\\=\frac{10}{45}+\frac{36}{45}+\frac{18}{45}\\=\frac{10+36+18}{45}\\=\frac{64}{45}\)