Breuken haakjesregel (reeks 1)

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Bereken

1. \(+\left(\frac{-6}{-5}\right)-\left(\frac{2}{13}\right)\)
2. \(-\left(\frac{-2}{7}\right)-\left(\frac{6}{-7}\right)\)
3. \(+\left(\frac{5}{7}\right)+\left(\frac{-8}{11}\right)\)
4. \(-\left(\frac{-14}{-11}\right)-\left(\frac{15}{7}\right)\)
5. \(-\left(\frac{15}{-13}\right)+\left(\frac{15}{13}\right)\)
6. \(-\left(\frac{10}{-13}\right)+\left(\frac{-13}{14}\right)\)
7. \(-\left(\frac{12}{13}\right)+\left(\frac{-5}{-6}\right)\)
8. \(+\left(\frac{-4}{-11}\right)-\left(\frac{7}{-3}\right)\)
9. \(+\left(\frac{-2}{-5}\right)-\left(\frac{7}{-11}\right)\)
10. \(+\left(\frac{-2}{-5}\right)-\left(\frac{-15}{13}\right)\)
11. \(-\left(\frac{10}{-9}\right)+\left(\frac{10}{-7}\right)\)
12. \(-\left(\frac{-5}{2}\right)+\left(\frac{-11}{-6}\right)\)

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Bereken

Verbetersleutel

1. \(+\left(\frac{-6}{-5}\right)-\left(\frac{2}{13}\right)\\= \frac{6}{5}-\frac{2}{13}\\=\frac{78}{65}-\frac{10}{65}\\=\frac{78-10}{65}\\=\frac{68}{65}\)
2. \(-\left(\frac{-2}{7}\right)-\left(\frac{6}{-7}\right)\\= \frac{2}{7}+\frac{6}{7}\\=\frac{2+6}{7}\\=\frac{8}{7}\)
3. \(+\left(\frac{5}{7}\right)+\left(\frac{-8}{11}\right)\\= \frac{5}{7}-\frac{8}{11}\\=\frac{55}{77}-\frac{56}{77}\\=\frac{55-56}{77}\\=\frac{-1}{77}\)
4. \(-\left(\frac{-14}{-11}\right)-\left(\frac{15}{7}\right)\\= \frac{-14}{11}-\frac{15}{7}\\=\frac{-98}{77}-\frac{165}{77}\\=\frac{-98-165}{77}\\=\frac{-263}{77}\)
5. \(-\left(\frac{15}{-13}\right)+\left(\frac{15}{13}\right)\\= \frac{15}{13}+\frac{15}{13}\\=\frac{15+15}{13}\\=\frac{30}{13}\)
6. \(-\left(\frac{10}{-13}\right)+\left(\frac{-13}{14}\right)\\= \frac{10}{13}-\frac{13}{14}\\=\frac{140}{182}-\frac{169}{182}\\=\frac{140-169}{182}\\=\frac{-29}{182}\)
7. \(-\left(\frac{12}{13}\right)+\left(\frac{-5}{-6}\right)\\= \frac{-12}{13}+\frac{5}{6}\\=\frac{-72}{78}+\frac{65}{78}\\=\frac{-72+65}{78}\\=\frac{-7}{78}\)
8. \(+\left(\frac{-4}{-11}\right)-\left(\frac{7}{-3}\right)\\= \frac{4}{11}+\frac{7}{3}\\=\frac{12}{33}+\frac{77}{33}\\=\frac{12+77}{33}\\=\frac{89}{33}\)
9. \(+\left(\frac{-2}{-5}\right)-\left(\frac{7}{-11}\right)\\= \frac{2}{5}+\frac{7}{11}\\=\frac{22}{55}+\frac{35}{55}\\=\frac{22+35}{55}\\=\frac{57}{55}\)
10. \(+\left(\frac{-2}{-5}\right)-\left(\frac{-15}{13}\right)\\= \frac{2}{5}+\frac{15}{13}\\=\frac{26}{65}+\frac{75}{65}\\=\frac{26+75}{65}\\=\frac{101}{65}\)
11. \(-\left(\frac{10}{-9}\right)+\left(\frac{10}{-7}\right)\\= \frac{10}{9}-\frac{10}{7}\\=\frac{70}{63}-\frac{90}{63}\\=\frac{70-90}{63}\\=\frac{-20}{63}\)
12. \(-\left(\frac{-5}{2}\right)+\left(\frac{-11}{-6}\right)\\= \frac{5}{2}+\frac{11}{6}\\=\frac{15}{6}+\frac{11}{6}\\=\frac{15+11}{6}\\=\frac{26}{6}\\=\frac{13}{3}\)