Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{9}{13}\right)-\left(\frac{14}{-9}\right)\\= \frac{9}{13}+\frac{14}{9}\\=\frac{81}{117}+\frac{182}{117}\\=\frac{81+182}{117}\\=\frac{263}{117}\)
2. \(-\left(\frac{6}{-11}\right)+\left(\frac{-11}{13}\right)\\= \frac{6}{11}-\frac{11}{13}\\=\frac{78}{143}-\frac{121}{143}\\=\frac{78-121}{143}\\=\frac{-43}{143}\)
3. \(+\left(\frac{13}{5}\right)+\left(\frac{6}{-5}\right)\\= \frac{13}{5}-\frac{6}{5}\\=\frac{13-6}{5}\\=\frac{7}{5}\)
4. \(-\left(\frac{-7}{-13}\right)-\left(\frac{12}{13}\right)\\= \frac{-7}{13}-\frac{12}{13}\\=\frac{-7-12}{13}\\=\frac{-19}{13}\)
5. \(-\left(\frac{-11}{-12}\right)+\left(\frac{-2}{9}\right)\\= \frac{-11}{12}-\frac{2}{9}\\=\frac{-33}{36}-\frac{8}{36}\\=\frac{-33-8}{36}\\=\frac{-41}{36}\)
6. \(-\left(\frac{-12}{11}\right)-\left(\frac{-11}{9}\right)\\= \frac{12}{11}+\frac{11}{9}\\=\frac{108}{99}+\frac{121}{99}\\=\frac{108+121}{99}\\=\frac{229}{99}\)
7. \(+\left(\frac{-4}{-13}\right)+\left(\frac{-14}{-11}\right)\\= \frac{4}{13}+\frac{14}{11}\\=\frac{44}{143}+\frac{182}{143}\\=\frac{44+182}{143}\\=\frac{226}{143}\)
8. \(+\left(\frac{5}{-3}\right)-\left(\frac{-4}{3}\right)\\= \frac{-5}{3}+\frac{4}{3}\\=\frac{-5+4}{3}\\=\frac{-1}{3}\)
9. \(-\left(\frac{-2}{5}\right)+\left(\frac{14}{9}\right)\\= \frac{2}{5}+\frac{14}{9}\\=\frac{18}{45}+\frac{70}{45}\\=\frac{18+70}{45}\\=\frac{88}{45}\)
10. \(-\left(\frac{-10}{-3}\right)+\left(\frac{-7}{-2}\right)\\= \frac{-10}{3}+\frac{7}{2}\\=\frac{-20}{6}+\frac{21}{6}\\=\frac{-20+21}{6}\\=\frac{1}{6}\)
11. \(-\left(\frac{-13}{-14}\right)-\left(\frac{-11}{13}\right)\\= \frac{-13}{14}+\frac{11}{13}\\=\frac{-169}{182}+\frac{154}{182}\\=\frac{-169+154}{182}\\=\frac{-15}{182}\)
12. \(+\left(\frac{-6}{-5}\right)-\left(\frac{13}{11}\right)\\= \frac{6}{5}-\frac{13}{11}\\=\frac{66}{55}-\frac{65}{55}\\=\frac{66-65}{55}\\=\frac{1}{55}\)