Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{12}{13}\right)-\left(\frac{-9}{-10}\right)\\= \frac{12}{13}-\frac{9}{10}\\=\frac{120}{130}-\frac{117}{130}\\=\frac{120-117}{130}\\=\frac{3}{130}\)
2. \(+\left(\frac{3}{-14}\right)-\left(\frac{4}{3}\right)\\= \frac{-3}{14}-\frac{4}{3}\\=\frac{-9}{42}-\frac{56}{42}\\=\frac{-9-56}{42}\\=\frac{-65}{42}\)
3. \(+\left(\frac{6}{5}\right)+\left(\frac{6}{7}\right)\\= \frac{6}{5}+\frac{6}{7}\\=\frac{42}{35}+\frac{30}{35}\\=\frac{42+30}{35}\\=\frac{72}{35}\)
4. \(-\left(\frac{-13}{-2}\right)-\left(\frac{8}{-3}\right)\\= \frac{-13}{2}+\frac{8}{3}\\=\frac{-39}{6}+\frac{16}{6}\\=\frac{-39+16}{6}\\=\frac{-23}{6}\)
5. \(+\left(\frac{2}{11}\right)+\left(\frac{-3}{13}\right)\\= \frac{2}{11}-\frac{3}{13}\\=\frac{26}{143}-\frac{33}{143}\\=\frac{26-33}{143}\\=\frac{-7}{143}\)
6. \(-\left(\frac{-15}{2}\right)+\left(\frac{-8}{5}\right)\\= \frac{15}{2}-\frac{8}{5}\\=\frac{75}{10}-\frac{16}{10}\\=\frac{75-16}{10}\\=\frac{59}{10}\)
7. \(-\left(\frac{-3}{13}\right)-\left(\frac{-3}{-7}\right)\\= \frac{3}{13}-\frac{3}{7}\\=\frac{21}{91}-\frac{39}{91}\\=\frac{21-39}{91}\\=\frac{-18}{91}\)
8. \(+\left(\frac{-2}{13}\right)+\left(\frac{13}{-5}\right)\\= \frac{-2}{13}-\frac{13}{5}\\=\frac{-10}{65}-\frac{169}{65}\\=\frac{-10-169}{65}\\=\frac{-179}{65}\)
9. \(+\left(\frac{-11}{-13}\right)+\left(\frac{-15}{11}\right)\\= \frac{11}{13}-\frac{15}{11}\\=\frac{121}{143}-\frac{195}{143}\\=\frac{121-195}{143}\\=\frac{-74}{143}\)
10. \(+\left(\frac{5}{11}\right)+\left(\frac{9}{10}\right)\\= \frac{5}{11}+\frac{9}{10}\\=\frac{50}{110}+\frac{99}{110}\\=\frac{50+99}{110}\\=\frac{149}{110}\)
11. \(-\left(\frac{10}{-3}\right)+\left(\frac{-13}{-6}\right)\\= \frac{10}{3}+\frac{13}{6}\\=\frac{20}{6}+\frac{13}{6}\\=\frac{20+13}{6}\\=\frac{33}{6}\\=\frac{11}{2}\)
12. \(+\left(\frac{11}{-9}\right)-\left(\frac{-8}{7}\right)\\= \frac{-11}{9}+\frac{8}{7}\\=\frac{-77}{63}+\frac{72}{63}\\=\frac{-77+72}{63}\\=\frac{-5}{63}\)