Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-3}{5}\right)+\left(\frac{-9}{2}\right)\\= \frac{3}{5}-\frac{9}{2}\\=\frac{6}{10}-\frac{45}{10}\\=\frac{6-45}{10}\\=\frac{-39}{10}\)
2. \(+\left(\frac{-6}{-5}\right)-\left(\frac{6}{-5}\right)\\= \frac{6}{5}+\frac{6}{5}\\=\frac{6+6}{5}\\=\frac{12}{5}\)
3. \(+\left(\frac{-14}{9}\right)+\left(\frac{-2}{-11}\right)\\= \frac{-14}{9}+\frac{2}{11}\\=\frac{-154}{99}+\frac{18}{99}\\=\frac{-154+18}{99}\\=\frac{-136}{99}\)
4. \(-\left(\frac{2}{-11}\right)-\left(\frac{8}{13}\right)\\= \frac{2}{11}-\frac{8}{13}\\=\frac{26}{143}-\frac{88}{143}\\=\frac{26-88}{143}\\=\frac{-62}{143}\)
5. \(+\left(\frac{5}{6}\right)-\left(\frac{-15}{-13}\right)\\= \frac{5}{6}-\frac{15}{13}\\=\frac{65}{78}-\frac{90}{78}\\=\frac{65-90}{78}\\=\frac{-25}{78}\)
6. \(-\left(\frac{2}{3}\right)-\left(\frac{6}{11}\right)\\= \frac{-2}{3}-\frac{6}{11}\\=\frac{-22}{33}-\frac{18}{33}\\=\frac{-22-18}{33}\\=\frac{-40}{33}\)
7. \(+\left(\frac{15}{11}\right)-\left(\frac{-7}{2}\right)\\= \frac{15}{11}+\frac{7}{2}\\=\frac{30}{22}+\frac{77}{22}\\=\frac{30+77}{22}\\=\frac{107}{22}\)
8. \(+\left(\frac{9}{-11}\right)-\left(\frac{12}{-13}\right)\\= \frac{-9}{11}+\frac{12}{13}\\=\frac{-117}{143}+\frac{132}{143}\\=\frac{-117+132}{143}\\=\frac{15}{143}\)
9. \(-\left(\frac{-9}{11}\right)+\left(\frac{-3}{-8}\right)\\= \frac{9}{11}+\frac{3}{8}\\=\frac{72}{88}+\frac{33}{88}\\=\frac{72+33}{88}\\=\frac{105}{88}\)
10. \(+\left(\frac{-11}{14}\right)+\left(\frac{13}{14}\right)\\= \frac{-11}{14}+\frac{13}{14}\\=\frac{-11+13}{14}\\=\frac{2}{14}\\=\frac{1}{7}\)
11. \(+\left(\frac{3}{10}\right)+\left(\frac{2}{13}\right)\\= \frac{3}{10}+\frac{2}{13}\\=\frac{39}{130}+\frac{20}{130}\\=\frac{39+20}{130}\\=\frac{59}{130}\)
12. \(-\left(\frac{-3}{13}\right)-\left(\frac{13}{5}\right)\\= \frac{3}{13}-\frac{13}{5}\\=\frac{15}{65}-\frac{169}{65}\\=\frac{15-169}{65}\\=\frac{-154}{65}\)