Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{11}{-2}\right)+\left(\frac{-11}{-3}\right)\\= \frac{11}{2}+\frac{11}{3}\\=\frac{33}{6}+\frac{22}{6}\\=\frac{33+22}{6}\\=\frac{55}{6}\)
2. \(+\left(\frac{-13}{-10}\right)-\left(\frac{5}{-6}\right)\\= \frac{13}{10}+\frac{5}{6}\\=\frac{39}{30}+\frac{25}{30}\\=\frac{39+25}{30}\\=\frac{64}{30}\\=\frac{32}{15}\)
3. \(-\left(\frac{-10}{13}\right)+\left(\frac{3}{-13}\right)\\= \frac{10}{13}-\frac{3}{13}\\=\frac{10-3}{13}\\=\frac{7}{13}\)
4. \(+\left(\frac{-4}{5}\right)-\left(\frac{7}{2}\right)\\= \frac{-4}{5}-\frac{7}{2}\\=\frac{-8}{10}-\frac{35}{10}\\=\frac{-8-35}{10}\\=\frac{-43}{10}\)
5. \(+\left(\frac{14}{11}\right)+\left(\frac{-14}{-11}\right)\\= \frac{14}{11}+\frac{14}{11}\\=\frac{14+14}{11}\\=\frac{28}{11}\)
6. \(+\left(\frac{-14}{9}\right)+\left(\frac{-8}{13}\right)\\= \frac{-14}{9}-\frac{8}{13}\\=\frac{-182}{117}-\frac{72}{117}\\=\frac{-182-72}{117}\\=\frac{-254}{117}\)
7. \(-\left(\frac{7}{-9}\right)-\left(\frac{-13}{8}\right)\\= \frac{7}{9}+\frac{13}{8}\\=\frac{56}{72}+\frac{117}{72}\\=\frac{56+117}{72}\\=\frac{173}{72}\)
8. \(-\left(\frac{-10}{9}\right)+\left(\frac{-5}{-6}\right)\\= \frac{10}{9}+\frac{5}{6}\\=\frac{20}{18}+\frac{15}{18}\\=\frac{20+15}{18}\\=\frac{35}{18}\)
9. \(+\left(\frac{7}{-3}\right)-\left(\frac{-8}{-3}\right)\\= \frac{-7}{3}-\frac{8}{3}\\=\frac{-7-8}{3}\\=\frac{-15}{3}\\=\frac{-5}{1}\)
10. \(+\left(\frac{11}{5}\right)-\left(\frac{9}{5}\right)\\= \frac{11}{5}-\frac{9}{5}\\=\frac{11-9}{5}\\=\frac{2}{5}\)
11. \(-\left(\frac{-14}{3}\right)+\left(\frac{-11}{4}\right)\\= \frac{14}{3}-\frac{11}{4}\\=\frac{56}{12}-\frac{33}{12}\\=\frac{56-33}{12}\\=\frac{23}{12}\)
12. \(-\left(\frac{9}{10}\right)+\left(\frac{-3}{-13}\right)\\= \frac{-9}{10}+\frac{3}{13}\\=\frac{-117}{130}+\frac{30}{130}\\=\frac{-117+30}{130}\\=\frac{-87}{130}\)