Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{2}{-3}\right)-\left(\frac{10}{13}\right)\\= \frac{2}{3}-\frac{10}{13}\\=\frac{26}{39}-\frac{30}{39}\\=\frac{26-30}{39}\\=\frac{-4}{39}\)
2. \(-\left(\frac{-10}{9}\right)+\left(\frac{15}{8}\right)\\= \frac{10}{9}+\frac{15}{8}\\=\frac{80}{72}+\frac{135}{72}\\=\frac{80+135}{72}\\=\frac{215}{72}\)
3. \(+\left(\frac{-14}{-9}\right)-\left(\frac{12}{-7}\right)\\= \frac{14}{9}+\frac{12}{7}\\=\frac{98}{63}+\frac{108}{63}\\=\frac{98+108}{63}\\=\frac{206}{63}\)
4. \(+\left(\frac{5}{-4}\right)+\left(\frac{-2}{13}\right)\\= \frac{-5}{4}-\frac{2}{13}\\=\frac{-65}{52}-\frac{8}{52}\\=\frac{-65-8}{52}\\=\frac{-73}{52}\)
5. \(-\left(\frac{2}{-13}\right)+\left(\frac{-5}{-11}\right)\\= \frac{2}{13}+\frac{5}{11}\\=\frac{22}{143}+\frac{65}{143}\\=\frac{22+65}{143}\\=\frac{87}{143}\)
6. \(+\left(\frac{-14}{-3}\right)+\left(\frac{14}{3}\right)\\= \frac{14}{3}+\frac{14}{3}\\=\frac{14+14}{3}\\=\frac{28}{3}\)
7. \(-\left(\frac{15}{11}\right)-\left(\frac{9}{-7}\right)\\= \frac{-15}{11}+\frac{9}{7}\\=\frac{-105}{77}+\frac{99}{77}\\=\frac{-105+99}{77}\\=\frac{-6}{77}\)
8. \(+\left(\frac{11}{2}\right)-\left(\frac{-3}{2}\right)\\= \frac{11}{2}+\frac{3}{2}\\=\frac{11+3}{2}\\=\frac{14}{2}\\=\frac{7}{1}\)
9. \(+\left(\frac{11}{6}\right)-\left(\frac{-10}{-3}\right)\\= \frac{11}{6}-\frac{10}{3}\\=\frac{11-10}{6}\\=\frac{1}{6}\)
10. \(-\left(\frac{6}{7}\right)-\left(\frac{-7}{13}\right)\\= \frac{-6}{7}+\frac{7}{13}\\=\frac{-78}{91}+\frac{49}{91}\\=\frac{-78+49}{91}\\=\frac{-29}{91}\)
11. \(-\left(\frac{-3}{-2}\right)-\left(\frac{-3}{-2}\right)\\= \frac{-3}{2}-\frac{3}{2}\\=\frac{-3-3}{2}\\=\frac{-6}{2}\\=\frac{-3}{1}\)
12. \(-\left(\frac{8}{-3}\right)+\left(\frac{-9}{-11}\right)\\= \frac{8}{3}+\frac{9}{11}\\=\frac{88}{33}+\frac{27}{33}\\=\frac{88+27}{33}\\=\frac{115}{33}\)