Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{7}{13}\right)-\left(\frac{-7}{3}\right)\\= \frac{7}{13}+\frac{7}{3}\\=\frac{21}{39}+\frac{91}{39}\\=\frac{21+91}{39}\\=\frac{112}{39}\)
2. \(-\left(\frac{4}{-13}\right)-\left(\frac{-15}{-13}\right)\\= \frac{4}{13}-\frac{15}{13}\\=\frac{4-15}{13}\\=\frac{-11}{13}\)
3. \(-\left(\frac{6}{-5}\right)+\left(\frac{-7}{12}\right)\\= \frac{6}{5}-\frac{7}{12}\\=\frac{72}{60}-\frac{35}{60}\\=\frac{72-35}{60}\\=\frac{37}{60}\)
4. \(+\left(\frac{9}{-2}\right)+\left(\frac{2}{3}\right)\\= \frac{-9}{2}+\frac{2}{3}\\=\frac{-27}{6}+\frac{4}{6}\\=\frac{-27+4}{6}\\=\frac{-23}{6}\)
5. \(-\left(\frac{8}{7}\right)+\left(\frac{8}{-13}\right)\\= \frac{-8}{7}-\frac{8}{13}\\=\frac{-104}{91}-\frac{56}{91}\\=\frac{-104-56}{91}\\=\frac{-160}{91}\)
6. \(-\left(\frac{-7}{-3}\right)-\left(\frac{-7}{8}\right)\\= \frac{-7}{3}+\frac{7}{8}\\=\frac{-56}{24}+\frac{21}{24}\\=\frac{-56+21}{24}\\=\frac{-35}{24}\)
7. \(-\left(\frac{-6}{11}\right)-\left(\frac{-14}{5}\right)\\= \frac{6}{11}+\frac{14}{5}\\=\frac{30}{55}+\frac{154}{55}\\=\frac{30+154}{55}\\=\frac{184}{55}\)
8. \(+\left(\frac{-15}{7}\right)+\left(\frac{-5}{12}\right)\\= \frac{-15}{7}-\frac{5}{12}\\=\frac{-180}{84}-\frac{35}{84}\\=\frac{-180-35}{84}\\=\frac{-215}{84}\)
9. \(-\left(\frac{-8}{-7}\right)-\left(\frac{-14}{-3}\right)\\= \frac{-8}{7}-\frac{14}{3}\\=\frac{-24}{21}-\frac{98}{21}\\=\frac{-24-98}{21}\\=\frac{-122}{21}\)
10. \(-\left(\frac{-6}{-5}\right)-\left(\frac{-7}{-8}\right)\\= \frac{-6}{5}-\frac{7}{8}\\=\frac{-48}{40}-\frac{35}{40}\\=\frac{-48-35}{40}\\=\frac{-83}{40}\)
11. \(+\left(\frac{5}{-3}\right)+\left(\frac{5}{7}\right)\\= \frac{-5}{3}+\frac{5}{7}\\=\frac{-35}{21}+\frac{15}{21}\\=\frac{-35+15}{21}\\=\frac{-20}{21}\)
12. \(-\left(\frac{-7}{2}\right)-\left(\frac{9}{-5}\right)\\= \frac{7}{2}+\frac{9}{5}\\=\frac{35}{10}+\frac{18}{10}\\=\frac{35+18}{10}\\=\frac{53}{10}\)