Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{7}\right)+\left(\frac{-10}{3}\right)\\= \frac{-10}{7}-\frac{10}{3}\\=\frac{-30}{21}-\frac{70}{21}\\=\frac{-30-70}{21}\\=\frac{-100}{21}\)
2. \(+\left(\frac{6}{-7}\right)+\left(\frac{12}{-13}\right)\\= \frac{-6}{7}-\frac{12}{13}\\=\frac{-78}{91}-\frac{84}{91}\\=\frac{-78-84}{91}\\=\frac{-162}{91}\)
3. \(+\left(\frac{-12}{13}\right)+\left(\frac{-9}{-10}\right)\\= \frac{-12}{13}+\frac{9}{10}\\=\frac{-120}{130}+\frac{117}{130}\\=\frac{-120+117}{130}\\=\frac{-3}{130}\)
4. \(-\left(\frac{-7}{-2}\right)-\left(\frac{10}{7}\right)\\= \frac{-7}{2}-\frac{10}{7}\\=\frac{-49}{14}-\frac{20}{14}\\=\frac{-49-20}{14}\\=\frac{-69}{14}\)
5. \(-\left(\frac{-9}{-8}\right)-\left(\frac{-3}{-2}\right)\\= \frac{-9}{8}-\frac{3}{2}\\=\frac{-9-3}{8}\\=\frac{-12}{8}\\=\frac{-3}{2}\)
6. \(+\left(\frac{3}{-11}\right)-\left(\frac{12}{7}\right)\\= \frac{-3}{11}-\frac{12}{7}\\=\frac{-21}{77}-\frac{132}{77}\\=\frac{-21-132}{77}\\=\frac{-153}{77}\)
7. \(+\left(\frac{-3}{-10}\right)-\left(\frac{-12}{5}\right)\\= \frac{3}{10}+\frac{12}{5}\\=\frac{3+12}{10}\\=\frac{15}{10}\\=\frac{3}{2}\)
8. \(-\left(\frac{-2}{-3}\right)+\left(\frac{-3}{11}\right)\\= \frac{-2}{3}-\frac{3}{11}\\=\frac{-22}{33}-\frac{9}{33}\\=\frac{-22-9}{33}\\=\frac{-31}{33}\)
9. \(+\left(\frac{-3}{7}\right)+\left(\frac{-14}{-3}\right)\\= \frac{-3}{7}+\frac{14}{3}\\=\frac{-9}{21}+\frac{98}{21}\\=\frac{-9+98}{21}\\=\frac{89}{21}\)
10. \(+\left(\frac{15}{-7}\right)+\left(\frac{-5}{-2}\right)\\= \frac{-15}{7}+\frac{5}{2}\\=\frac{-30}{14}+\frac{35}{14}\\=\frac{-30+35}{14}\\=\frac{5}{14}\)
11. \(+\left(\frac{-12}{11}\right)+\left(\frac{-5}{-11}\right)\\= \frac{-12}{11}+\frac{5}{11}\\=\frac{-12+5}{11}\\=\frac{-7}{11}\)
12. \(-\left(\frac{11}{12}\right)+\left(\frac{-14}{3}\right)\\= \frac{-11}{12}-\frac{14}{3}\\=\frac{-11-14}{12}\\=\frac{-25}{12}\)