Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{-13}\right)+\left(\frac{-15}{-2}\right)\\= \frac{-10}{13}+\frac{15}{2}\\=\frac{-20}{26}+\frac{195}{26}\\=\frac{-20+195}{26}\\=\frac{175}{26}\)
2. \(-\left(\frac{-3}{10}\right)+\left(\frac{-7}{-10}\right)\\= \frac{3}{10}+\frac{7}{10}\\=\frac{3+7}{10}\\=\frac{10}{10}\\=\frac{1}{1}\)
3. \(+\left(\frac{-14}{-3}\right)-\left(\frac{10}{9}\right)\\= \frac{14}{3}-\frac{10}{9}\\=\frac{42}{9}-\frac{10}{9}\\=\frac{42-10}{9}\\=\frac{32}{9}\)
4. \(+\left(\frac{8}{7}\right)+\left(\frac{5}{-4}\right)\\= \frac{8}{7}-\frac{5}{4}\\=\frac{32}{28}-\frac{35}{28}\\=\frac{32-35}{28}\\=\frac{-3}{28}\)
5. \(-\left(\frac{-4}{11}\right)+\left(\frac{7}{-8}\right)\\= \frac{4}{11}-\frac{7}{8}\\=\frac{32}{88}-\frac{77}{88}\\=\frac{32-77}{88}\\=\frac{-45}{88}\)
6. \(+\left(\frac{2}{7}\right)-\left(\frac{7}{13}\right)\\= \frac{2}{7}-\frac{7}{13}\\=\frac{26}{91}-\frac{49}{91}\\=\frac{26-49}{91}\\=\frac{-23}{91}\)
7. \(+\left(\frac{8}{-13}\right)-\left(\frac{-2}{3}\right)\\= \frac{-8}{13}+\frac{2}{3}\\=\frac{-24}{39}+\frac{26}{39}\\=\frac{-24+26}{39}\\=\frac{2}{39}\)
8. \(+\left(\frac{15}{-4}\right)-\left(\frac{7}{5}\right)\\= \frac{-15}{4}-\frac{7}{5}\\=\frac{-75}{20}-\frac{28}{20}\\=\frac{-75-28}{20}\\=\frac{-103}{20}\)
9. \(-\left(\frac{7}{2}\right)-\left(\frac{-3}{-2}\right)\\= \frac{-7}{2}-\frac{3}{2}\\=\frac{-7-3}{2}\\=\frac{-10}{2}\\=\frac{-5}{1}\)
10. \(+\left(\frac{-9}{11}\right)+\left(\frac{7}{6}\right)\\= \frac{-9}{11}+\frac{7}{6}\\=\frac{-54}{66}+\frac{77}{66}\\=\frac{-54+77}{66}\\=\frac{23}{66}\)
11. \(+\left(\frac{-2}{-5}\right)-\left(\frac{7}{12}\right)\\= \frac{2}{5}-\frac{7}{12}\\=\frac{24}{60}-\frac{35}{60}\\=\frac{24-35}{60}\\=\frac{-11}{60}\)
12. \(+\left(\frac{-3}{8}\right)+\left(\frac{-6}{-11}\right)\\= \frac{-3}{8}+\frac{6}{11}\\=\frac{-33}{88}+\frac{48}{88}\\=\frac{-33+48}{88}\\=\frac{15}{88}\)