Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{8}{-9}\right)+\left(\frac{3}{2}\right)\\= \frac{-8}{9}+\frac{3}{2}\\=\frac{-16}{18}+\frac{27}{18}\\=\frac{-16+27}{18}\\=\frac{11}{18}\)
2. \(+\left(\frac{-8}{11}\right)+\left(\frac{3}{-2}\right)\\= \frac{-8}{11}-\frac{3}{2}\\=\frac{-16}{22}-\frac{33}{22}\\=\frac{-16-33}{22}\\=\frac{-49}{22}\)
3. \(+\left(\frac{-3}{14}\right)+\left(\frac{-5}{6}\right)\\= \frac{-3}{14}-\frac{5}{6}\\=\frac{-9}{42}-\frac{35}{42}\\=\frac{-9-35}{42}\\=\frac{-44}{42}\\=\frac{-22}{21}\)
4. \(+\left(\frac{4}{3}\right)-\left(\frac{-10}{-3}\right)\\= \frac{4}{3}-\frac{10}{3}\\=\frac{4-10}{3}\\=\frac{-6}{3}\\=\frac{-2}{1}\)
5. \(+\left(\frac{2}{13}\right)-\left(\frac{7}{-13}\right)\\= \frac{2}{13}+\frac{7}{13}\\=\frac{2+7}{13}\\=\frac{9}{13}\)
6. \(+\left(\frac{-4}{-5}\right)+\left(\frac{-5}{-2}\right)\\= \frac{4}{5}+\frac{5}{2}\\=\frac{8}{10}+\frac{25}{10}\\=\frac{8+25}{10}\\=\frac{33}{10}\)
7. \(-\left(\frac{14}{-3}\right)-\left(\frac{5}{-13}\right)\\= \frac{14}{3}+\frac{5}{13}\\=\frac{182}{39}+\frac{15}{39}\\=\frac{182+15}{39}\\=\frac{197}{39}\)
8. \(+\left(\frac{14}{-13}\right)-\left(\frac{3}{13}\right)\\= \frac{-14}{13}-\frac{3}{13}\\=\frac{-14-3}{13}\\=\frac{-17}{13}\)
9. \(-\left(\frac{4}{-7}\right)-\left(\frac{6}{-7}\right)\\= \frac{4}{7}+\frac{6}{7}\\=\frac{4+6}{7}\\=\frac{10}{7}\)
10. \(+\left(\frac{-6}{-11}\right)+\left(\frac{-14}{9}\right)\\= \frac{6}{11}-\frac{14}{9}\\=\frac{54}{99}-\frac{154}{99}\\=\frac{54-154}{99}\\=\frac{-100}{99}\)
11. \(-\left(\frac{-3}{-13}\right)+\left(\frac{-15}{-2}\right)\\= \frac{-3}{13}+\frac{15}{2}\\=\frac{-6}{26}+\frac{195}{26}\\=\frac{-6+195}{26}\\=\frac{189}{26}\)
12. \(+\left(\frac{12}{-11}\right)-\left(\frac{8}{3}\right)\\= \frac{-12}{11}-\frac{8}{3}\\=\frac{-36}{33}-\frac{88}{33}\\=\frac{-36-88}{33}\\=\frac{-124}{33}\)