Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{5}\right)+\left(\frac{2}{-5}\right)\\= \frac{9}{5}-\frac{2}{5}\\=\frac{9-2}{5}\\=\frac{7}{5}\)
2. \(+\left(\frac{5}{-4}\right)-\left(\frac{-9}{13}\right)\\= \frac{-5}{4}+\frac{9}{13}\\=\frac{-65}{52}+\frac{36}{52}\\=\frac{-65+36}{52}\\=\frac{-29}{52}\)
3. \(+\left(\frac{3}{14}\right)-\left(\frac{8}{-11}\right)\\= \frac{3}{14}+\frac{8}{11}\\=\frac{33}{154}+\frac{112}{154}\\=\frac{33+112}{154}\\=\frac{145}{154}\)
4. \(+\left(\frac{8}{-9}\right)+\left(\frac{-15}{7}\right)\\= \frac{-8}{9}-\frac{15}{7}\\=\frac{-56}{63}-\frac{135}{63}\\=\frac{-56-135}{63}\\=\frac{-191}{63}\)
5. \(+\left(\frac{5}{13}\right)-\left(\frac{8}{7}\right)\\= \frac{5}{13}-\frac{8}{7}\\=\frac{35}{91}-\frac{104}{91}\\=\frac{35-104}{91}\\=\frac{-69}{91}\)
6. \(-\left(\frac{-12}{-7}\right)-\left(\frac{3}{-11}\right)\\= \frac{-12}{7}+\frac{3}{11}\\=\frac{-132}{77}+\frac{21}{77}\\=\frac{-132+21}{77}\\=\frac{-111}{77}\)
7. \(+\left(\frac{-9}{11}\right)+\left(\frac{10}{-13}\right)\\= \frac{-9}{11}-\frac{10}{13}\\=\frac{-117}{143}-\frac{110}{143}\\=\frac{-117-110}{143}\\=\frac{-227}{143}\)
8. \(-\left(\frac{5}{-6}\right)-\left(\frac{14}{-5}\right)\\= \frac{5}{6}+\frac{14}{5}\\=\frac{25}{30}+\frac{84}{30}\\=\frac{25+84}{30}\\=\frac{109}{30}\)
9. \(+\left(\frac{10}{9}\right)-\left(\frac{-8}{5}\right)\\= \frac{10}{9}+\frac{8}{5}\\=\frac{50}{45}+\frac{72}{45}\\=\frac{50+72}{45}\\=\frac{122}{45}\)
10. \(+\left(\frac{7}{6}\right)+\left(\frac{7}{6}\right)\\= \frac{7}{6}+\frac{7}{6}\\=\frac{7+7}{6}\\=\frac{14}{6}\\=\frac{7}{3}\)
11. \(+\left(\frac{9}{-7}\right)-\left(\frac{-6}{11}\right)\\= \frac{-9}{7}+\frac{6}{11}\\=\frac{-99}{77}+\frac{42}{77}\\=\frac{-99+42}{77}\\=\frac{-57}{77}\)
12. \(+\left(\frac{-9}{14}\right)-\left(\frac{2}{-9}\right)\\= \frac{-9}{14}+\frac{2}{9}\\=\frac{-81}{126}+\frac{28}{126}\\=\frac{-81+28}{126}\\=\frac{-53}{126}\)