Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{6}{-5}\right)-\left(\frac{-4}{9}\right)\\= \frac{6}{5}+\frac{4}{9}\\=\frac{54}{45}+\frac{20}{45}\\=\frac{54+20}{45}\\=\frac{74}{45}\)
2. \(+\left(\frac{-10}{13}\right)-\left(\frac{12}{11}\right)\\= \frac{-10}{13}-\frac{12}{11}\\=\frac{-110}{143}-\frac{156}{143}\\=\frac{-110-156}{143}\\=\frac{-266}{143}\)
3. \(+\left(\frac{-2}{11}\right)+\left(\frac{-9}{-11}\right)\\= \frac{-2}{11}+\frac{9}{11}\\=\frac{-2+9}{11}\\=\frac{7}{11}\)
4. \(+\left(\frac{15}{11}\right)-\left(\frac{-2}{5}\right)\\= \frac{15}{11}+\frac{2}{5}\\=\frac{75}{55}+\frac{22}{55}\\=\frac{75+22}{55}\\=\frac{97}{55}\)
5. \(+\left(\frac{-4}{3}\right)+\left(\frac{14}{-9}\right)\\= \frac{-4}{3}-\frac{14}{9}\\=\frac{-12}{9}-\frac{14}{9}\\=\frac{-12-14}{9}\\=\frac{-26}{9}\)
6. \(-\left(\frac{11}{10}\right)-\left(\frac{-9}{-2}\right)\\= \frac{-11}{10}-\frac{9}{2}\\=\frac{-11-9}{10}\\=\frac{-20}{10}\\=\frac{-2}{1}\)
7. \(+\left(\frac{-5}{6}\right)-\left(\frac{11}{-9}\right)\\= \frac{-5}{6}+\frac{11}{9}\\=\frac{-15}{18}+\frac{22}{18}\\=\frac{-15+22}{18}\\=\frac{7}{18}\)
8. \(+\left(\frac{-12}{-7}\right)-\left(\frac{12}{-13}\right)\\= \frac{12}{7}+\frac{12}{13}\\=\frac{156}{91}+\frac{84}{91}\\=\frac{156+84}{91}\\=\frac{240}{91}\)
9. \(+\left(\frac{9}{-4}\right)-\left(\frac{5}{-4}\right)\\= \frac{-9}{4}+\frac{5}{4}\\=\frac{-9+5}{4}\\=\frac{-4}{4}\\=\frac{-1}{1}\)
10. \(-\left(\frac{-5}{-7}\right)-\left(\frac{-11}{-13}\right)\\= \frac{-5}{7}-\frac{11}{13}\\=\frac{-65}{91}-\frac{77}{91}\\=\frac{-65-77}{91}\\=\frac{-142}{91}\)
11. \(-\left(\frac{-15}{-7}\right)+\left(\frac{-10}{9}\right)\\= \frac{-15}{7}-\frac{10}{9}\\=\frac{-135}{63}-\frac{70}{63}\\=\frac{-135-70}{63}\\=\frac{-205}{63}\)
12. \(+\left(\frac{-2}{13}\right)+\left(\frac{-11}{3}\right)\\= \frac{-2}{13}-\frac{11}{3}\\=\frac{-6}{39}-\frac{143}{39}\\=\frac{-6-143}{39}\\=\frac{-149}{39}\)