Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{4}{-9}\right)+\left(\frac{-10}{13}\right)\\= \frac{4}{9}-\frac{10}{13}\\=\frac{52}{117}-\frac{90}{117}\\=\frac{52-90}{117}\\=\frac{-38}{117}\)
2. \(-\left(\frac{-11}{-7}\right)+\left(\frac{10}{13}\right)\\= \frac{-11}{7}+\frac{10}{13}\\=\frac{-143}{91}+\frac{70}{91}\\=\frac{-143+70}{91}\\=\frac{-73}{91}\)
3. \(-\left(\frac{10}{-11}\right)-\left(\frac{14}{13}\right)\\= \frac{10}{11}-\frac{14}{13}\\=\frac{130}{143}-\frac{154}{143}\\=\frac{130-154}{143}\\=\frac{-24}{143}\)
4. \(+\left(\frac{-8}{-3}\right)+\left(\frac{-5}{-6}\right)\\= \frac{8}{3}+\frac{5}{6}\\=\frac{16}{6}+\frac{5}{6}\\=\frac{16+5}{6}\\=\frac{21}{6}\\=\frac{7}{2}\)
5. \(-\left(\frac{5}{-2}\right)-\left(\frac{-10}{-3}\right)\\= \frac{5}{2}-\frac{10}{3}\\=\frac{15}{6}-\frac{20}{6}\\=\frac{15-20}{6}\\=\frac{-5}{6}\)
6. \(-\left(\frac{-10}{3}\right)-\left(\frac{-8}{-11}\right)\\= \frac{10}{3}-\frac{8}{11}\\=\frac{110}{33}-\frac{24}{33}\\=\frac{110-24}{33}\\=\frac{86}{33}\)
7. \(+\left(\frac{-4}{-9}\right)-\left(\frac{6}{5}\right)\\= \frac{4}{9}-\frac{6}{5}\\=\frac{20}{45}-\frac{54}{45}\\=\frac{20-54}{45}\\=\frac{-34}{45}\)
8. \(+\left(\frac{5}{11}\right)+\left(\frac{-7}{-4}\right)\\= \frac{5}{11}+\frac{7}{4}\\=\frac{20}{44}+\frac{77}{44}\\=\frac{20+77}{44}\\=\frac{97}{44}\)
9. \(-\left(\frac{-15}{-11}\right)+\left(\frac{14}{-5}\right)\\= \frac{-15}{11}-\frac{14}{5}\\=\frac{-75}{55}-\frac{154}{55}\\=\frac{-75-154}{55}\\=\frac{-229}{55}\)
10. \(+\left(\frac{-6}{13}\right)-\left(\frac{14}{11}\right)\\= \frac{-6}{13}-\frac{14}{11}\\=\frac{-66}{143}-\frac{182}{143}\\=\frac{-66-182}{143}\\=\frac{-248}{143}\)
11. \(+\left(\frac{-13}{-10}\right)+\left(\frac{-9}{-10}\right)\\= \frac{13}{10}+\frac{9}{10}\\=\frac{13+9}{10}\\=\frac{22}{10}\\=\frac{11}{5}\)
12. \(+\left(\frac{-14}{-13}\right)-\left(\frac{-15}{-2}\right)\\= \frac{14}{13}-\frac{15}{2}\\=\frac{28}{26}-\frac{195}{26}\\=\frac{28-195}{26}\\=\frac{-167}{26}\)