Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-15}{-13}\right)+\left(\frac{-11}{-12}\right)\\= \frac{-15}{13}+\frac{11}{12}\\=\frac{-180}{156}+\frac{143}{156}\\=\frac{-180+143}{156}\\=\frac{-37}{156}\)
2. \(+\left(\frac{10}{9}\right)+\left(\frac{14}{9}\right)\\= \frac{10}{9}+\frac{14}{9}\\=\frac{10+14}{9}\\=\frac{24}{9}\\=\frac{8}{3}\)
3. \(-\left(\frac{-3}{-13}\right)-\left(\frac{10}{13}\right)\\= \frac{-3}{13}-\frac{10}{13}\\=\frac{-3-10}{13}\\=\frac{-13}{13}\\=\frac{-1}{1}\)
4. \(+\left(\frac{8}{-7}\right)+\left(\frac{-7}{-12}\right)\\= \frac{-8}{7}+\frac{7}{12}\\=\frac{-96}{84}+\frac{49}{84}\\=\frac{-96+49}{84}\\=\frac{-47}{84}\)
5. \(-\left(\frac{3}{7}\right)-\left(\frac{11}{12}\right)\\= \frac{-3}{7}-\frac{11}{12}\\=\frac{-36}{84}-\frac{77}{84}\\=\frac{-36-77}{84}\\=\frac{-113}{84}\)
6. \(+\left(\frac{-9}{-11}\right)+\left(\frac{-13}{-10}\right)\\= \frac{9}{11}+\frac{13}{10}\\=\frac{90}{110}+\frac{143}{110}\\=\frac{90+143}{110}\\=\frac{233}{110}\)
7. \(+\left(\frac{5}{-2}\right)-\left(\frac{-8}{-3}\right)\\= \frac{-5}{2}-\frac{8}{3}\\=\frac{-15}{6}-\frac{16}{6}\\=\frac{-15-16}{6}\\=\frac{-31}{6}\)
8. \(-\left(\frac{-8}{-9}\right)+\left(\frac{15}{13}\right)\\= \frac{-8}{9}+\frac{15}{13}\\=\frac{-104}{117}+\frac{135}{117}\\=\frac{-104+135}{117}\\=\frac{31}{117}\)
9. \(-\left(\frac{3}{-7}\right)+\left(\frac{13}{2}\right)\\= \frac{3}{7}+\frac{13}{2}\\=\frac{6}{14}+\frac{91}{14}\\=\frac{6+91}{14}\\=\frac{97}{14}\)
10. \(+\left(\frac{8}{-5}\right)+\left(\frac{2}{-11}\right)\\= \frac{-8}{5}-\frac{2}{11}\\=\frac{-88}{55}-\frac{10}{55}\\=\frac{-88-10}{55}\\=\frac{-98}{55}\)
11. \(+\left(\frac{-14}{-9}\right)-\left(\frac{-10}{-9}\right)\\= \frac{14}{9}-\frac{10}{9}\\=\frac{14-10}{9}\\=\frac{4}{9}\)
12. \(-\left(\frac{8}{3}\right)+\left(\frac{-6}{-11}\right)\\= \frac{-8}{3}+\frac{6}{11}\\=\frac{-88}{33}+\frac{18}{33}\\=\frac{-88+18}{33}\\=\frac{-70}{33}\)