Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-7}{11}\right)+\left(\frac{13}{3}\right)\\= \frac{7}{11}+\frac{13}{3}\\=\frac{21}{33}+\frac{143}{33}\\=\frac{21+143}{33}\\=\frac{164}{33}\)
2. \(+\left(\frac{2}{13}\right)+\left(\frac{-6}{11}\right)\\= \frac{2}{13}-\frac{6}{11}\\=\frac{22}{143}-\frac{78}{143}\\=\frac{22-78}{143}\\=\frac{-56}{143}\)
3. \(-\left(\frac{-12}{5}\right)+\left(\frac{-15}{7}\right)\\= \frac{12}{5}-\frac{15}{7}\\=\frac{84}{35}-\frac{75}{35}\\=\frac{84-75}{35}\\=\frac{9}{35}\)
4. \(-\left(\frac{-14}{-3}\right)+\left(\frac{15}{-14}\right)\\= \frac{-14}{3}-\frac{15}{14}\\=\frac{-196}{42}-\frac{45}{42}\\=\frac{-196-45}{42}\\=\frac{-241}{42}\)
5. \(+\left(\frac{-9}{-2}\right)+\left(\frac{9}{-4}\right)\\= \frac{9}{2}-\frac{9}{4}\\=\frac{18}{4}-\frac{9}{4}\\=\frac{18-9}{4}\\=\frac{9}{4}\)
6. \(-\left(\frac{-9}{-13}\right)-\left(\frac{-11}{9}\right)\\= \frac{-9}{13}+\frac{11}{9}\\=\frac{-81}{117}+\frac{143}{117}\\=\frac{-81+143}{117}\\=\frac{62}{117}\)
7. \(-\left(\frac{11}{12}\right)-\left(\frac{-10}{-3}\right)\\= \frac{-11}{12}-\frac{10}{3}\\=\frac{-11-10}{12}\\=\frac{-21}{12}\\=\frac{-7}{4}\)
8. \(-\left(\frac{-13}{-8}\right)+\left(\frac{-15}{13}\right)\\= \frac{-13}{8}-\frac{15}{13}\\=\frac{-169}{104}-\frac{120}{104}\\=\frac{-169-120}{104}\\=\frac{-289}{104}\)
9. \(+\left(\frac{-11}{7}\right)-\left(\frac{-10}{-11}\right)\\= \frac{-11}{7}-\frac{10}{11}\\=\frac{-121}{77}-\frac{70}{77}\\=\frac{-121-70}{77}\\=\frac{-191}{77}\)
10. \(-\left(\frac{10}{11}\right)+\left(\frac{-8}{9}\right)\\= \frac{-10}{11}-\frac{8}{9}\\=\frac{-90}{99}-\frac{88}{99}\\=\frac{-90-88}{99}\\=\frac{-178}{99}\)
11. \(+\left(\frac{-3}{7}\right)-\left(\frac{-2}{11}\right)\\= \frac{-3}{7}+\frac{2}{11}\\=\frac{-33}{77}+\frac{14}{77}\\=\frac{-33+14}{77}\\=\frac{-19}{77}\)
12. \(+\left(\frac{-7}{-2}\right)-\left(\frac{5}{6}\right)\\= \frac{7}{2}-\frac{5}{6}\\=\frac{21}{6}-\frac{5}{6}\\=\frac{21-5}{6}\\=\frac{16}{6}\\=\frac{8}{3}\)