Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-13}{-5}\right)+\left(\frac{-2}{5}\right)\\= \frac{13}{5}-\frac{2}{5}\\=\frac{13-2}{5}\\=\frac{11}{5}\)
2. \(-\left(\frac{-8}{-3}\right)+\left(\frac{-4}{9}\right)\\= \frac{-8}{3}-\frac{4}{9}\\=\frac{-24}{9}-\frac{4}{9}\\=\frac{-24-4}{9}\\=\frac{-28}{9}\)
3. \(+\left(\frac{-3}{11}\right)-\left(\frac{-13}{5}\right)\\= \frac{-3}{11}+\frac{13}{5}\\=\frac{-15}{55}+\frac{143}{55}\\=\frac{-15+143}{55}\\=\frac{128}{55}\)
4. \(+\left(\frac{5}{-7}\right)+\left(\frac{8}{9}\right)\\= \frac{-5}{7}+\frac{8}{9}\\=\frac{-45}{63}+\frac{56}{63}\\=\frac{-45+56}{63}\\=\frac{11}{63}\)
5. \(-\left(\frac{-5}{6}\right)-\left(\frac{-4}{7}\right)\\= \frac{5}{6}+\frac{4}{7}\\=\frac{35}{42}+\frac{24}{42}\\=\frac{35+24}{42}\\=\frac{59}{42}\)
6. \(+\left(\frac{-5}{-6}\right)-\left(\frac{-12}{-5}\right)\\= \frac{5}{6}-\frac{12}{5}\\=\frac{25}{30}-\frac{72}{30}\\=\frac{25-72}{30}\\=\frac{-47}{30}\)
7. \(+\left(\frac{13}{-3}\right)+\left(\frac{5}{7}\right)\\= \frac{-13}{3}+\frac{5}{7}\\=\frac{-91}{21}+\frac{15}{21}\\=\frac{-91+15}{21}\\=\frac{-76}{21}\)
8. \(+\left(\frac{-2}{-5}\right)-\left(\frac{14}{-9}\right)\\= \frac{2}{5}+\frac{14}{9}\\=\frac{18}{45}+\frac{70}{45}\\=\frac{18+70}{45}\\=\frac{88}{45}\)
9. \(+\left(\frac{-13}{3}\right)-\left(\frac{15}{-4}\right)\\= \frac{-13}{3}+\frac{15}{4}\\=\frac{-52}{12}+\frac{45}{12}\\=\frac{-52+45}{12}\\=\frac{-7}{12}\)
10. \(+\left(\frac{10}{-11}\right)-\left(\frac{-15}{11}\right)\\= \frac{-10}{11}+\frac{15}{11}\\=\frac{-10+15}{11}\\=\frac{5}{11}\)
11. \(+\left(\frac{-5}{-14}\right)+\left(\frac{-10}{-13}\right)\\= \frac{5}{14}+\frac{10}{13}\\=\frac{65}{182}+\frac{140}{182}\\=\frac{65+140}{182}\\=\frac{205}{182}\)
12. \(+\left(\frac{15}{-8}\right)+\left(\frac{-15}{-4}\right)\\= \frac{-15}{8}+\frac{15}{4}\\=\frac{-15+15}{8}\\=\frac{0}{8}\\=\frac{0}{1}\)