Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{2}{11}\right)+\left(\frac{9}{13}\right)\\= \frac{-2}{11}+\frac{9}{13}\\=\frac{-26}{143}+\frac{99}{143}\\=\frac{-26+99}{143}\\=\frac{73}{143}\)
2. \(+\left(\frac{13}{-3}\right)+\left(\frac{13}{14}\right)\\= \frac{-13}{3}+\frac{13}{14}\\=\frac{-182}{42}+\frac{39}{42}\\=\frac{-182+39}{42}\\=\frac{-143}{42}\)
3. \(+\left(\frac{-10}{7}\right)+\left(\frac{-6}{5}\right)\\= \frac{-10}{7}-\frac{6}{5}\\=\frac{-50}{35}-\frac{42}{35}\\=\frac{-50-42}{35}\\=\frac{-92}{35}\)
4. \(+\left(\frac{8}{13}\right)+\left(\frac{15}{-2}\right)\\= \frac{8}{13}-\frac{15}{2}\\=\frac{16}{26}-\frac{195}{26}\\=\frac{16-195}{26}\\=\frac{-179}{26}\)
5. \(+\left(\frac{-8}{-7}\right)+\left(\frac{-7}{5}\right)\\= \frac{8}{7}-\frac{7}{5}\\=\frac{40}{35}-\frac{49}{35}\\=\frac{40-49}{35}\\=\frac{-9}{35}\)
6. \(-\left(\frac{-2}{3}\right)+\left(\frac{-15}{-7}\right)\\= \frac{2}{3}+\frac{15}{7}\\=\frac{14}{21}+\frac{45}{21}\\=\frac{14+45}{21}\\=\frac{59}{21}\)
7. \(+\left(\frac{15}{14}\right)+\left(\frac{-13}{9}\right)\\= \frac{15}{14}-\frac{13}{9}\\=\frac{135}{126}-\frac{182}{126}\\=\frac{135-182}{126}\\=\frac{-47}{126}\)
8. \(+\left(\frac{12}{-5}\right)-\left(\frac{6}{11}\right)\\= \frac{-12}{5}-\frac{6}{11}\\=\frac{-132}{55}-\frac{30}{55}\\=\frac{-132-30}{55}\\=\frac{-162}{55}\)
9. \(+\left(\frac{2}{-5}\right)+\left(\frac{12}{13}\right)\\= \frac{-2}{5}+\frac{12}{13}\\=\frac{-26}{65}+\frac{60}{65}\\=\frac{-26+60}{65}\\=\frac{34}{65}\)
10. \(-\left(\frac{3}{2}\right)+\left(\frac{-10}{7}\right)\\= \frac{-3}{2}-\frac{10}{7}\\=\frac{-21}{14}-\frac{20}{14}\\=\frac{-21-20}{14}\\=\frac{-41}{14}\)
11. \(-\left(\frac{6}{13}\right)-\left(\frac{3}{-13}\right)\\= \frac{-6}{13}+\frac{3}{13}\\=\frac{-6+3}{13}\\=\frac{-3}{13}\)
12. \(+\left(\frac{2}{3}\right)-\left(\frac{8}{13}\right)\\= \frac{2}{3}-\frac{8}{13}\\=\frac{26}{39}-\frac{24}{39}\\=\frac{26-24}{39}\\=\frac{2}{39}\)