Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-15}{-7}\right)-\left(\frac{-8}{-7}\right)\\= \frac{-15}{7}-\frac{8}{7}\\=\frac{-15-8}{7}\\=\frac{-23}{7}\)
2. \(+\left(\frac{2}{11}\right)+\left(\frac{6}{7}\right)\\= \frac{2}{11}+\frac{6}{7}\\=\frac{14}{77}+\frac{66}{77}\\=\frac{14+66}{77}\\=\frac{80}{77}\)
3. \(-\left(\frac{4}{5}\right)+\left(\frac{-10}{7}\right)\\= \frac{-4}{5}-\frac{10}{7}\\=\frac{-28}{35}-\frac{50}{35}\\=\frac{-28-50}{35}\\=\frac{-78}{35}\)
4. \(-\left(\frac{15}{4}\right)+\left(\frac{-4}{-9}\right)\\= \frac{-15}{4}+\frac{4}{9}\\=\frac{-135}{36}+\frac{16}{36}\\=\frac{-135+16}{36}\\=\frac{-119}{36}\)
5. \(-\left(\frac{2}{13}\right)-\left(\frac{-3}{-2}\right)\\= \frac{-2}{13}-\frac{3}{2}\\=\frac{-4}{26}-\frac{39}{26}\\=\frac{-4-39}{26}\\=\frac{-43}{26}\)
6. \(+\left(\frac{14}{5}\right)-\left(\frac{-14}{5}\right)\\= \frac{14}{5}+\frac{14}{5}\\=\frac{14+14}{5}\\=\frac{28}{5}\)
7. \(+\left(\frac{3}{7}\right)+\left(\frac{3}{-7}\right)\\= \frac{3}{7}-\frac{3}{7}\\=\frac{3-3}{7}\\=\frac{0}{7}\\=\frac{0}{1}\)
8. \(+\left(\frac{-5}{-6}\right)+\left(\frac{5}{-9}\right)\\= \frac{5}{6}-\frac{5}{9}\\=\frac{15}{18}-\frac{10}{18}\\=\frac{15-10}{18}\\=\frac{5}{18}\)
9. \(-\left(\frac{-7}{-4}\right)+\left(\frac{-14}{5}\right)\\= \frac{-7}{4}-\frac{14}{5}\\=\frac{-35}{20}-\frac{56}{20}\\=\frac{-35-56}{20}\\=\frac{-91}{20}\)
10. \(-\left(\frac{9}{-4}\right)+\left(\frac{-11}{-10}\right)\\= \frac{9}{4}+\frac{11}{10}\\=\frac{45}{20}+\frac{22}{20}\\=\frac{45+22}{20}\\=\frac{67}{20}\)
11. \(+\left(\frac{-4}{-3}\right)-\left(\frac{-9}{-4}\right)\\= \frac{4}{3}-\frac{9}{4}\\=\frac{16}{12}-\frac{27}{12}\\=\frac{16-27}{12}\\=\frac{-11}{12}\)
12. \(+\left(\frac{-11}{2}\right)+\left(\frac{11}{-7}\right)\\= \frac{-11}{2}-\frac{11}{7}\\=\frac{-77}{14}-\frac{22}{14}\\=\frac{-77-22}{14}\\=\frac{-99}{14}\)