Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-5}{11}\right)-\left(\frac{14}{-13}\right)\\= \frac{5}{11}+\frac{14}{13}\\=\frac{65}{143}+\frac{154}{143}\\=\frac{65+154}{143}\\=\frac{219}{143}\)
2. \(+\left(\frac{-3}{10}\right)-\left(\frac{2}{9}\right)\\= \frac{-3}{10}-\frac{2}{9}\\=\frac{-27}{90}-\frac{20}{90}\\=\frac{-27-20}{90}\\=\frac{-47}{90}\)
3. \(-\left(\frac{8}{-3}\right)-\left(\frac{6}{7}\right)\\= \frac{8}{3}-\frac{6}{7}\\=\frac{56}{21}-\frac{18}{21}\\=\frac{56-18}{21}\\=\frac{38}{21}\)
4. \(-\left(\frac{9}{-8}\right)+\left(\frac{-14}{-9}\right)\\= \frac{9}{8}+\frac{14}{9}\\=\frac{81}{72}+\frac{112}{72}\\=\frac{81+112}{72}\\=\frac{193}{72}\)
5. \(+\left(\frac{7}{13}\right)+\left(\frac{-12}{11}\right)\\= \frac{7}{13}-\frac{12}{11}\\=\frac{77}{143}-\frac{156}{143}\\=\frac{77-156}{143}\\=\frac{-79}{143}\)
6. \(+\left(\frac{9}{2}\right)-\left(\frac{7}{-5}\right)\\= \frac{9}{2}+\frac{7}{5}\\=\frac{45}{10}+\frac{14}{10}\\=\frac{45+14}{10}\\=\frac{59}{10}\)
7. \(-\left(\frac{-10}{9}\right)+\left(\frac{-14}{11}\right)\\= \frac{10}{9}-\frac{14}{11}\\=\frac{110}{99}-\frac{126}{99}\\=\frac{110-126}{99}\\=\frac{-16}{99}\)
8. \(-\left(\frac{-3}{2}\right)-\left(\frac{-15}{-7}\right)\\= \frac{3}{2}-\frac{15}{7}\\=\frac{21}{14}-\frac{30}{14}\\=\frac{21-30}{14}\\=\frac{-9}{14}\)
9. \(+\left(\frac{7}{8}\right)-\left(\frac{3}{5}\right)\\= \frac{7}{8}-\frac{3}{5}\\=\frac{35}{40}-\frac{24}{40}\\=\frac{35-24}{40}\\=\frac{11}{40}\)
10. \(-\left(\frac{8}{5}\right)+\left(\frac{-11}{-5}\right)\\= \frac{-8}{5}+\frac{11}{5}\\=\frac{-8+11}{5}\\=\frac{3}{5}\)
11. \(+\left(\frac{-4}{5}\right)-\left(\frac{-10}{13}\right)\\= \frac{-4}{5}+\frac{10}{13}\\=\frac{-52}{65}+\frac{50}{65}\\=\frac{-52+50}{65}\\=\frac{-2}{65}\)
12. \(-\left(\frac{12}{5}\right)+\left(\frac{4}{-5}\right)\\= \frac{-12}{5}-\frac{4}{5}\\=\frac{-12-4}{5}\\=\frac{-16}{5}\)