Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{2}{3}\right)-\left(\frac{-15}{-4}\right)\\= \frac{2}{3}-\frac{15}{4}\\=\frac{8}{12}-\frac{45}{12}\\=\frac{8-45}{12}\\=\frac{-37}{12}\)
2. \(-\left(\frac{-11}{6}\right)-\left(\frac{-14}{3}\right)\\= \frac{11}{6}+\frac{14}{3}\\=\frac{11+14}{6}\\=\frac{25}{6}\)
3. \(-\left(\frac{-5}{14}\right)-\left(\frac{-10}{-11}\right)\\= \frac{5}{14}-\frac{10}{11}\\=\frac{55}{154}-\frac{140}{154}\\=\frac{55-140}{154}\\=\frac{-85}{154}\)
4. \(-\left(\frac{9}{-4}\right)-\left(\frac{-7}{-5}\right)\\= \frac{9}{4}-\frac{7}{5}\\=\frac{45}{20}-\frac{28}{20}\\=\frac{45-28}{20}\\=\frac{17}{20}\)
5. \(+\left(\frac{14}{5}\right)+\left(\frac{-14}{-9}\right)\\= \frac{14}{5}+\frac{14}{9}\\=\frac{126}{45}+\frac{70}{45}\\=\frac{126+70}{45}\\=\frac{196}{45}\)
6. \(-\left(\frac{14}{13}\right)+\left(\frac{-11}{14}\right)\\= \frac{-14}{13}-\frac{11}{14}\\=\frac{-196}{182}-\frac{143}{182}\\=\frac{-196-143}{182}\\=\frac{-339}{182}\)
7. \(+\left(\frac{-2}{5}\right)+\left(\frac{7}{2}\right)\\= \frac{-2}{5}+\frac{7}{2}\\=\frac{-4}{10}+\frac{35}{10}\\=\frac{-4+35}{10}\\=\frac{31}{10}\)
8. \(-\left(\frac{2}{-13}\right)-\left(\frac{2}{5}\right)\\= \frac{2}{13}-\frac{2}{5}\\=\frac{10}{65}-\frac{26}{65}\\=\frac{10-26}{65}\\=\frac{-16}{65}\)
9. \(-\left(\frac{-13}{2}\right)-\left(\frac{15}{-7}\right)\\= \frac{13}{2}+\frac{15}{7}\\=\frac{91}{14}+\frac{30}{14}\\=\frac{91+30}{14}\\=\frac{121}{14}\)
10. \(+\left(\frac{5}{11}\right)-\left(\frac{-12}{5}\right)\\= \frac{5}{11}+\frac{12}{5}\\=\frac{25}{55}+\frac{132}{55}\\=\frac{25+132}{55}\\=\frac{157}{55}\)
11. \(-\left(\frac{-10}{-7}\right)+\left(\frac{-5}{-7}\right)\\= \frac{-10}{7}+\frac{5}{7}\\=\frac{-10+5}{7}\\=\frac{-5}{7}\)
12. \(+\left(\frac{-8}{-5}\right)+\left(\frac{-7}{5}\right)\\= \frac{8}{5}-\frac{7}{5}\\=\frac{8-7}{5}\\=\frac{1}{5}\)