Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-6}{13}\right)+\left(\frac{-4}{7}\right)\\= \frac{6}{13}-\frac{4}{7}\\=\frac{42}{91}-\frac{52}{91}\\=\frac{42-52}{91}\\=\frac{-10}{91}\)
2. \(-\left(\frac{12}{-5}\right)+\left(\frac{-9}{-7}\right)\\= \frac{12}{5}+\frac{9}{7}\\=\frac{84}{35}+\frac{45}{35}\\=\frac{84+45}{35}\\=\frac{129}{35}\)
3. \(-\left(\frac{3}{13}\right)+\left(\frac{8}{7}\right)\\= \frac{-3}{13}+\frac{8}{7}\\=\frac{-21}{91}+\frac{104}{91}\\=\frac{-21+104}{91}\\=\frac{83}{91}\)
4. \(+\left(\frac{13}{14}\right)+\left(\frac{14}{-13}\right)\\= \frac{13}{14}-\frac{14}{13}\\=\frac{169}{182}-\frac{196}{182}\\=\frac{169-196}{182}\\=\frac{-27}{182}\)
5. \(+\left(\frac{-8}{9}\right)-\left(\frac{-5}{4}\right)\\= \frac{-8}{9}+\frac{5}{4}\\=\frac{-32}{36}+\frac{45}{36}\\=\frac{-32+45}{36}\\=\frac{13}{36}\)
6. \(+\left(\frac{8}{11}\right)-\left(\frac{-6}{-11}\right)\\= \frac{8}{11}-\frac{6}{11}\\=\frac{8-6}{11}\\=\frac{2}{11}\)
7. \(-\left(\frac{-10}{7}\right)+\left(\frac{2}{11}\right)\\= \frac{10}{7}+\frac{2}{11}\\=\frac{110}{77}+\frac{14}{77}\\=\frac{110+14}{77}\\=\frac{124}{77}\)
8. \(-\left(\frac{8}{9}\right)+\left(\frac{-8}{9}\right)\\= \frac{-8}{9}-\frac{8}{9}\\=\frac{-8-8}{9}\\=\frac{-16}{9}\)
9. \(-\left(\frac{11}{-12}\right)-\left(\frac{10}{3}\right)\\= \frac{11}{12}-\frac{10}{3}\\=\frac{11-10}{12}\\=\frac{1}{12}\)
10. \(+\left(\frac{-9}{-14}\right)-\left(\frac{2}{-13}\right)\\= \frac{9}{14}+\frac{2}{13}\\=\frac{117}{182}+\frac{28}{182}\\=\frac{117+28}{182}\\=\frac{145}{182}\)
11. \(+\left(\frac{12}{5}\right)+\left(\frac{15}{-4}\right)\\= \frac{12}{5}-\frac{15}{4}\\=\frac{48}{20}-\frac{75}{20}\\=\frac{48-75}{20}\\=\frac{-27}{20}\)
12. \(+\left(\frac{11}{-4}\right)-\left(\frac{2}{7}\right)\\= \frac{-11}{4}-\frac{2}{7}\\=\frac{-77}{28}-\frac{8}{28}\\=\frac{-77-8}{28}\\=\frac{-85}{28}\)