Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-12}{13}\right)-\left(\frac{-11}{-14}\right)\\= \frac{12}{13}-\frac{11}{14}\\=\frac{168}{182}-\frac{143}{182}\\=\frac{168-143}{182}\\=\frac{25}{182}\)
2. \(+\left(\frac{-6}{7}\right)-\left(\frac{13}{8}\right)\\= \frac{-6}{7}-\frac{13}{8}\\=\frac{-48}{56}-\frac{91}{56}\\=\frac{-48-91}{56}\\=\frac{-139}{56}\)
3. \(+\left(\frac{7}{9}\right)-\left(\frac{-9}{-4}\right)\\= \frac{7}{9}-\frac{9}{4}\\=\frac{28}{36}-\frac{81}{36}\\=\frac{28-81}{36}\\=\frac{-53}{36}\)
4. \(+\left(\frac{12}{11}\right)-\left(\frac{8}{3}\right)\\= \frac{12}{11}-\frac{8}{3}\\=\frac{36}{33}-\frac{88}{33}\\=\frac{36-88}{33}\\=\frac{-52}{33}\)
5. \(-\left(\frac{11}{-12}\right)-\left(\frac{4}{13}\right)\\= \frac{11}{12}-\frac{4}{13}\\=\frac{143}{156}-\frac{48}{156}\\=\frac{143-48}{156}\\=\frac{95}{156}\)
6. \(+\left(\frac{-9}{7}\right)+\left(\frac{3}{-13}\right)\\= \frac{-9}{7}-\frac{3}{13}\\=\frac{-117}{91}-\frac{21}{91}\\=\frac{-117-21}{91}\\=\frac{-138}{91}\)
7. \(+\left(\frac{-11}{-3}\right)+\left(\frac{-10}{13}\right)\\= \frac{11}{3}-\frac{10}{13}\\=\frac{143}{39}-\frac{30}{39}\\=\frac{143-30}{39}\\=\frac{113}{39}\)
8. \(-\left(\frac{2}{9}\right)+\left(\frac{-8}{-3}\right)\\= \frac{-2}{9}+\frac{8}{3}\\=\frac{-2+8}{9}\\=\frac{6}{9}\\=\frac{2}{3}\)
9. \(-\left(\frac{12}{-5}\right)-\left(\frac{7}{-12}\right)\\= \frac{12}{5}+\frac{7}{12}\\=\frac{144}{60}+\frac{35}{60}\\=\frac{144+35}{60}\\=\frac{179}{60}\)
10. \(-\left(\frac{-6}{-11}\right)+\left(\frac{10}{7}\right)\\= \frac{-6}{11}+\frac{10}{7}\\=\frac{-42}{77}+\frac{110}{77}\\=\frac{-42+110}{77}\\=\frac{68}{77}\)
11. \(+\left(\frac{-10}{13}\right)+\left(\frac{15}{-7}\right)\\= \frac{-10}{13}-\frac{15}{7}\\=\frac{-70}{91}-\frac{195}{91}\\=\frac{-70-195}{91}\\=\frac{-265}{91}\)
12. \(+\left(\frac{-2}{5}\right)-\left(\frac{6}{-7}\right)\\= \frac{-2}{5}+\frac{6}{7}\\=\frac{-14}{35}+\frac{30}{35}\\=\frac{-14+30}{35}\\=\frac{16}{35}\)