Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{14}{13}\right)+\left(\frac{7}{-12}\right)\\= \frac{-14}{13}-\frac{7}{12}\\=\frac{-168}{156}-\frac{91}{156}\\=\frac{-168-91}{156}\\=\frac{-259}{156}\)
2. \(-\left(\frac{-12}{7}\right)-\left(\frac{11}{12}\right)\\= \frac{12}{7}-\frac{11}{12}\\=\frac{144}{84}-\frac{77}{84}\\=\frac{144-77}{84}\\=\frac{67}{84}\)
3. \(+\left(\frac{-3}{-2}\right)-\left(\frac{-7}{-6}\right)\\= \frac{3}{2}-\frac{7}{6}\\=\frac{9}{6}-\frac{7}{6}\\=\frac{9-7}{6}\\=\frac{2}{6}\\=\frac{1}{3}\)
4. \(-\left(\frac{13}{-14}\right)+\left(\frac{6}{13}\right)\\= \frac{13}{14}+\frac{6}{13}\\=\frac{169}{182}+\frac{84}{182}\\=\frac{169+84}{182}\\=\frac{253}{182}\)
5. \(-\left(\frac{6}{-13}\right)+\left(\frac{8}{-7}\right)\\= \frac{6}{13}-\frac{8}{7}\\=\frac{42}{91}-\frac{104}{91}\\=\frac{42-104}{91}\\=\frac{-62}{91}\)
6. \(-\left(\frac{5}{11}\right)+\left(\frac{-2}{-5}\right)\\= \frac{-5}{11}+\frac{2}{5}\\=\frac{-25}{55}+\frac{22}{55}\\=\frac{-25+22}{55}\\=\frac{-3}{55}\)
7. \(-\left(\frac{-6}{-11}\right)+\left(\frac{-5}{-6}\right)\\= \frac{-6}{11}+\frac{5}{6}\\=\frac{-36}{66}+\frac{55}{66}\\=\frac{-36+55}{66}\\=\frac{19}{66}\)
8. \(-\left(\frac{-10}{3}\right)-\left(\frac{7}{-3}\right)\\= \frac{10}{3}+\frac{7}{3}\\=\frac{10+7}{3}\\=\frac{17}{3}\)
9. \(-\left(\frac{9}{2}\right)+\left(\frac{8}{-5}\right)\\= \frac{-9}{2}-\frac{8}{5}\\=\frac{-45}{10}-\frac{16}{10}\\=\frac{-45-16}{10}\\=\frac{-61}{10}\)
10. \(+\left(\frac{7}{-2}\right)+\left(\frac{7}{-6}\right)\\= \frac{-7}{2}-\frac{7}{6}\\=\frac{-21}{6}-\frac{7}{6}\\=\frac{-21-7}{6}\\=\frac{-28}{6}\\=\frac{-14}{3}\)
11. \(-\left(\frac{5}{13}\right)+\left(\frac{8}{-3}\right)\\= \frac{-5}{13}-\frac{8}{3}\\=\frac{-15}{39}-\frac{104}{39}\\=\frac{-15-104}{39}\\=\frac{-119}{39}\)
12. \(+\left(\frac{-9}{13}\right)+\left(\frac{6}{-7}\right)\\= \frac{-9}{13}-\frac{6}{7}\\=\frac{-63}{91}-\frac{78}{91}\\=\frac{-63-78}{91}\\=\frac{-141}{91}\)