Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-5}{7}\right)-\left(\frac{-4}{-3}\right)\\= \frac{5}{7}-\frac{4}{3}\\=\frac{15}{21}-\frac{28}{21}\\=\frac{15-28}{21}\\=\frac{-13}{21}\)
2. \(-\left(\frac{-8}{11}\right)-\left(\frac{5}{-13}\right)\\= \frac{8}{11}+\frac{5}{13}\\=\frac{104}{143}+\frac{55}{143}\\=\frac{104+55}{143}\\=\frac{159}{143}\)
3. \(+\left(\frac{-13}{-11}\right)-\left(\frac{-7}{-11}\right)\\= \frac{13}{11}-\frac{7}{11}\\=\frac{13-7}{11}\\=\frac{6}{11}\)
4. \(-\left(\frac{-13}{10}\right)+\left(\frac{15}{2}\right)\\= \frac{13}{10}+\frac{15}{2}\\=\frac{13+15}{10}\\=\frac{28}{10}\\=\frac{14}{5}\)
5. \(+\left(\frac{8}{-5}\right)+\left(\frac{-8}{-3}\right)\\= \frac{-8}{5}+\frac{8}{3}\\=\frac{-24}{15}+\frac{40}{15}\\=\frac{-24+40}{15}\\=\frac{16}{15}\)
6. \(+\left(\frac{-9}{-4}\right)-\left(\frac{-7}{11}\right)\\= \frac{9}{4}+\frac{7}{11}\\=\frac{99}{44}+\frac{28}{44}\\=\frac{99+28}{44}\\=\frac{127}{44}\)
7. \(-\left(\frac{-7}{2}\right)+\left(\frac{-11}{8}\right)\\= \frac{7}{2}-\frac{11}{8}\\=\frac{28}{8}-\frac{11}{8}\\=\frac{28-11}{8}\\=\frac{17}{8}\)
8. \(+\left(\frac{13}{-5}\right)-\left(\frac{3}{-4}\right)\\= \frac{-13}{5}+\frac{3}{4}\\=\frac{-52}{20}+\frac{15}{20}\\=\frac{-52+15}{20}\\=\frac{-37}{20}\)
9. \(-\left(\frac{-10}{-13}\right)-\left(\frac{13}{-14}\right)\\= \frac{-10}{13}+\frac{13}{14}\\=\frac{-140}{182}+\frac{169}{182}\\=\frac{-140+169}{182}\\=\frac{29}{182}\)
10. \(-\left(\frac{15}{-11}\right)-\left(\frac{-10}{7}\right)\\= \frac{15}{11}+\frac{10}{7}\\=\frac{105}{77}+\frac{110}{77}\\=\frac{105+110}{77}\\=\frac{215}{77}\)
11. \(-\left(\frac{-6}{11}\right)+\left(\frac{-7}{-3}\right)\\= \frac{6}{11}+\frac{7}{3}\\=\frac{18}{33}+\frac{77}{33}\\=\frac{18+77}{33}\\=\frac{95}{33}\)
12. \(-\left(\frac{13}{11}\right)-\left(\frac{8}{-7}\right)\\= \frac{-13}{11}+\frac{8}{7}\\=\frac{-91}{77}+\frac{88}{77}\\=\frac{-91+88}{77}\\=\frac{-3}{77}\)