Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{15}{2}\right)+\left(\frac{2}{3}\right)\\= \frac{-15}{2}+\frac{2}{3}\\=\frac{-45}{6}+\frac{4}{6}\\=\frac{-45+4}{6}\\=\frac{-41}{6}\)
2. \(+\left(\frac{-5}{-2}\right)+\left(\frac{-8}{-3}\right)\\= \frac{5}{2}+\frac{8}{3}\\=\frac{15}{6}+\frac{16}{6}\\=\frac{15+16}{6}\\=\frac{31}{6}\)
3. \(-\left(\frac{-7}{-8}\right)-\left(\frac{8}{13}\right)\\= \frac{-7}{8}-\frac{8}{13}\\=\frac{-91}{104}-\frac{64}{104}\\=\frac{-91-64}{104}\\=\frac{-155}{104}\)
4. \(-\left(\frac{5}{8}\right)+\left(\frac{10}{-7}\right)\\= \frac{-5}{8}-\frac{10}{7}\\=\frac{-35}{56}-\frac{80}{56}\\=\frac{-35-80}{56}\\=\frac{-115}{56}\)
5. \(+\left(\frac{13}{2}\right)+\left(\frac{-12}{13}\right)\\= \frac{13}{2}-\frac{12}{13}\\=\frac{169}{26}-\frac{24}{26}\\=\frac{169-24}{26}\\=\frac{145}{26}\)
6. \(-\left(\frac{6}{11}\right)-\left(\frac{13}{-4}\right)\\= \frac{-6}{11}+\frac{13}{4}\\=\frac{-24}{44}+\frac{143}{44}\\=\frac{-24+143}{44}\\=\frac{119}{44}\)
7. \(+\left(\frac{-10}{7}\right)+\left(\frac{-4}{11}\right)\\= \frac{-10}{7}-\frac{4}{11}\\=\frac{-110}{77}-\frac{28}{77}\\=\frac{-110-28}{77}\\=\frac{-138}{77}\)
8. \(+\left(\frac{8}{-3}\right)-\left(\frac{-3}{7}\right)\\= \frac{-8}{3}+\frac{3}{7}\\=\frac{-56}{21}+\frac{9}{21}\\=\frac{-56+9}{21}\\=\frac{-47}{21}\)
9. \(-\left(\frac{11}{-13}\right)-\left(\frac{-5}{7}\right)\\= \frac{11}{13}+\frac{5}{7}\\=\frac{77}{91}+\frac{65}{91}\\=\frac{77+65}{91}\\=\frac{142}{91}\)
10. \(+\left(\frac{-2}{-3}\right)-\left(\frac{-8}{-7}\right)\\= \frac{2}{3}-\frac{8}{7}\\=\frac{14}{21}-\frac{24}{21}\\=\frac{14-24}{21}\\=\frac{-10}{21}\)
11. \(-\left(\frac{6}{5}\right)-\left(\frac{8}{-5}\right)\\= \frac{-6}{5}+\frac{8}{5}\\=\frac{-6+8}{5}\\=\frac{2}{5}\)
12. \(+\left(\frac{8}{13}\right)-\left(\frac{3}{7}\right)\\= \frac{8}{13}-\frac{3}{7}\\=\frac{56}{91}-\frac{39}{91}\\=\frac{56-39}{91}\\=\frac{17}{91}\)