Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{10}{-7}\right)-\left(\frac{15}{8}\right)\\= \frac{10}{7}-\frac{15}{8}\\=\frac{80}{56}-\frac{105}{56}\\=\frac{80-105}{56}\\=\frac{-25}{56}\)
2. \(+\left(\frac{7}{-9}\right)+\left(\frac{-13}{-9}\right)\\= \frac{-7}{9}+\frac{13}{9}\\=\frac{-7+13}{9}\\=\frac{6}{9}\\=\frac{2}{3}\)
3. \(-\left(\frac{-3}{7}\right)+\left(\frac{-9}{14}\right)\\= \frac{3}{7}-\frac{9}{14}\\=\frac{6}{14}-\frac{9}{14}\\=\frac{6-9}{14}\\=\frac{-3}{14}\)
4. \(+\left(\frac{7}{-6}\right)-\left(\frac{6}{-5}\right)\\= \frac{-7}{6}+\frac{6}{5}\\=\frac{-35}{30}+\frac{36}{30}\\=\frac{-35+36}{30}\\=\frac{1}{30}\)
5. \(-\left(\frac{10}{-7}\right)+\left(\frac{-14}{-9}\right)\\= \frac{10}{7}+\frac{14}{9}\\=\frac{90}{63}+\frac{98}{63}\\=\frac{90+98}{63}\\=\frac{188}{63}\)
6. \(-\left(\frac{2}{-9}\right)-\left(\frac{3}{-5}\right)\\= \frac{2}{9}+\frac{3}{5}\\=\frac{10}{45}+\frac{27}{45}\\=\frac{10+27}{45}\\=\frac{37}{45}\)
7. \(+\left(\frac{-13}{-14}\right)+\left(\frac{14}{-3}\right)\\= \frac{13}{14}-\frac{14}{3}\\=\frac{39}{42}-\frac{196}{42}\\=\frac{39-196}{42}\\=\frac{-157}{42}\)
8. \(+\left(\frac{2}{-9}\right)-\left(\frac{-12}{13}\right)\\= \frac{-2}{9}+\frac{12}{13}\\=\frac{-26}{117}+\frac{108}{117}\\=\frac{-26+108}{117}\\=\frac{82}{117}\)
9. \(+\left(\frac{13}{-3}\right)-\left(\frac{2}{13}\right)\\= \frac{-13}{3}-\frac{2}{13}\\=\frac{-169}{39}-\frac{6}{39}\\=\frac{-169-6}{39}\\=\frac{-175}{39}\)
10. \(-\left(\frac{-2}{11}\right)-\left(\frac{-14}{-3}\right)\\= \frac{2}{11}-\frac{14}{3}\\=\frac{6}{33}-\frac{154}{33}\\=\frac{6-154}{33}\\=\frac{-148}{33}\)
11. \(-\left(\frac{-15}{-7}\right)-\left(\frac{13}{2}\right)\\= \frac{-15}{7}-\frac{13}{2}\\=\frac{-30}{14}-\frac{91}{14}\\=\frac{-30-91}{14}\\=\frac{-121}{14}\)
12. \(-\left(\frac{7}{-2}\right)-\left(\frac{-15}{11}\right)\\= \frac{7}{2}+\frac{15}{11}\\=\frac{77}{22}+\frac{30}{22}\\=\frac{77+30}{22}\\=\frac{107}{22}\)