Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{10}{-9}\right)+\left(\frac{-2}{-13}\right)\\= \frac{10}{9}+\frac{2}{13}\\=\frac{130}{117}+\frac{18}{117}\\=\frac{130+18}{117}\\=\frac{148}{117}\)
2. \(-\left(\frac{14}{-13}\right)+\left(\frac{3}{10}\right)\\= \frac{14}{13}+\frac{3}{10}\\=\frac{140}{130}+\frac{39}{130}\\=\frac{140+39}{130}\\=\frac{179}{130}\)
3. \(+\left(\frac{-9}{-4}\right)+\left(\frac{-5}{-11}\right)\\= \frac{9}{4}+\frac{5}{11}\\=\frac{99}{44}+\frac{20}{44}\\=\frac{99+20}{44}\\=\frac{119}{44}\)
4. \(+\left(\frac{-7}{4}\right)-\left(\frac{-11}{-3}\right)\\= \frac{-7}{4}-\frac{11}{3}\\=\frac{-21}{12}-\frac{44}{12}\\=\frac{-21-44}{12}\\=\frac{-65}{12}\)
5. \(+\left(\frac{-14}{9}\right)-\left(\frac{-8}{3}\right)\\= \frac{-14}{9}+\frac{8}{3}\\=\frac{-14+8}{9}\\=\frac{-6}{9}\\=\frac{-2}{3}\)
6. \(-\left(\frac{7}{3}\right)-\left(\frac{10}{7}\right)\\= \frac{-7}{3}-\frac{10}{7}\\=\frac{-49}{21}-\frac{30}{21}\\=\frac{-49-30}{21}\\=\frac{-79}{21}\)
7. \(+\left(\frac{4}{-3}\right)+\left(\frac{9}{-7}\right)\\= \frac{-4}{3}-\frac{9}{7}\\=\frac{-28}{21}-\frac{27}{21}\\=\frac{-28-27}{21}\\=\frac{-55}{21}\)
8. \(-\left(\frac{-13}{-6}\right)+\left(\frac{-14}{-3}\right)\\= \frac{-13}{6}+\frac{14}{3}\\=\frac{-13+14}{6}\\=\frac{1}{6}\)
9. \(-\left(\frac{-6}{-5}\right)+\left(\frac{-5}{-2}\right)\\= \frac{-6}{5}+\frac{5}{2}\\=\frac{-12}{10}+\frac{25}{10}\\=\frac{-12+25}{10}\\=\frac{13}{10}\)
10. \(-\left(\frac{6}{7}\right)-\left(\frac{-15}{4}\right)\\= \frac{-6}{7}+\frac{15}{4}\\=\frac{-24}{28}+\frac{105}{28}\\=\frac{-24+105}{28}\\=\frac{81}{28}\)
11. \(+\left(\frac{-12}{13}\right)-\left(\frac{-7}{-13}\right)\\= \frac{-12}{13}-\frac{7}{13}\\=\frac{-12-7}{13}\\=\frac{-19}{13}\)
12. \(-\left(\frac{-6}{-5}\right)+\left(\frac{6}{5}\right)\\= \frac{-6}{5}+\frac{6}{5}\\=\frac{-6+6}{5}\\=\frac{0}{5}\\=\frac{0}{1}\)