Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{13}{-6}\right)+\left(\frac{11}{-4}\right)\\= \frac{13}{6}-\frac{11}{4}\\=\frac{26}{12}-\frac{33}{12}\\=\frac{26-33}{12}\\=\frac{-7}{12}\)
2. \(+\left(\frac{-4}{-5}\right)+\left(\frac{7}{10}\right)\\= \frac{4}{5}+\frac{7}{10}\\=\frac{8}{10}+\frac{7}{10}\\=\frac{8+7}{10}\\=\frac{15}{10}\\=\frac{3}{2}\)
3. \(-\left(\frac{3}{13}\right)-\left(\frac{-14}{-13}\right)\\= \frac{-3}{13}-\frac{14}{13}\\=\frac{-3-14}{13}\\=\frac{-17}{13}\)
4. \(+\left(\frac{-4}{-3}\right)-\left(\frac{10}{9}\right)\\= \frac{4}{3}-\frac{10}{9}\\=\frac{12}{9}-\frac{10}{9}\\=\frac{12-10}{9}\\=\frac{2}{9}\)
5. \(+\left(\frac{-11}{9}\right)-\left(\frac{-5}{8}\right)\\= \frac{-11}{9}+\frac{5}{8}\\=\frac{-88}{72}+\frac{45}{72}\\=\frac{-88+45}{72}\\=\frac{-43}{72}\)
6. \(+\left(\frac{15}{7}\right)+\left(\frac{-2}{-7}\right)\\= \frac{15}{7}+\frac{2}{7}\\=\frac{15+2}{7}\\=\frac{17}{7}\)
7. \(-\left(\frac{-9}{-8}\right)+\left(\frac{-6}{11}\right)\\= \frac{-9}{8}-\frac{6}{11}\\=\frac{-99}{88}-\frac{48}{88}\\=\frac{-99-48}{88}\\=\frac{-147}{88}\)
8. \(+\left(\frac{11}{7}\right)+\left(\frac{4}{-13}\right)\\= \frac{11}{7}-\frac{4}{13}\\=\frac{143}{91}-\frac{28}{91}\\=\frac{143-28}{91}\\=\frac{115}{91}\)
9. \(-\left(\frac{7}{9}\right)-\left(\frac{-8}{13}\right)\\= \frac{-7}{9}+\frac{8}{13}\\=\frac{-91}{117}+\frac{72}{117}\\=\frac{-91+72}{117}\\=\frac{-19}{117}\)
10. \(+\left(\frac{2}{-13}\right)-\left(\frac{8}{-13}\right)\\= \frac{-2}{13}+\frac{8}{13}\\=\frac{-2+8}{13}\\=\frac{6}{13}\)
11. \(-\left(\frac{13}{-4}\right)+\left(\frac{-11}{-2}\right)\\= \frac{13}{4}+\frac{11}{2}\\=\frac{13+11}{4}\\=\frac{24}{4}\\=\frac{6}{1}\)
12. \(-\left(\frac{14}{-13}\right)+\left(\frac{-7}{-6}\right)\\= \frac{14}{13}+\frac{7}{6}\\=\frac{84}{78}+\frac{91}{78}\\=\frac{84+91}{78}\\=\frac{175}{78}\)