Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{5}{-9}\right)-\left(\frac{6}{5}\right)\\= \frac{5}{9}-\frac{6}{5}\\=\frac{25}{45}-\frac{54}{45}\\=\frac{25-54}{45}\\=\frac{-29}{45}\)
2. \(+\left(\frac{-15}{-4}\right)-\left(\frac{-6}{11}\right)\\= \frac{15}{4}+\frac{6}{11}\\=\frac{165}{44}+\frac{24}{44}\\=\frac{165+24}{44}\\=\frac{189}{44}\)
3. \(-\left(\frac{12}{-5}\right)-\left(\frac{-13}{-4}\right)\\= \frac{12}{5}-\frac{13}{4}\\=\frac{48}{20}-\frac{65}{20}\\=\frac{48-65}{20}\\=\frac{-17}{20}\)
4. \(-\left(\frac{-9}{-2}\right)+\left(\frac{-2}{3}\right)\\= \frac{-9}{2}-\frac{2}{3}\\=\frac{-27}{6}-\frac{4}{6}\\=\frac{-27-4}{6}\\=\frac{-31}{6}\)
5. \(-\left(\frac{-4}{9}\right)+\left(\frac{-14}{9}\right)\\= \frac{4}{9}-\frac{14}{9}\\=\frac{4-14}{9}\\=\frac{-10}{9}\)
6. \(+\left(\frac{-13}{-14}\right)-\left(\frac{-15}{13}\right)\\= \frac{13}{14}+\frac{15}{13}\\=\frac{169}{182}+\frac{210}{182}\\=\frac{169+210}{182}\\=\frac{379}{182}\)
7. \(-\left(\frac{-5}{-12}\right)-\left(\frac{-11}{2}\right)\\= \frac{-5}{12}+\frac{11}{2}\\=\frac{-5+11}{12}\\=\frac{6}{12}\\=\frac{1}{2}\)
8. \(+\left(\frac{4}{-7}\right)-\left(\frac{15}{7}\right)\\= \frac{-4}{7}-\frac{15}{7}\\=\frac{-4-15}{7}\\=\frac{-19}{7}\)
9. \(+\left(\frac{-8}{-5}\right)+\left(\frac{14}{-9}\right)\\= \frac{8}{5}-\frac{14}{9}\\=\frac{72}{45}-\frac{70}{45}\\=\frac{72-70}{45}\\=\frac{2}{45}\)
10. \(-\left(\frac{-13}{-9}\right)-\left(\frac{-2}{3}\right)\\= \frac{-13}{9}+\frac{2}{3}\\=\frac{-13+2}{9}\\=\frac{-11}{9}\)
11. \(+\left(\frac{-3}{-2}\right)+\left(\frac{6}{7}\right)\\= \frac{3}{2}+\frac{6}{7}\\=\frac{21}{14}+\frac{12}{14}\\=\frac{21+12}{14}\\=\frac{33}{14}\)
12. \(-\left(\frac{-11}{10}\right)+\left(\frac{12}{-5}\right)\\= \frac{11}{10}-\frac{12}{5}\\=\frac{11-12}{10}\\=\frac{-1}{10}\)