Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{12}{-5}\right)-\left(\frac{3}{10}\right)\\= \frac{12}{5}-\frac{3}{10}\\=\frac{24}{10}-\frac{3}{10}\\=\frac{24-3}{10}\\=\frac{21}{10}\)
2. \(+\left(\frac{2}{11}\right)-\left(\frac{11}{-10}\right)\\= \frac{2}{11}+\frac{11}{10}\\=\frac{20}{110}+\frac{121}{110}\\=\frac{20+121}{110}\\=\frac{141}{110}\)
3. \(-\left(\frac{-4}{5}\right)-\left(\frac{-14}{-9}\right)\\= \frac{4}{5}-\frac{14}{9}\\=\frac{36}{45}-\frac{70}{45}\\=\frac{36-70}{45}\\=\frac{-34}{45}\)
4. \(+\left(\frac{-6}{13}\right)-\left(\frac{-15}{-7}\right)\\= \frac{-6}{13}-\frac{15}{7}\\=\frac{-42}{91}-\frac{195}{91}\\=\frac{-42-195}{91}\\=\frac{-237}{91}\)
5. \(-\left(\frac{-14}{-9}\right)-\left(\frac{-2}{7}\right)\\= \frac{-14}{9}+\frac{2}{7}\\=\frac{-98}{63}+\frac{18}{63}\\=\frac{-98+18}{63}\\=\frac{-80}{63}\)
6. \(+\left(\frac{-8}{7}\right)+\left(\frac{-13}{-9}\right)\\= \frac{-8}{7}+\frac{13}{9}\\=\frac{-72}{63}+\frac{91}{63}\\=\frac{-72+91}{63}\\=\frac{19}{63}\)
7. \(+\left(\frac{9}{-13}\right)+\left(\frac{-10}{13}\right)\\= \frac{-9}{13}-\frac{10}{13}\\=\frac{-9-10}{13}\\=\frac{-19}{13}\)
8. \(+\left(\frac{6}{13}\right)-\left(\frac{5}{-7}\right)\\= \frac{6}{13}+\frac{5}{7}\\=\frac{42}{91}+\frac{65}{91}\\=\frac{42+65}{91}\\=\frac{107}{91}\)
9. \(-\left(\frac{13}{2}\right)+\left(\frac{4}{11}\right)\\= \frac{-13}{2}+\frac{4}{11}\\=\frac{-143}{22}+\frac{8}{22}\\=\frac{-143+8}{22}\\=\frac{-135}{22}\)
10. \(+\left(\frac{2}{-3}\right)+\left(\frac{-5}{2}\right)\\= \frac{-2}{3}-\frac{5}{2}\\=\frac{-4}{6}-\frac{15}{6}\\=\frac{-4-15}{6}\\=\frac{-19}{6}\)
11. \(+\left(\frac{-7}{-4}\right)-\left(\frac{9}{2}\right)\\= \frac{7}{4}-\frac{9}{2}\\=\frac{7-9}{4}\\=\frac{-2}{4}\\=\frac{-1}{2}\)
12. \(+\left(\frac{13}{12}\right)-\left(\frac{5}{13}\right)\\= \frac{13}{12}-\frac{5}{13}\\=\frac{169}{156}-\frac{60}{156}\\=\frac{169-60}{156}\\=\frac{109}{156}\)