Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-6}{5}\right)+\left(\frac{-2}{3}\right)\\= \frac{6}{5}-\frac{2}{3}\\=\frac{18}{15}-\frac{10}{15}\\=\frac{18-10}{15}\\=\frac{8}{15}\)
2. \(-\left(\frac{13}{10}\right)+\left(\frac{7}{-9}\right)\\= \frac{-13}{10}-\frac{7}{9}\\=\frac{-117}{90}-\frac{70}{90}\\=\frac{-117-70}{90}\\=\frac{-187}{90}\)
3. \(-\left(\frac{-15}{-11}\right)-\left(\frac{-10}{-13}\right)\\= \frac{-15}{11}-\frac{10}{13}\\=\frac{-195}{143}-\frac{110}{143}\\=\frac{-195-110}{143}\\=\frac{-305}{143}\)
4. \(-\left(\frac{15}{11}\right)+\left(\frac{8}{11}\right)\\= \frac{-15}{11}+\frac{8}{11}\\=\frac{-15+8}{11}\\=\frac{-7}{11}\)
5. \(-\left(\frac{-12}{-7}\right)+\left(\frac{2}{-9}\right)\\= \frac{-12}{7}-\frac{2}{9}\\=\frac{-108}{63}-\frac{14}{63}\\=\frac{-108-14}{63}\\=\frac{-122}{63}\)
6. \(+\left(\frac{2}{5}\right)+\left(\frac{-9}{8}\right)\\= \frac{2}{5}-\frac{9}{8}\\=\frac{16}{40}-\frac{45}{40}\\=\frac{16-45}{40}\\=\frac{-29}{40}\)
7. \(+\left(\frac{15}{13}\right)+\left(\frac{-12}{-5}\right)\\= \frac{15}{13}+\frac{12}{5}\\=\frac{75}{65}+\frac{156}{65}\\=\frac{75+156}{65}\\=\frac{231}{65}\)
8. \(+\left(\frac{-4}{5}\right)+\left(\frac{8}{-3}\right)\\= \frac{-4}{5}-\frac{8}{3}\\=\frac{-12}{15}-\frac{40}{15}\\=\frac{-12-40}{15}\\=\frac{-52}{15}\)
9. \(+\left(\frac{3}{5}\right)-\left(\frac{-4}{-3}\right)\\= \frac{3}{5}-\frac{4}{3}\\=\frac{9}{15}-\frac{20}{15}\\=\frac{9-20}{15}\\=\frac{-11}{15}\)
10. \(-\left(\frac{7}{-3}\right)+\left(\frac{-7}{-6}\right)\\= \frac{7}{3}+\frac{7}{6}\\=\frac{14}{6}+\frac{7}{6}\\=\frac{14+7}{6}\\=\frac{21}{6}\\=\frac{7}{2}\)
11. \(-\left(\frac{5}{-6}\right)-\left(\frac{7}{13}\right)\\= \frac{5}{6}-\frac{7}{13}\\=\frac{65}{78}-\frac{42}{78}\\=\frac{65-42}{78}\\=\frac{23}{78}\)
12. \(+\left(\frac{13}{-12}\right)-\left(\frac{-6}{-5}\right)\\= \frac{-13}{12}-\frac{6}{5}\\=\frac{-65}{60}-\frac{72}{60}\\=\frac{-65-72}{60}\\=\frac{-137}{60}\)