Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{14}{3}\right)+\left(\frac{9}{10}\right)\\= \frac{-14}{3}+\frac{9}{10}\\=\frac{-140}{30}+\frac{27}{30}\\=\frac{-140+27}{30}\\=\frac{-113}{30}\)
2. \(+\left(\frac{14}{9}\right)+\left(\frac{6}{-7}\right)\\= \frac{14}{9}-\frac{6}{7}\\=\frac{98}{63}-\frac{54}{63}\\=\frac{98-54}{63}\\=\frac{44}{63}\)
3. \(-\left(\frac{-3}{-4}\right)+\left(\frac{4}{9}\right)\\= \frac{-3}{4}+\frac{4}{9}\\=\frac{-27}{36}+\frac{16}{36}\\=\frac{-27+16}{36}\\=\frac{-11}{36}\)
4. \(-\left(\frac{-5}{6}\right)-\left(\frac{12}{5}\right)\\= \frac{5}{6}-\frac{12}{5}\\=\frac{25}{30}-\frac{72}{30}\\=\frac{25-72}{30}\\=\frac{-47}{30}\)
5. \(+\left(\frac{3}{4}\right)+\left(\frac{13}{-14}\right)\\= \frac{3}{4}-\frac{13}{14}\\=\frac{21}{28}-\frac{26}{28}\\=\frac{21-26}{28}\\=\frac{-5}{28}\)
6. \(+\left(\frac{7}{-13}\right)-\left(\frac{-3}{5}\right)\\= \frac{-7}{13}+\frac{3}{5}\\=\frac{-35}{65}+\frac{39}{65}\\=\frac{-35+39}{65}\\=\frac{4}{65}\)
7. \(+\left(\frac{-13}{6}\right)+\left(\frac{13}{-6}\right)\\= \frac{-13}{6}-\frac{13}{6}\\=\frac{-13-13}{6}\\=\frac{-26}{6}\\=\frac{-13}{3}\)
8. \(-\left(\frac{-8}{-9}\right)-\left(\frac{14}{-5}\right)\\= \frac{-8}{9}+\frac{14}{5}\\=\frac{-40}{45}+\frac{126}{45}\\=\frac{-40+126}{45}\\=\frac{86}{45}\)
9. \(-\left(\frac{-14}{-9}\right)-\left(\frac{13}{-8}\right)\\= \frac{-14}{9}+\frac{13}{8}\\=\frac{-112}{72}+\frac{117}{72}\\=\frac{-112+117}{72}\\=\frac{5}{72}\)
10. \(-\left(\frac{7}{-9}\right)-\left(\frac{-15}{-13}\right)\\= \frac{7}{9}-\frac{15}{13}\\=\frac{91}{117}-\frac{135}{117}\\=\frac{91-135}{117}\\=\frac{-44}{117}\)
11. \(+\left(\frac{-7}{2}\right)+\left(\frac{-13}{-3}\right)\\= \frac{-7}{2}+\frac{13}{3}\\=\frac{-21}{6}+\frac{26}{6}\\=\frac{-21+26}{6}\\=\frac{5}{6}\)
12. \(+\left(\frac{8}{5}\right)-\left(\frac{-8}{-9}\right)\\= \frac{8}{5}-\frac{8}{9}\\=\frac{72}{45}-\frac{40}{45}\\=\frac{72-40}{45}\\=\frac{32}{45}\)