Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{9}{14}\right)+\left(\frac{8}{11}\right)\\= \frac{9}{14}+\frac{8}{11}\\=\frac{99}{154}+\frac{112}{154}\\=\frac{99+112}{154}\\=\frac{211}{154}\)
2. \(+\left(\frac{14}{11}\right)-\left(\frac{13}{14}\right)\\= \frac{14}{11}-\frac{13}{14}\\=\frac{196}{154}-\frac{143}{154}\\=\frac{196-143}{154}\\=\frac{53}{154}\)
3. \(+\left(\frac{9}{11}\right)+\left(\frac{2}{-11}\right)\\= \frac{9}{11}-\frac{2}{11}\\=\frac{9-2}{11}\\=\frac{7}{11}\)
4. \(-\left(\frac{13}{-5}\right)-\left(\frac{-14}{3}\right)\\= \frac{13}{5}+\frac{14}{3}\\=\frac{39}{15}+\frac{70}{15}\\=\frac{39+70}{15}\\=\frac{109}{15}\)
5. \(+\left(\frac{-4}{13}\right)+\left(\frac{4}{5}\right)\\= \frac{-4}{13}+\frac{4}{5}\\=\frac{-20}{65}+\frac{52}{65}\\=\frac{-20+52}{65}\\=\frac{32}{65}\)
6. \(+\left(\frac{8}{15}\right)-\left(\frac{15}{-2}\right)\\= \frac{8}{15}+\frac{15}{2}\\=\frac{16}{30}+\frac{225}{30}\\=\frac{16+225}{30}\\=\frac{241}{30}\)
7. \(-\left(\frac{6}{-7}\right)-\left(\frac{5}{-6}\right)\\= \frac{6}{7}+\frac{5}{6}\\=\frac{36}{42}+\frac{35}{42}\\=\frac{36+35}{42}\\=\frac{71}{42}\)
8. \(-\left(\frac{-4}{15}\right)-\left(\frac{14}{-9}\right)\\= \frac{4}{15}+\frac{14}{9}\\=\frac{12}{45}+\frac{70}{45}\\=\frac{12+70}{45}\\=\frac{82}{45}\)
9. \(-\left(\frac{-14}{5}\right)-\left(\frac{11}{15}\right)\\= \frac{14}{5}-\frac{11}{15}\\=\frac{42}{15}-\frac{11}{15}\\=\frac{42-11}{15}\\=\frac{31}{15}\)
10. \(+\left(\frac{7}{-12}\right)+\left(\frac{13}{-3}\right)\\= \frac{-7}{12}-\frac{13}{3}\\=\frac{-7-13}{12}\\=\frac{-20}{12}\\=\frac{-5}{3}\)
11. \(+\left(\frac{15}{-13}\right)-\left(\frac{-10}{-13}\right)\\= \frac{-15}{13}-\frac{10}{13}\\=\frac{-15-10}{13}\\=\frac{-25}{13}\)
12. \(-\left(\frac{6}{5}\right)-\left(\frac{5}{8}\right)\\= \frac{-6}{5}-\frac{5}{8}\\=\frac{-48}{40}-\frac{25}{40}\\=\frac{-48-25}{40}\\=\frac{-73}{40}\)