Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-3}{4}\right)+\left(\frac{4}{3}\right)\\= \frac{-3}{4}+\frac{4}{3}\\=\frac{-9}{12}+\frac{16}{12}\\=\frac{-9+16}{12}\\=\frac{7}{12}\)
2. \(-\left(\frac{-2}{-13}\right)+\left(\frac{8}{13}\right)\\= \frac{-2}{13}+\frac{8}{13}\\=\frac{-2+8}{13}\\=\frac{6}{13}\)
3. \(+\left(\frac{-13}{-7}\right)-\left(\frac{-10}{-7}\right)\\= \frac{13}{7}-\frac{10}{7}\\=\frac{13-10}{7}\\=\frac{3}{7}\)
4. \(+\left(\frac{11}{-14}\right)+\left(\frac{12}{11}\right)\\= \frac{-11}{14}+\frac{12}{11}\\=\frac{-121}{154}+\frac{168}{154}\\=\frac{-121+168}{154}\\=\frac{47}{154}\)
5. \(+\left(\frac{-7}{13}\right)+\left(\frac{13}{2}\right)\\= \frac{-7}{13}+\frac{13}{2}\\=\frac{-14}{26}+\frac{169}{26}\\=\frac{-14+169}{26}\\=\frac{155}{26}\)
6. \(-\left(\frac{15}{8}\right)+\left(\frac{6}{-5}\right)\\= \frac{-15}{8}-\frac{6}{5}\\=\frac{-75}{40}-\frac{48}{40}\\=\frac{-75-48}{40}\\=\frac{-123}{40}\)
7. \(+\left(\frac{11}{-14}\right)+\left(\frac{-14}{3}\right)\\= \frac{-11}{14}-\frac{14}{3}\\=\frac{-33}{42}-\frac{196}{42}\\=\frac{-33-196}{42}\\=\frac{-229}{42}\)
8. \(+\left(\frac{-9}{-14}\right)-\left(\frac{-2}{7}\right)\\= \frac{9}{14}+\frac{2}{7}\\=\frac{9+2}{14}\\=\frac{11}{14}\)
9. \(-\left(\frac{11}{13}\right)+\left(\frac{15}{-7}\right)\\= \frac{-11}{13}-\frac{15}{7}\\=\frac{-77}{91}-\frac{195}{91}\\=\frac{-77-195}{91}\\=\frac{-272}{91}\)
10. \(+\left(\frac{-2}{11}\right)-\left(\frac{9}{-13}\right)\\= \frac{-2}{11}+\frac{9}{13}\\=\frac{-26}{143}+\frac{99}{143}\\=\frac{-26+99}{143}\\=\frac{73}{143}\)
11. \(-\left(\frac{-13}{-10}\right)-\left(\frac{-15}{-13}\right)\\= \frac{-13}{10}-\frac{15}{13}\\=\frac{-169}{130}-\frac{150}{130}\\=\frac{-169-150}{130}\\=\frac{-319}{130}\)
12. \(+\left(\frac{-2}{3}\right)+\left(\frac{-7}{3}\right)\\= \frac{-2}{3}-\frac{7}{3}\\=\frac{-2-7}{3}\\=\frac{-9}{3}\\=\frac{-3}{1}\)