Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-13}{2}\right)+\left(\frac{-7}{6}\right)\\= \frac{-13}{2}-\frac{7}{6}\\=\frac{-39}{6}-\frac{7}{6}\\=\frac{-39-7}{6}\\=\frac{-46}{6}\\=\frac{-23}{3}\)
2. \(+\left(\frac{-11}{-7}\right)-\left(\frac{7}{-2}\right)\\= \frac{11}{7}+\frac{7}{2}\\=\frac{22}{14}+\frac{49}{14}\\=\frac{22+49}{14}\\=\frac{71}{14}\)
3. \(+\left(\frac{14}{-11}\right)+\left(\frac{6}{-11}\right)\\= \frac{-14}{11}-\frac{6}{11}\\=\frac{-14-6}{11}\\=\frac{-20}{11}\)
4. \(-\left(\frac{15}{-11}\right)-\left(\frac{11}{8}\right)\\= \frac{15}{11}-\frac{11}{8}\\=\frac{120}{88}-\frac{121}{88}\\=\frac{120-121}{88}\\=\frac{-1}{88}\)
5. \(-\left(\frac{-4}{-3}\right)+\left(\frac{-15}{-11}\right)\\= \frac{-4}{3}+\frac{15}{11}\\=\frac{-44}{33}+\frac{45}{33}\\=\frac{-44+45}{33}\\=\frac{1}{33}\)
6. \(+\left(\frac{-15}{11}\right)+\left(\frac{10}{11}\right)\\= \frac{-15}{11}+\frac{10}{11}\\=\frac{-15+10}{11}\\=\frac{-5}{11}\)
7. \(-\left(\frac{4}{-9}\right)+\left(\frac{-11}{12}\right)\\= \frac{4}{9}-\frac{11}{12}\\=\frac{16}{36}-\frac{33}{36}\\=\frac{16-33}{36}\\=\frac{-17}{36}\)
8. \(-\left(\frac{7}{11}\right)+\left(\frac{-11}{7}\right)\\= \frac{-7}{11}-\frac{11}{7}\\=\frac{-49}{77}-\frac{121}{77}\\=\frac{-49-121}{77}\\=\frac{-170}{77}\)
9. \(-\left(\frac{-5}{2}\right)-\left(\frac{-7}{2}\right)\\= \frac{5}{2}+\frac{7}{2}\\=\frac{5+7}{2}\\=\frac{12}{2}\\=\frac{6}{1}\)
10. \(+\left(\frac{-13}{-8}\right)+\left(\frac{-6}{5}\right)\\= \frac{13}{8}-\frac{6}{5}\\=\frac{65}{40}-\frac{48}{40}\\=\frac{65-48}{40}\\=\frac{17}{40}\)
11. \(+\left(\frac{5}{14}\right)-\left(\frac{9}{13}\right)\\= \frac{5}{14}-\frac{9}{13}\\=\frac{65}{182}-\frac{126}{182}\\=\frac{65-126}{182}\\=\frac{-61}{182}\)
12. \(-\left(\frac{6}{5}\right)-\left(\frac{5}{-6}\right)\\= \frac{-6}{5}+\frac{5}{6}\\=\frac{-36}{30}+\frac{25}{30}\\=\frac{-36+25}{30}\\=\frac{-11}{30}\)