Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{10}{11}\right)+\left(\frac{6}{-11}\right)\\= \frac{-10}{11}-\frac{6}{11}\\=\frac{-10-6}{11}\\=\frac{-16}{11}\)
2. \(+\left(\frac{3}{-11}\right)+\left(\frac{-2}{13}\right)\\= \frac{-3}{11}-\frac{2}{13}\\=\frac{-39}{143}-\frac{22}{143}\\=\frac{-39-22}{143}\\=\frac{-61}{143}\)
3. \(+\left(\frac{-3}{-7}\right)-\left(\frac{-4}{7}\right)\\= \frac{3}{7}+\frac{4}{7}\\=\frac{3+4}{7}\\=\frac{7}{7}\\=\frac{1}{1}\)
4. \(+\left(\frac{-9}{2}\right)-\left(\frac{11}{10}\right)\\= \frac{-9}{2}-\frac{11}{10}\\=\frac{-45}{10}-\frac{11}{10}\\=\frac{-45-11}{10}\\=\frac{-56}{10}\\=\frac{-28}{5}\)
5. \(+\left(\frac{12}{-5}\right)+\left(\frac{5}{-9}\right)\\= \frac{-12}{5}-\frac{5}{9}\\=\frac{-108}{45}-\frac{25}{45}\\=\frac{-108-25}{45}\\=\frac{-133}{45}\)
6. \(+\left(\frac{7}{9}\right)+\left(\frac{-2}{3}\right)\\= \frac{7}{9}-\frac{2}{3}\\=\frac{7-2}{9}\\=\frac{5}{9}\)
7. \(-\left(\frac{-11}{8}\right)+\left(\frac{12}{11}\right)\\= \frac{11}{8}+\frac{12}{11}\\=\frac{121}{88}+\frac{96}{88}\\=\frac{121+96}{88}\\=\frac{217}{88}\)
8. \(-\left(\frac{-4}{3}\right)+\left(\frac{8}{5}\right)\\= \frac{4}{3}+\frac{8}{5}\\=\frac{20}{15}+\frac{24}{15}\\=\frac{20+24}{15}\\=\frac{44}{15}\)
9. \(+\left(\frac{-6}{5}\right)+\left(\frac{4}{-9}\right)\\= \frac{-6}{5}-\frac{4}{9}\\=\frac{-54}{45}-\frac{20}{45}\\=\frac{-54-20}{45}\\=\frac{-74}{45}\)
10. \(+\left(\frac{7}{2}\right)+\left(\frac{4}{-9}\right)\\= \frac{7}{2}-\frac{4}{9}\\=\frac{63}{18}-\frac{8}{18}\\=\frac{63-8}{18}\\=\frac{55}{18}\)
11. \(-\left(\frac{2}{-3}\right)+\left(\frac{3}{2}\right)\\= \frac{2}{3}+\frac{3}{2}\\=\frac{4}{6}+\frac{9}{6}\\=\frac{4+9}{6}\\=\frac{13}{6}\)
12. \(-\left(\frac{8}{3}\right)+\left(\frac{7}{10}\right)\\= \frac{-8}{3}+\frac{7}{10}\\=\frac{-80}{30}+\frac{21}{30}\\=\frac{-80+21}{30}\\=\frac{-59}{30}\)