Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{-11}\right)+\left(\frac{3}{10}\right)\\= \frac{-10}{11}+\frac{3}{10}\\=\frac{-100}{110}+\frac{33}{110}\\=\frac{-100+33}{110}\\=\frac{-67}{110}\)
2. \(-\left(\frac{15}{-11}\right)+\left(\frac{-12}{5}\right)\\= \frac{15}{11}-\frac{12}{5}\\=\frac{75}{55}-\frac{132}{55}\\=\frac{75-132}{55}\\=\frac{-57}{55}\)
3. \(-\left(\frac{6}{7}\right)+\left(\frac{-2}{5}\right)\\= \frac{-6}{7}-\frac{2}{5}\\=\frac{-30}{35}-\frac{14}{35}\\=\frac{-30-14}{35}\\=\frac{-44}{35}\)
4. \(+\left(\frac{14}{3}\right)+\left(\frac{-11}{-5}\right)\\= \frac{14}{3}+\frac{11}{5}\\=\frac{70}{15}+\frac{33}{15}\\=\frac{70+33}{15}\\=\frac{103}{15}\)
5. \(+\left(\frac{6}{5}\right)-\left(\frac{5}{2}\right)\\= \frac{6}{5}-\frac{5}{2}\\=\frac{12}{10}-\frac{25}{10}\\=\frac{12-25}{10}\\=\frac{-13}{10}\)
6. \(+\left(\frac{14}{-11}\right)-\left(\frac{15}{8}\right)\\= \frac{-14}{11}-\frac{15}{8}\\=\frac{-112}{88}-\frac{165}{88}\\=\frac{-112-165}{88}\\=\frac{-277}{88}\)
7. \(-\left(\frac{10}{-7}\right)-\left(\frac{14}{-11}\right)\\= \frac{10}{7}+\frac{14}{11}\\=\frac{110}{77}+\frac{98}{77}\\=\frac{110+98}{77}\\=\frac{208}{77}\)
8. \(+\left(\frac{-2}{-13}\right)-\left(\frac{-13}{10}\right)\\= \frac{2}{13}+\frac{13}{10}\\=\frac{20}{130}+\frac{169}{130}\\=\frac{20+169}{130}\\=\frac{189}{130}\)
9. \(+\left(\frac{14}{-5}\right)-\left(\frac{5}{-2}\right)\\= \frac{-14}{5}+\frac{5}{2}\\=\frac{-28}{10}+\frac{25}{10}\\=\frac{-28+25}{10}\\=\frac{-3}{10}\)
10. \(+\left(\frac{4}{-11}\right)-\left(\frac{-6}{7}\right)\\= \frac{-4}{11}+\frac{6}{7}\\=\frac{-28}{77}+\frac{66}{77}\\=\frac{-28+66}{77}\\=\frac{38}{77}\)
11. \(+\left(\frac{-2}{-5}\right)-\left(\frac{-4}{-3}\right)\\= \frac{2}{5}-\frac{4}{3}\\=\frac{6}{15}-\frac{20}{15}\\=\frac{6-20}{15}\\=\frac{-14}{15}\)
12. \(+\left(\frac{-8}{-11}\right)+\left(\frac{-5}{-13}\right)\\= \frac{8}{11}+\frac{5}{13}\\=\frac{104}{143}+\frac{55}{143}\\=\frac{104+55}{143}\\=\frac{159}{143}\)