Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-6}{-11}\right)-\left(\frac{10}{-11}\right)\\= \frac{-6}{11}+\frac{10}{11}\\=\frac{-6+10}{11}\\=\frac{4}{11}\)
2. \(-\left(\frac{-8}{3}\right)-\left(\frac{15}{-14}\right)\\= \frac{8}{3}+\frac{15}{14}\\=\frac{112}{42}+\frac{45}{42}\\=\frac{112+45}{42}\\=\frac{157}{42}\)
3. \(+\left(\frac{-6}{5}\right)-\left(\frac{-15}{7}\right)\\= \frac{-6}{5}+\frac{15}{7}\\=\frac{-42}{35}+\frac{75}{35}\\=\frac{-42+75}{35}\\=\frac{33}{35}\)
4. \(-\left(\frac{14}{-5}\right)-\left(\frac{5}{-6}\right)\\= \frac{14}{5}+\frac{5}{6}\\=\frac{84}{30}+\frac{25}{30}\\=\frac{84+25}{30}\\=\frac{109}{30}\)
5. \(+\left(\frac{2}{-3}\right)+\left(\frac{5}{7}\right)\\= \frac{-2}{3}+\frac{5}{7}\\=\frac{-14}{21}+\frac{15}{21}\\=\frac{-14+15}{21}\\=\frac{1}{21}\)
6. \(+\left(\frac{10}{-13}\right)+\left(\frac{-15}{-7}\right)\\= \frac{-10}{13}+\frac{15}{7}\\=\frac{-70}{91}+\frac{195}{91}\\=\frac{-70+195}{91}\\=\frac{125}{91}\)
7. \(-\left(\frac{6}{-11}\right)+\left(\frac{-14}{11}\right)\\= \frac{6}{11}-\frac{14}{11}\\=\frac{6-14}{11}\\=\frac{-8}{11}\)
8. \(-\left(\frac{-8}{-3}\right)+\left(\frac{-11}{4}\right)\\= \frac{-8}{3}-\frac{11}{4}\\=\frac{-32}{12}-\frac{33}{12}\\=\frac{-32-33}{12}\\=\frac{-65}{12}\)
9. \(-\left(\frac{-3}{10}\right)-\left(\frac{-12}{5}\right)\\= \frac{3}{10}+\frac{12}{5}\\=\frac{3+12}{10}\\=\frac{15}{10}\\=\frac{3}{2}\)
10. \(-\left(\frac{14}{-11}\right)-\left(\frac{9}{-13}\right)\\= \frac{14}{11}+\frac{9}{13}\\=\frac{182}{143}+\frac{99}{143}\\=\frac{182+99}{143}\\=\frac{281}{143}\)
11. \(+\left(\frac{-10}{-9}\right)-\left(\frac{14}{5}\right)\\= \frac{10}{9}-\frac{14}{5}\\=\frac{50}{45}-\frac{126}{45}\\=\frac{50-126}{45}\\=\frac{-76}{45}\)
12. \(+\left(\frac{-5}{-14}\right)+\left(\frac{-2}{7}\right)\\= \frac{5}{14}-\frac{2}{7}\\=\frac{5-2}{14}\\=\frac{3}{14}\)