Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{5}{-12}\right)+\left(\frac{6}{5}\right)\\= \frac{5}{12}+\frac{6}{5}\\=\frac{25}{60}+\frac{72}{60}\\=\frac{25+72}{60}\\=\frac{97}{60}\)
2. \(+\left(\frac{2}{13}\right)-\left(\frac{-15}{-11}\right)\\= \frac{2}{13}-\frac{15}{11}\\=\frac{22}{143}-\frac{195}{143}\\=\frac{22-195}{143}\\=\frac{-173}{143}\)
3. \(-\left(\frac{15}{11}\right)-\left(\frac{12}{-11}\right)\\= \frac{-15}{11}+\frac{12}{11}\\=\frac{-15+12}{11}\\=\frac{-3}{11}\)
4. \(-\left(\frac{-3}{-7}\right)+\left(\frac{15}{-7}\right)\\= \frac{-3}{7}-\frac{15}{7}\\=\frac{-3-15}{7}\\=\frac{-18}{7}\)
5. \(-\left(\frac{2}{3}\right)-\left(\frac{-14}{-3}\right)\\= \frac{-2}{3}-\frac{14}{3}\\=\frac{-2-14}{3}\\=\frac{-16}{3}\)
6. \(-\left(\frac{8}{-9}\right)+\left(\frac{7}{-8}\right)\\= \frac{8}{9}-\frac{7}{8}\\=\frac{64}{72}-\frac{63}{72}\\=\frac{64-63}{72}\\=\frac{1}{72}\)
7. \(+\left(\frac{-10}{11}\right)+\left(\frac{13}{11}\right)\\= \frac{-10}{11}+\frac{13}{11}\\=\frac{-10+13}{11}\\=\frac{3}{11}\)
8. \(-\left(\frac{-10}{-13}\right)+\left(\frac{10}{-13}\right)\\= \frac{-10}{13}-\frac{10}{13}\\=\frac{-10-10}{13}\\=\frac{-20}{13}\)
9. \(+\left(\frac{9}{14}\right)+\left(\frac{15}{11}\right)\\= \frac{9}{14}+\frac{15}{11}\\=\frac{99}{154}+\frac{210}{154}\\=\frac{99+210}{154}\\=\frac{309}{154}\)
10. \(-\left(\frac{-10}{7}\right)-\left(\frac{-8}{-9}\right)\\= \frac{10}{7}-\frac{8}{9}\\=\frac{90}{63}-\frac{56}{63}\\=\frac{90-56}{63}\\=\frac{34}{63}\)
11. \(-\left(\frac{-10}{11}\right)+\left(\frac{6}{7}\right)\\= \frac{10}{11}+\frac{6}{7}\\=\frac{70}{77}+\frac{66}{77}\\=\frac{70+66}{77}\\=\frac{136}{77}\)
12. \(+\left(\frac{2}{13}\right)-\left(\frac{14}{-13}\right)\\= \frac{2}{13}+\frac{14}{13}\\=\frac{2+14}{13}\\=\frac{16}{13}\)