Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-6}{13}\right)-\left(\frac{-6}{7}\right)\\= \frac{6}{13}+\frac{6}{7}\\=\frac{42}{91}+\frac{78}{91}\\=\frac{42+78}{91}\\=\frac{120}{91}\)
2. \(+\left(\frac{-15}{-8}\right)+\left(\frac{5}{-13}\right)\\= \frac{15}{8}-\frac{5}{13}\\=\frac{195}{104}-\frac{40}{104}\\=\frac{195-40}{104}\\=\frac{155}{104}\)
3. \(-\left(\frac{-6}{-13}\right)+\left(\frac{-9}{13}\right)\\= \frac{-6}{13}-\frac{9}{13}\\=\frac{-6-9}{13}\\=\frac{-15}{13}\)
4. \(-\left(\frac{-10}{-9}\right)-\left(\frac{8}{3}\right)\\= \frac{-10}{9}-\frac{8}{3}\\=\frac{-10-8}{9}\\=\frac{-18}{9}\\=\frac{-2}{1}\)
5. \(-\left(\frac{4}{3}\right)-\left(\frac{-7}{2}\right)\\= \frac{-4}{3}+\frac{7}{2}\\=\frac{-8}{6}+\frac{21}{6}\\=\frac{-8+21}{6}\\=\frac{13}{6}\)
6. \(-\left(\frac{-4}{9}\right)+\left(\frac{15}{2}\right)\\= \frac{4}{9}+\frac{15}{2}\\=\frac{8}{18}+\frac{135}{18}\\=\frac{8+135}{18}\\=\frac{143}{18}\)
7. \(-\left(\frac{-14}{-3}\right)-\left(\frac{-11}{10}\right)\\= \frac{-14}{3}+\frac{11}{10}\\=\frac{-140}{30}+\frac{33}{30}\\=\frac{-140+33}{30}\\=\frac{-107}{30}\)
8. \(-\left(\frac{14}{-9}\right)-\left(\frac{3}{2}\right)\\= \frac{14}{9}-\frac{3}{2}\\=\frac{28}{18}-\frac{27}{18}\\=\frac{28-27}{18}\\=\frac{1}{18}\)
9. \(-\left(\frac{-4}{7}\right)-\left(\frac{-2}{-3}\right)\\= \frac{4}{7}-\frac{2}{3}\\=\frac{12}{21}-\frac{14}{21}\\=\frac{12-14}{21}\\=\frac{-2}{21}\)
10. \(-\left(\frac{-11}{-7}\right)-\left(\frac{-15}{13}\right)\\= \frac{-11}{7}+\frac{15}{13}\\=\frac{-143}{91}+\frac{105}{91}\\=\frac{-143+105}{91}\\=\frac{-38}{91}\)
11. \(+\left(\frac{12}{-11}\right)-\left(\frac{-10}{3}\right)\\= \frac{-12}{11}+\frac{10}{3}\\=\frac{-36}{33}+\frac{110}{33}\\=\frac{-36+110}{33}\\=\frac{74}{33}\)
12. \(-\left(\frac{4}{7}\right)+\left(\frac{-4}{-5}\right)\\= \frac{-4}{7}+\frac{4}{5}\\=\frac{-20}{35}+\frac{28}{35}\\=\frac{-20+28}{35}\\=\frac{8}{35}\)