Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{10}{-13}\right)+\left(\frac{-12}{-13}\right)\\= \frac{10}{13}+\frac{12}{13}\\=\frac{10+12}{13}\\=\frac{22}{13}\)
2. \(-\left(\frac{5}{-6}\right)+\left(\frac{14}{-3}\right)\\= \frac{5}{6}-\frac{14}{3}\\=\frac{5-14}{6}\\=\frac{-9}{6}\\=\frac{-3}{2}\)
3. \(+\left(\frac{-6}{-7}\right)-\left(\frac{10}{9}\right)\\= \frac{6}{7}-\frac{10}{9}\\=\frac{54}{63}-\frac{70}{63}\\=\frac{54-70}{63}\\=\frac{-16}{63}\)
4. \(-\left(\frac{14}{13}\right)+\left(\frac{13}{-12}\right)\\= \frac{-14}{13}-\frac{13}{12}\\=\frac{-168}{156}-\frac{169}{156}\\=\frac{-168-169}{156}\\=\frac{-337}{156}\)
5. \(-\left(\frac{-3}{-8}\right)+\left(\frac{2}{-5}\right)\\= \frac{-3}{8}-\frac{2}{5}\\=\frac{-15}{40}-\frac{16}{40}\\=\frac{-15-16}{40}\\=\frac{-31}{40}\)
6. \(-\left(\frac{10}{7}\right)-\left(\frac{-9}{-10}\right)\\= \frac{-10}{7}-\frac{9}{10}\\=\frac{-100}{70}-\frac{63}{70}\\=\frac{-100-63}{70}\\=\frac{-163}{70}\)
7. \(+\left(\frac{5}{-6}\right)-\left(\frac{-9}{-8}\right)\\= \frac{-5}{6}-\frac{9}{8}\\=\frac{-20}{24}-\frac{27}{24}\\=\frac{-20-27}{24}\\=\frac{-47}{24}\)
8. \(+\left(\frac{-9}{11}\right)+\left(\frac{11}{-6}\right)\\= \frac{-9}{11}-\frac{11}{6}\\=\frac{-54}{66}-\frac{121}{66}\\=\frac{-54-121}{66}\\=\frac{-175}{66}\)
9. \(+\left(\frac{10}{-3}\right)-\left(\frac{-3}{-10}\right)\\= \frac{-10}{3}-\frac{3}{10}\\=\frac{-100}{30}-\frac{9}{30}\\=\frac{-100-9}{30}\\=\frac{-109}{30}\)
10. \(-\left(\frac{10}{-13}\right)+\left(\frac{-9}{7}\right)\\= \frac{10}{13}-\frac{9}{7}\\=\frac{70}{91}-\frac{117}{91}\\=\frac{70-117}{91}\\=\frac{-47}{91}\)
11. \(+\left(\frac{-10}{7}\right)-\left(\frac{-4}{-5}\right)\\= \frac{-10}{7}-\frac{4}{5}\\=\frac{-50}{35}-\frac{28}{35}\\=\frac{-50-28}{35}\\=\frac{-78}{35}\)
12. \(-\left(\frac{-2}{-11}\right)-\left(\frac{11}{-2}\right)\\= \frac{-2}{11}+\frac{11}{2}\\=\frac{-4}{22}+\frac{121}{22}\\=\frac{-4+121}{22}\\=\frac{117}{22}\)