Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{15}{-11}\right)+\left(\frac{9}{-13}\right)\\= \frac{-15}{11}-\frac{9}{13}\\=\frac{-195}{143}-\frac{99}{143}\\=\frac{-195-99}{143}\\=\frac{-294}{143}\)
2. \(-\left(\frac{14}{-13}\right)+\left(\frac{-7}{-4}\right)\\= \frac{14}{13}+\frac{7}{4}\\=\frac{56}{52}+\frac{91}{52}\\=\frac{56+91}{52}\\=\frac{147}{52}\)
3. \(-\left(\frac{7}{8}\right)+\left(\frac{-4}{3}\right)\\= \frac{-7}{8}-\frac{4}{3}\\=\frac{-21}{24}-\frac{32}{24}\\=\frac{-21-32}{24}\\=\frac{-53}{24}\)
4. \(-\left(\frac{-13}{12}\right)-\left(\frac{5}{-3}\right)\\= \frac{13}{12}+\frac{5}{3}\\=\frac{13+5}{12}\\=\frac{18}{12}\\=\frac{3}{2}\)
5. \(-\left(\frac{-10}{13}\right)+\left(\frac{5}{2}\right)\\= \frac{10}{13}+\frac{5}{2}\\=\frac{20}{26}+\frac{65}{26}\\=\frac{20+65}{26}\\=\frac{85}{26}\)
6. \(-\left(\frac{12}{-7}\right)-\left(\frac{-6}{-7}\right)\\= \frac{12}{7}-\frac{6}{7}\\=\frac{12-6}{7}\\=\frac{6}{7}\)
7. \(+\left(\frac{12}{5}\right)+\left(\frac{9}{-5}\right)\\= \frac{12}{5}-\frac{9}{5}\\=\frac{12-9}{5}\\=\frac{3}{5}\)
8. \(+\left(\frac{-7}{-10}\right)-\left(\frac{-10}{-11}\right)\\= \frac{7}{10}-\frac{10}{11}\\=\frac{77}{110}-\frac{100}{110}\\=\frac{77-100}{110}\\=\frac{-23}{110}\)
9. \(+\left(\frac{-9}{-10}\right)-\left(\frac{-10}{7}\right)\\= \frac{9}{10}+\frac{10}{7}\\=\frac{63}{70}+\frac{100}{70}\\=\frac{63+100}{70}\\=\frac{163}{70}\)
10. \(-\left(\frac{13}{-14}\right)+\left(\frac{15}{2}\right)\\= \frac{13}{14}+\frac{15}{2}\\=\frac{13+15}{14}\\=\frac{28}{14}\\=\frac{2}{1}\)
11. \(-\left(\frac{-5}{3}\right)+\left(\frac{15}{-4}\right)\\= \frac{5}{3}-\frac{15}{4}\\=\frac{20}{12}-\frac{45}{12}\\=\frac{20-45}{12}\\=\frac{-25}{12}\)
12. \(+\left(\frac{9}{8}\right)-\left(\frac{-9}{-10}\right)\\= \frac{9}{8}-\frac{9}{10}\\=\frac{45}{40}-\frac{36}{40}\\=\frac{45-36}{40}\\=\frac{9}{40}\)