Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-5}{13}\right)+\left(\frac{15}{-7}\right)\\= \frac{5}{13}-\frac{15}{7}\\=\frac{35}{91}-\frac{195}{91}\\=\frac{35-195}{91}\\=\frac{-160}{91}\)
2. \(-\left(\frac{5}{8}\right)+\left(\frac{-8}{-13}\right)\\= \frac{-5}{8}+\frac{8}{13}\\=\frac{-65}{104}+\frac{64}{104}\\=\frac{-65+64}{104}\\=\frac{-1}{104}\)
3. \(+\left(\frac{6}{5}\right)-\left(\frac{-13}{14}\right)\\= \frac{6}{5}+\frac{13}{14}\\=\frac{84}{70}+\frac{65}{70}\\=\frac{84+65}{70}\\=\frac{149}{70}\)
4. \(-\left(\frac{11}{5}\right)-\left(\frac{-12}{-5}\right)\\= \frac{-11}{5}-\frac{12}{5}\\=\frac{-11-12}{5}\\=\frac{-23}{5}\)
5. \(-\left(\frac{14}{-9}\right)-\left(\frac{-13}{-11}\right)\\= \frac{14}{9}-\frac{13}{11}\\=\frac{154}{99}-\frac{117}{99}\\=\frac{154-117}{99}\\=\frac{37}{99}\)
6. \(-\left(\frac{4}{-9}\right)-\left(\frac{-6}{-5}\right)\\= \frac{4}{9}-\frac{6}{5}\\=\frac{20}{45}-\frac{54}{45}\\=\frac{20-54}{45}\\=\frac{-34}{45}\)
7. \(+\left(\frac{-6}{5}\right)+\left(\frac{-6}{13}\right)\\= \frac{-6}{5}-\frac{6}{13}\\=\frac{-78}{65}-\frac{30}{65}\\=\frac{-78-30}{65}\\=\frac{-108}{65}\)
8. \(-\left(\frac{2}{-3}\right)+\left(\frac{8}{3}\right)\\= \frac{2}{3}+\frac{8}{3}\\=\frac{2+8}{3}\\=\frac{10}{3}\)
9. \(+\left(\frac{11}{-4}\right)+\left(\frac{5}{11}\right)\\= \frac{-11}{4}+\frac{5}{11}\\=\frac{-121}{44}+\frac{20}{44}\\=\frac{-121+20}{44}\\=\frac{-101}{44}\)
10. \(-\left(\frac{9}{-7}\right)+\left(\frac{-12}{-5}\right)\\= \frac{9}{7}+\frac{12}{5}\\=\frac{45}{35}+\frac{84}{35}\\=\frac{45+84}{35}\\=\frac{129}{35}\)
11. \(+\left(\frac{2}{-9}\right)+\left(\frac{15}{-13}\right)\\= \frac{-2}{9}-\frac{15}{13}\\=\frac{-26}{117}-\frac{135}{117}\\=\frac{-26-135}{117}\\=\frac{-161}{117}\)
12. \(+\left(\frac{-6}{5}\right)+\left(\frac{4}{-9}\right)\\= \frac{-6}{5}-\frac{4}{9}\\=\frac{-54}{45}-\frac{20}{45}\\=\frac{-54-20}{45}\\=\frac{-74}{45}\)