Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{10}{-3}\right)-\left(\frac{-2}{-11}\right)\\= \frac{10}{3}-\frac{2}{11}\\=\frac{110}{33}-\frac{6}{33}\\=\frac{110-6}{33}\\=\frac{104}{33}\)
2. \(+\left(\frac{-10}{3}\right)+\left(\frac{5}{-8}\right)\\= \frac{-10}{3}-\frac{5}{8}\\=\frac{-80}{24}-\frac{15}{24}\\=\frac{-80-15}{24}\\=\frac{-95}{24}\)
3. \(+\left(\frac{-10}{11}\right)+\left(\frac{5}{11}\right)\\= \frac{-10}{11}+\frac{5}{11}\\=\frac{-10+5}{11}\\=\frac{-5}{11}\)
4. \(-\left(\frac{-8}{-11}\right)-\left(\frac{-8}{-9}\right)\\= \frac{-8}{11}-\frac{8}{9}\\=\frac{-72}{99}-\frac{88}{99}\\=\frac{-72-88}{99}\\=\frac{-160}{99}\)
5. \(-\left(\frac{-11}{-5}\right)-\left(\frac{11}{-2}\right)\\= \frac{-11}{5}+\frac{11}{2}\\=\frac{-22}{10}+\frac{55}{10}\\=\frac{-22+55}{10}\\=\frac{33}{10}\)
6. \(-\left(\frac{15}{-8}\right)+\left(\frac{11}{12}\right)\\= \frac{15}{8}+\frac{11}{12}\\=\frac{45}{24}+\frac{22}{24}\\=\frac{45+22}{24}\\=\frac{67}{24}\)
7. \(+\left(\frac{-5}{-9}\right)-\left(\frac{-4}{11}\right)\\= \frac{5}{9}+\frac{4}{11}\\=\frac{55}{99}+\frac{36}{99}\\=\frac{55+36}{99}\\=\frac{91}{99}\)
8. \(+\left(\frac{-6}{-5}\right)-\left(\frac{-4}{5}\right)\\= \frac{6}{5}+\frac{4}{5}\\=\frac{6+4}{5}\\=\frac{10}{5}\\=\frac{2}{1}\)
9. \(+\left(\frac{4}{13}\right)+\left(\frac{6}{-11}\right)\\= \frac{4}{13}-\frac{6}{11}\\=\frac{44}{143}-\frac{78}{143}\\=\frac{44-78}{143}\\=\frac{-34}{143}\)
10. \(+\left(\frac{15}{-13}\right)-\left(\frac{-2}{-5}\right)\\= \frac{-15}{13}-\frac{2}{5}\\=\frac{-75}{65}-\frac{26}{65}\\=\frac{-75-26}{65}\\=\frac{-101}{65}\)
11. \(+\left(\frac{-13}{-5}\right)-\left(\frac{-5}{-2}\right)\\= \frac{13}{5}-\frac{5}{2}\\=\frac{26}{10}-\frac{25}{10}\\=\frac{26-25}{10}\\=\frac{1}{10}\)
12. \(-\left(\frac{10}{-3}\right)+\left(\frac{-7}{-8}\right)\\= \frac{10}{3}+\frac{7}{8}\\=\frac{80}{24}+\frac{21}{24}\\=\frac{80+21}{24}\\=\frac{101}{24}\)