Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{15}{-13}\right)-\left(\frac{-12}{11}\right)\\= \frac{15}{13}+\frac{12}{11}\\=\frac{165}{143}+\frac{156}{143}\\=\frac{165+156}{143}\\=\frac{321}{143}\)
2. \(+\left(\frac{-8}{3}\right)+\left(\frac{8}{11}\right)\\= \frac{-8}{3}+\frac{8}{11}\\=\frac{-88}{33}+\frac{24}{33}\\=\frac{-88+24}{33}\\=\frac{-64}{33}\)
3. \(+\left(\frac{-2}{-13}\right)+\left(\frac{-2}{13}\right)\\= \frac{2}{13}-\frac{2}{13}\\=\frac{2-2}{13}\\=\frac{0}{13}\\=\frac{0}{1}\)
4. \(+\left(\frac{-13}{2}\right)-\left(\frac{13}{9}\right)\\= \frac{-13}{2}-\frac{13}{9}\\=\frac{-117}{18}-\frac{26}{18}\\=\frac{-117-26}{18}\\=\frac{-143}{18}\)
5. \(+\left(\frac{4}{7}\right)+\left(\frac{-2}{7}\right)\\= \frac{4}{7}-\frac{2}{7}\\=\frac{4-2}{7}\\=\frac{2}{7}\)
6. \(+\left(\frac{12}{-5}\right)-\left(\frac{15}{11}\right)\\= \frac{-12}{5}-\frac{15}{11}\\=\frac{-132}{55}-\frac{75}{55}\\=\frac{-132-75}{55}\\=\frac{-207}{55}\)
7. \(-\left(\frac{12}{-5}\right)-\left(\frac{13}{-10}\right)\\= \frac{12}{5}+\frac{13}{10}\\=\frac{24}{10}+\frac{13}{10}\\=\frac{24+13}{10}\\=\frac{37}{10}\)
8. \(+\left(\frac{-3}{-8}\right)+\left(\frac{8}{9}\right)\\= \frac{3}{8}+\frac{8}{9}\\=\frac{27}{72}+\frac{64}{72}\\=\frac{27+64}{72}\\=\frac{91}{72}\)
9. \(+\left(\frac{15}{4}\right)+\left(\frac{7}{-2}\right)\\= \frac{15}{4}-\frac{7}{2}\\=\frac{15-7}{4}\\=\frac{8}{4}\\=\frac{2}{1}\)
10. \(+\left(\frac{-4}{-3}\right)+\left(\frac{-10}{-9}\right)\\= \frac{4}{3}+\frac{10}{9}\\=\frac{12}{9}+\frac{10}{9}\\=\frac{12+10}{9}\\=\frac{22}{9}\)
11. \(-\left(\frac{2}{11}\right)+\left(\frac{-2}{-9}\right)\\= \frac{-2}{11}+\frac{2}{9}\\=\frac{-18}{99}+\frac{22}{99}\\=\frac{-18+22}{99}\\=\frac{4}{99}\)
12. \(-\left(\frac{6}{11}\right)-\left(\frac{-10}{-13}\right)\\= \frac{-6}{11}-\frac{10}{13}\\=\frac{-78}{143}-\frac{110}{143}\\=\frac{-78-110}{143}\\=\frac{-188}{143}\)