Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-14}{-11}\right)+\left(\frac{2}{3}\right)\\= \frac{14}{11}+\frac{2}{3}\\=\frac{42}{33}+\frac{22}{33}\\=\frac{42+22}{33}\\=\frac{64}{33}\)
2. \(+\left(\frac{-3}{-10}\right)+\left(\frac{-2}{-5}\right)\\= \frac{3}{10}+\frac{2}{5}\\=\frac{3+2}{10}\\=\frac{5}{10}\\=\frac{1}{2}\)
3. \(+\left(\frac{-5}{-14}\right)+\left(\frac{-11}{5}\right)\\= \frac{5}{14}-\frac{11}{5}\\=\frac{25}{70}-\frac{154}{70}\\=\frac{25-154}{70}\\=\frac{-129}{70}\)
4. \(+\left(\frac{15}{-13}\right)+\left(\frac{-11}{4}\right)\\= \frac{-15}{13}-\frac{11}{4}\\=\frac{-60}{52}-\frac{143}{52}\\=\frac{-60-143}{52}\\=\frac{-203}{52}\)
5. \(-\left(\frac{8}{-13}\right)+\left(\frac{7}{-2}\right)\\= \frac{8}{13}-\frac{7}{2}\\=\frac{16}{26}-\frac{91}{26}\\=\frac{16-91}{26}\\=\frac{-75}{26}\)
6. \(+\left(\frac{-14}{-3}\right)-\left(\frac{-11}{-4}\right)\\= \frac{14}{3}-\frac{11}{4}\\=\frac{56}{12}-\frac{33}{12}\\=\frac{56-33}{12}\\=\frac{23}{12}\)
7. \(-\left(\frac{8}{-11}\right)+\left(\frac{15}{-2}\right)\\= \frac{8}{11}-\frac{15}{2}\\=\frac{16}{22}-\frac{165}{22}\\=\frac{16-165}{22}\\=\frac{-149}{22}\)
8. \(+\left(\frac{14}{-3}\right)+\left(\frac{11}{3}\right)\\= \frac{-14}{3}+\frac{11}{3}\\=\frac{-14+11}{3}\\=\frac{-3}{3}\\=\frac{-1}{1}\)
9. \(+\left(\frac{8}{11}\right)-\left(\frac{-5}{6}\right)\\= \frac{8}{11}+\frac{5}{6}\\=\frac{48}{66}+\frac{55}{66}\\=\frac{48+55}{66}\\=\frac{103}{66}\)
10. \(+\left(\frac{12}{-11}\right)-\left(\frac{-2}{-11}\right)\\= \frac{-12}{11}-\frac{2}{11}\\=\frac{-12-2}{11}\\=\frac{-14}{11}\)
11. \(+\left(\frac{-13}{-5}\right)+\left(\frac{9}{-4}\right)\\= \frac{13}{5}-\frac{9}{4}\\=\frac{52}{20}-\frac{45}{20}\\=\frac{52-45}{20}\\=\frac{7}{20}\)
12. \(+\left(\frac{-15}{-11}\right)-\left(\frac{-2}{-5}\right)\\= \frac{15}{11}-\frac{2}{5}\\=\frac{75}{55}-\frac{22}{55}\\=\frac{75-22}{55}\\=\frac{53}{55}\)