Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{12}{5}\right)+\left(\frac{-3}{-11}\right)\\= \frac{12}{5}+\frac{3}{11}\\=\frac{132}{55}+\frac{15}{55}\\=\frac{132+15}{55}\\=\frac{147}{55}\)
2. \(-\left(\frac{2}{-3}\right)-\left(\frac{-5}{14}\right)\\= \frac{2}{3}+\frac{5}{14}\\=\frac{28}{42}+\frac{15}{42}\\=\frac{28+15}{42}\\=\frac{43}{42}\)
3. \(+\left(\frac{-11}{-14}\right)+\left(\frac{5}{-9}\right)\\= \frac{11}{14}-\frac{5}{9}\\=\frac{99}{126}-\frac{70}{126}\\=\frac{99-70}{126}\\=\frac{29}{126}\)
4. \(+\left(\frac{14}{-11}\right)-\left(\frac{7}{-2}\right)\\= \frac{-14}{11}+\frac{7}{2}\\=\frac{-28}{22}+\frac{77}{22}\\=\frac{-28+77}{22}\\=\frac{49}{22}\)
5. \(-\left(\frac{-5}{-6}\right)-\left(\frac{-10}{-13}\right)\\= \frac{-5}{6}-\frac{10}{13}\\=\frac{-65}{78}-\frac{60}{78}\\=\frac{-65-60}{78}\\=\frac{-125}{78}\)
6. \(+\left(\frac{-14}{3}\right)-\left(\frac{-11}{14}\right)\\= \frac{-14}{3}+\frac{11}{14}\\=\frac{-196}{42}+\frac{33}{42}\\=\frac{-196+33}{42}\\=\frac{-163}{42}\)
7. \(-\left(\frac{15}{13}\right)+\left(\frac{2}{-5}\right)\\= \frac{-15}{13}-\frac{2}{5}\\=\frac{-75}{65}-\frac{26}{65}\\=\frac{-75-26}{65}\\=\frac{-101}{65}\)
8. \(-\left(\frac{4}{13}\right)+\left(\frac{-5}{-3}\right)\\= \frac{-4}{13}+\frac{5}{3}\\=\frac{-12}{39}+\frac{65}{39}\\=\frac{-12+65}{39}\\=\frac{53}{39}\)
9. \(+\left(\frac{3}{-11}\right)+\left(\frac{-6}{11}\right)\\= \frac{-3}{11}-\frac{6}{11}\\=\frac{-3-6}{11}\\=\frac{-9}{11}\)
10. \(+\left(\frac{-13}{-6}\right)+\left(\frac{4}{3}\right)\\= \frac{13}{6}+\frac{4}{3}\\=\frac{13+4}{6}\\=\frac{17}{6}\)
11. \(+\left(\frac{-13}{12}\right)+\left(\frac{-11}{-3}\right)\\= \frac{-13}{12}+\frac{11}{3}\\=\frac{-13+11}{12}\\=\frac{-2}{12}\\=\frac{-1}{6}\)
12. \(+\left(\frac{-7}{-2}\right)+\left(\frac{9}{2}\right)\\= \frac{7}{2}+\frac{9}{2}\\=\frac{7+9}{2}\\=\frac{16}{2}\\=\frac{8}{1}\)