Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-5}{9}\right)+\left(\frac{2}{13}\right)\\= \frac{5}{9}+\frac{2}{13}\\=\frac{65}{117}+\frac{18}{117}\\=\frac{65+18}{117}\\=\frac{83}{117}\)
2. \(-\left(\frac{-15}{-7}\right)+\left(\frac{13}{14}\right)\\= \frac{-15}{7}+\frac{13}{14}\\=\frac{-30}{14}+\frac{13}{14}\\=\frac{-30+13}{14}\\=\frac{-17}{14}\)
3. \(-\left(\frac{4}{-7}\right)+\left(\frac{2}{-3}\right)\\= \frac{4}{7}-\frac{2}{3}\\=\frac{12}{21}-\frac{14}{21}\\=\frac{12-14}{21}\\=\frac{-2}{21}\)
4. \(-\left(\frac{-13}{2}\right)-\left(\frac{14}{11}\right)\\= \frac{13}{2}-\frac{14}{11}\\=\frac{143}{22}-\frac{28}{22}\\=\frac{143-28}{22}\\=\frac{115}{22}\)
5. \(-\left(\frac{14}{-9}\right)-\left(\frac{8}{9}\right)\\= \frac{14}{9}-\frac{8}{9}\\=\frac{14-8}{9}\\=\frac{6}{9}\\=\frac{2}{3}\)
6. \(-\left(\frac{4}{-7}\right)+\left(\frac{-7}{-3}\right)\\= \frac{4}{7}+\frac{7}{3}\\=\frac{12}{21}+\frac{49}{21}\\=\frac{12+49}{21}\\=\frac{61}{21}\)
7. \(+\left(\frac{11}{12}\right)-\left(\frac{-8}{3}\right)\\= \frac{11}{12}+\frac{8}{3}\\=\frac{11+8}{12}\\=\frac{19}{12}\)
8. \(-\left(\frac{10}{9}\right)+\left(\frac{10}{3}\right)\\= \frac{-10}{9}+\frac{10}{3}\\=\frac{-10+10}{9}\\=\frac{0}{9}\\=\frac{0}{1}\)
9. \(+\left(\frac{-6}{5}\right)-\left(\frac{-15}{2}\right)\\= \frac{-6}{5}+\frac{15}{2}\\=\frac{-12}{10}+\frac{75}{10}\\=\frac{-12+75}{10}\\=\frac{63}{10}\)
10. \(-\left(\frac{-14}{3}\right)+\left(\frac{2}{7}\right)\\= \frac{14}{3}+\frac{2}{7}\\=\frac{98}{21}+\frac{6}{21}\\=\frac{98+6}{21}\\=\frac{104}{21}\)
11. \(-\left(\frac{4}{-11}\right)+\left(\frac{13}{14}\right)\\= \frac{4}{11}+\frac{13}{14}\\=\frac{56}{154}+\frac{143}{154}\\=\frac{56+143}{154}\\=\frac{199}{154}\)
12. \(+\left(\frac{-13}{9}\right)+\left(\frac{-10}{7}\right)\\= \frac{-13}{9}-\frac{10}{7}\\=\frac{-91}{63}-\frac{90}{63}\\=\frac{-91-90}{63}\\=\frac{-181}{63}\)