Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{12}{-5}\right)+\left(\frac{9}{7}\right)\\= \frac{12}{5}+\frac{9}{7}\\=\frac{84}{35}+\frac{45}{35}\\=\frac{84+45}{35}\\=\frac{129}{35}\)
2. \(+\left(\frac{9}{2}\right)+\left(\frac{-15}{13}\right)\\= \frac{9}{2}-\frac{15}{13}\\=\frac{117}{26}-\frac{30}{26}\\=\frac{117-30}{26}\\=\frac{87}{26}\)
3. \(-\left(\frac{8}{13}\right)+\left(\frac{7}{4}\right)\\= \frac{-8}{13}+\frac{7}{4}\\=\frac{-32}{52}+\frac{91}{52}\\=\frac{-32+91}{52}\\=\frac{59}{52}\)
4. \(+\left(\frac{4}{-5}\right)+\left(\frac{4}{3}\right)\\= \frac{-4}{5}+\frac{4}{3}\\=\frac{-12}{15}+\frac{20}{15}\\=\frac{-12+20}{15}\\=\frac{8}{15}\)
5. \(+\left(\frac{11}{-2}\right)+\left(\frac{-4}{13}\right)\\= \frac{-11}{2}-\frac{4}{13}\\=\frac{-143}{26}-\frac{8}{26}\\=\frac{-143-8}{26}\\=\frac{-151}{26}\)
6. \(-\left(\frac{-11}{2}\right)+\left(\frac{-12}{-11}\right)\\= \frac{11}{2}+\frac{12}{11}\\=\frac{121}{22}+\frac{24}{22}\\=\frac{121+24}{22}\\=\frac{145}{22}\)
7. \(-\left(\frac{-3}{13}\right)-\left(\frac{-12}{13}\right)\\= \frac{3}{13}+\frac{12}{13}\\=\frac{3+12}{13}\\=\frac{15}{13}\)
8. \(+\left(\frac{-3}{-11}\right)+\left(\frac{14}{-3}\right)\\= \frac{3}{11}-\frac{14}{3}\\=\frac{9}{33}-\frac{154}{33}\\=\frac{9-154}{33}\\=\frac{-145}{33}\)
9. \(-\left(\frac{6}{-11}\right)-\left(\frac{5}{-12}\right)\\= \frac{6}{11}+\frac{5}{12}\\=\frac{72}{132}+\frac{55}{132}\\=\frac{72+55}{132}\\=\frac{127}{132}\)
10. \(-\left(\frac{-9}{2}\right)+\left(\frac{-8}{-13}\right)\\= \frac{9}{2}+\frac{8}{13}\\=\frac{117}{26}+\frac{16}{26}\\=\frac{117+16}{26}\\=\frac{133}{26}\)
11. \(-\left(\frac{-13}{12}\right)-\left(\frac{-13}{-8}\right)\\= \frac{13}{12}-\frac{13}{8}\\=\frac{26}{24}-\frac{39}{24}\\=\frac{26-39}{24}\\=\frac{-13}{24}\)
12. \(-\left(\frac{-6}{13}\right)+\left(\frac{-5}{-6}\right)\\= \frac{6}{13}+\frac{5}{6}\\=\frac{36}{78}+\frac{65}{78}\\=\frac{36+65}{78}\\=\frac{101}{78}\)