Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-5}{14}\right)+\left(\frac{2}{3}\right)\\= \frac{5}{14}+\frac{2}{3}\\=\frac{15}{42}+\frac{28}{42}\\=\frac{15+28}{42}\\=\frac{43}{42}\)
2. \(-\left(\frac{-7}{10}\right)-\left(\frac{7}{-3}\right)\\= \frac{7}{10}+\frac{7}{3}\\=\frac{21}{30}+\frac{70}{30}\\=\frac{21+70}{30}\\=\frac{91}{30}\)
3. \(+\left(\frac{-8}{-7}\right)-\left(\frac{15}{13}\right)\\= \frac{8}{7}-\frac{15}{13}\\=\frac{104}{91}-\frac{105}{91}\\=\frac{104-105}{91}\\=\frac{-1}{91}\)
4. \(+\left(\frac{12}{-11}\right)-\left(\frac{-14}{-3}\right)\\= \frac{-12}{11}-\frac{14}{3}\\=\frac{-36}{33}-\frac{154}{33}\\=\frac{-36-154}{33}\\=\frac{-190}{33}\)
5. \(-\left(\frac{-5}{-2}\right)-\left(\frac{-13}{6}\right)\\= \frac{-5}{2}+\frac{13}{6}\\=\frac{-15}{6}+\frac{13}{6}\\=\frac{-15+13}{6}\\=\frac{-2}{6}\\=\frac{-1}{3}\)
6. \(-\left(\frac{13}{-4}\right)-\left(\frac{4}{5}\right)\\= \frac{13}{4}-\frac{4}{5}\\=\frac{65}{20}-\frac{16}{20}\\=\frac{65-16}{20}\\=\frac{49}{20}\)
7. \(-\left(\frac{-14}{-9}\right)-\left(\frac{8}{3}\right)\\= \frac{-14}{9}-\frac{8}{3}\\=\frac{-14-8}{9}\\=\frac{-22}{9}\)
8. \(-\left(\frac{10}{-3}\right)+\left(\frac{-4}{-3}\right)\\= \frac{10}{3}+\frac{4}{3}\\=\frac{10+4}{3}\\=\frac{14}{3}\)
9. \(+\left(\frac{4}{7}\right)-\left(\frac{12}{-5}\right)\\= \frac{4}{7}+\frac{12}{5}\\=\frac{20}{35}+\frac{84}{35}\\=\frac{20+84}{35}\\=\frac{104}{35}\)
10. \(+\left(\frac{11}{7}\right)+\left(\frac{-7}{12}\right)\\= \frac{11}{7}-\frac{7}{12}\\=\frac{132}{84}-\frac{49}{84}\\=\frac{132-49}{84}\\=\frac{83}{84}\)
11. \(+\left(\frac{-7}{13}\right)+\left(\frac{12}{-5}\right)\\= \frac{-7}{13}-\frac{12}{5}\\=\frac{-35}{65}-\frac{156}{65}\\=\frac{-35-156}{65}\\=\frac{-191}{65}\)
12. \(+\left(\frac{15}{-4}\right)-\left(\frac{-13}{4}\right)\\= \frac{-15}{4}+\frac{13}{4}\\=\frac{-15+13}{4}\\=\frac{-2}{4}\\=\frac{-1}{2}\)