Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-3}{7}\right) -\left(\frac{3}{10}\right) +\left(\frac{5}{-11}\right)\\= \frac{3}{7}- \frac{3}{10}-\frac{5}{11}\\=\frac{330}{770}-\frac{231}{770}-\frac{350}{770}\\=\frac{330-231-350}{770}\\=\frac{-251}{770}\)
2. \(+\left(\frac{-9}{-4}\right) -\left(\frac{3}{-6}\right) +\left(\frac{3}{-9}\right)\\= \frac{9}{4}+ \frac{3}{6}-\frac{3}{9}\\=\frac{9}{4}+\frac{1}{2}-\frac{1}{3}\\=\frac{27}{12}+\frac{6}{12}-\frac{4}{12}\\=\frac{27+6-4}{12}\\=\frac{29}{12}\)
3. \(+\left(\frac{7}{2}\right) -\left(\frac{-4}{9}\right) +\left(\frac{-4}{-11}\right)\\= \frac{7}{2}+ \frac{4}{9}+\frac{4}{11}\\=\frac{693}{198}+\frac{88}{198}+\frac{72}{198}\\=\frac{693+88+72}{198}\\=\frac{853}{198}\)
4. \(-\left(\frac{-3}{-4}\right) +\left(\frac{-8}{-10}\right) +\left(\frac{7}{7}\right)\\= \frac{-3}{4}+ \frac{8}{10}+\frac{7}{7}\\=\frac{-3}{4}+\frac{4}{5}+\frac{1}{1}\\=\frac{-15}{20}+\frac{16}{20}+\frac{20}{20}\\=\frac{-15+16+20}{20}\\=\frac{21}{20}\)
5. \(+\left(\frac{8}{-7}\right) +\left(\frac{7}{-3}\right) -\left(\frac{-6}{5}\right)\\= \frac{-8}{7}- \frac{7}{3}+\frac{6}{5}\\=\frac{-120}{105}-\frac{245}{105}+\frac{126}{105}\\=\frac{-120-245+126}{105}\\=\frac{-239}{105}\)
6. \(+\left(\frac{10}{-7}\right) +\left(\frac{-3}{6}\right) +\left(\frac{10}{2}\right)\\= \frac{-10}{7}- \frac{3}{6}+\frac{10}{2}\\=\frac{-10}{7}-\frac{1}{2}+\frac{5}{1}\\=\frac{-20}{14}-\frac{7}{14}+\frac{70}{14}\\=\frac{-20-7+70}{14}\\=\frac{43}{14}\)
7. \(-\left(\frac{8}{-3}\right) +\left(\frac{-4}{-2}\right) -\left(\frac{-3}{-9}\right)\\= \frac{8}{3}+ \frac{4}{2}-\frac{3}{9}\\=\frac{8}{3}+\frac{2}{1}-\frac{1}{3}\\=\frac{8+2-1}{3}\\=\frac{9}{3}\\=\frac{3}{1}\)
8. \(-\left(\frac{-5}{-2}\right) -\left(\frac{-7}{9}\right) +\left(\frac{8}{2}\right)\\= \frac{-5}{2}+ \frac{7}{9}+\frac{8}{2}\\=\frac{-5}{2}+\frac{7}{9}+\frac{4}{1}\\=\frac{-45}{18}+\frac{14}{18}+\frac{72}{18}\\=\frac{-45+14+72}{18}\\=\frac{41}{18}\)
9. \(+\left(\frac{-3}{-4}\right) +\left(\frac{6}{-4}\right) +\left(\frac{-6}{10}\right)\\= \frac{3}{4}- \frac{6}{4}-\frac{6}{10}\\=\frac{3}{4}-\frac{3}{2}-\frac{3}{5}\\=\frac{15}{20}-\frac{30}{20}-\frac{12}{20}\\=\frac{15-30-12}{20}\\=\frac{-27}{20}\)
10. \(+\left(\frac{4}{7}\right) -\left(\frac{-4}{9}\right) -\left(\frac{-2}{-10}\right)\\= \frac{4}{7}+ \frac{4}{9}-\frac{2}{10}\\=\frac{4}{7}+\frac{4}{9}-\frac{1}{5}\\=\frac{180}{315}+\frac{140}{315}-\frac{63}{315}\\=\frac{180+140-63}{315}\\=\frac{257}{315}\)
11. \(+\left(\frac{-6}{5}\right) +\left(\frac{-5}{-5}\right) -\left(\frac{-3}{10}\right)\\= \frac{-6}{5}+ \frac{5}{5}+\frac{3}{10}\\=\frac{-6}{5}+\frac{1}{1}+\frac{3}{10}\\=\frac{-12}{10}+\frac{10}{10}+\frac{3}{10}\\=\frac{-12+10+3}{10}\\=\frac{1}{10}\)
12. \(+\left(\frac{8}{-5}\right) +\left(\frac{-10}{8}\right) -\left(\frac{-6}{-3}\right)\\= \frac{-8}{5}- \frac{10}{8}-\frac{6}{3}\\=\frac{-8}{5}-\frac{5}{4}-\frac{2}{1}\\=\frac{-32}{20}-\frac{25}{20}-\frac{40}{20}\\=\frac{-32-25-40}{20}\\=\frac{-97}{20}\)