Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{4}{9}\right) +\left(\frac{5}{-7}\right) -\left(\frac{-2}{11}\right)\\= \frac{-4}{9}- \frac{5}{7}+\frac{2}{11}\\=\frac{-308}{693}-\frac{495}{693}+\frac{126}{693}\\=\frac{-308-495+126}{693}\\=\frac{-677}{693}\)
2. \(-\left(\frac{2}{5}\right) -\left(\frac{7}{4}\right) +\left(\frac{-8}{-11}\right)\\= \frac{-2}{5}- \frac{7}{4}+\frac{8}{11}\\=\frac{-88}{220}-\frac{385}{220}+\frac{160}{220}\\=\frac{-88-385+160}{220}\\=\frac{-313}{220}\)
3. \(-\left(\frac{6}{7}\right) -\left(\frac{6}{5}\right) -\left(\frac{8}{7}\right)\\= \frac{-6}{7}- \frac{6}{5}-\frac{8}{7}\\=\frac{-30}{35}-\frac{42}{35}-\frac{40}{35}\\=\frac{-30-42-40}{35}\\=\frac{-112}{35}\\=\frac{-16}{5}\)
4. \(+\left(\frac{-8}{9}\right) -\left(\frac{-10}{-10}\right) -\left(\frac{-2}{10}\right)\\= \frac{-8}{9}- \frac{10}{10}+\frac{2}{10}\\=\frac{-8}{9}-\frac{1}{1}+\frac{1}{5}\\=\frac{-40}{45}-\frac{45}{45}+\frac{9}{45}\\=\frac{-40-45+9}{45}\\=\frac{-76}{45}\)
5. \(-\left(\frac{8}{-5}\right) +\left(\frac{6}{-3}\right) -\left(\frac{10}{12}\right)\\= \frac{8}{5}- \frac{6}{3}-\frac{10}{12}\\=\frac{8}{5}-\frac{2}{1}-\frac{5}{6}\\=\frac{48}{30}-\frac{60}{30}-\frac{25}{30}\\=\frac{48-60-25}{30}\\=\frac{-37}{30}\)
6. \(-\left(\frac{9}{-2}\right) -\left(\frac{-7}{3}\right) -\left(\frac{-7}{7}\right)\\= \frac{9}{2}+ \frac{7}{3}+\frac{7}{7}\\=\frac{9}{2}+\frac{7}{3}+\frac{1}{1}\\=\frac{27}{6}+\frac{14}{6}+\frac{6}{6}\\=\frac{27+14+6}{6}\\=\frac{47}{6}\)
7. \(-\left(\frac{-10}{9}\right) +\left(\frac{-7}{6}\right) +\left(\frac{10}{-4}\right)\\= \frac{10}{9}- \frac{7}{6}-\frac{10}{4}\\=\frac{10}{9}-\frac{7}{6}-\frac{5}{2}\\=\frac{20}{18}-\frac{21}{18}-\frac{45}{18}\\=\frac{20-21-45}{18}\\=\frac{-46}{18}\\=\frac{-23}{9}\)
8. \(-\left(\frac{-4}{3}\right) +\left(\frac{8}{-5}\right) -\left(\frac{6}{-5}\right)\\= \frac{4}{3}- \frac{8}{5}+\frac{6}{5}\\=\frac{20}{15}-\frac{24}{15}+\frac{18}{15}\\=\frac{20-24+18}{15}\\=\frac{14}{15}\)
9. \(+\left(\frac{6}{7}\right) -\left(\frac{-6}{-7}\right) -\left(\frac{-4}{7}\right)\\= \frac{6}{7}- \frac{6}{7}+\frac{4}{7}\\=\frac{6-6+4}{7}\\=\frac{4}{7}\)
10. \(-\left(\frac{9}{-2}\right) -\left(\frac{5}{3}\right) +\left(\frac{-7}{-4}\right)\\= \frac{9}{2}- \frac{5}{3}+\frac{7}{4}\\=\frac{54}{12}-\frac{20}{12}+\frac{21}{12}\\=\frac{54-20+21}{12}\\=\frac{55}{12}\)
11. \(-\left(\frac{6}{7}\right) +\left(\frac{-3}{3}\right) +\left(\frac{-11}{-3}\right)\\= \frac{-6}{7}- \frac{3}{3}+\frac{11}{3}\\=\frac{-6}{7}-\frac{1}{1}+\frac{11}{3}\\=\frac{-18}{21}-\frac{21}{21}+\frac{77}{21}\\=\frac{-18-21+77}{21}\\=\frac{38}{21}\)
12. \(+\left(\frac{-2}{-7}\right) -\left(\frac{6}{-8}\right) -\left(\frac{3}{8}\right)\\= \frac{2}{7}+ \frac{6}{8}-\frac{3}{8}\\=\frac{2}{7}+\frac{3}{4}-\frac{3}{8}\\=\frac{16}{56}+\frac{42}{56}-\frac{21}{56}\\=\frac{16+42-21}{56}\\=\frac{37}{56}\)