Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{9}{2}\right) -\left(\frac{8}{5}\right) -\left(\frac{8}{-11}\right)\\= \frac{-9}{2}- \frac{8}{5}+\frac{8}{11}\\=\frac{-495}{110}-\frac{176}{110}+\frac{80}{110}\\=\frac{-495-176+80}{110}\\=\frac{-591}{110}\)
2. \(+\left(\frac{10}{7}\right) -\left(\frac{8}{2}\right) +\left(\frac{-10}{-5}\right)\\= \frac{10}{7}- \frac{8}{2}+\frac{10}{5}\\=\frac{10}{7}-\frac{4}{1}+\frac{2}{1}\\=\frac{10-4+2}{7}\\=\frac{8}{7}\)
3. \(-\left(\frac{-4}{5}\right) -\left(\frac{-2}{4}\right) -\left(\frac{-3}{-7}\right)\\= \frac{4}{5}+ \frac{2}{4}-\frac{3}{7}\\=\frac{4}{5}+\frac{1}{2}-\frac{3}{7}\\=\frac{56}{70}+\frac{35}{70}-\frac{30}{70}\\=\frac{56+35-30}{70}\\=\frac{61}{70}\)
4. \(+\left(\frac{-8}{7}\right) -\left(\frac{4}{-3}\right) +\left(\frac{-7}{-6}\right)\\= \frac{-8}{7}+ \frac{4}{3}+\frac{7}{6}\\=\frac{-48}{42}+\frac{56}{42}+\frac{49}{42}\\=\frac{-48+56+49}{42}\\=\frac{57}{42}\\=\frac{19}{14}\)
5. \(-\left(\frac{9}{-2}\right) -\left(\frac{-7}{-3}\right) +\left(\frac{3}{3}\right)\\= \frac{9}{2}- \frac{7}{3}+\frac{3}{3}\\=\frac{9}{2}-\frac{7}{3}+\frac{1}{1}\\=\frac{27}{6}-\frac{14}{6}+\frac{6}{6}\\=\frac{27-14+6}{6}\\=\frac{19}{6}\)
6. \(+\left(\frac{-5}{-4}\right) -\left(\frac{-3}{-6}\right) -\left(\frac{-9}{10}\right)\\= \frac{5}{4}- \frac{3}{6}+\frac{9}{10}\\=\frac{5}{4}-\frac{1}{2}+\frac{9}{10}\\=\frac{25}{20}-\frac{10}{20}+\frac{18}{20}\\=\frac{25-10+18}{20}\\=\frac{33}{20}\)
7. \(-\left(\frac{3}{4}\right) -\left(\frac{9}{5}\right) +\left(\frac{-11}{-3}\right)\\= \frac{-3}{4}- \frac{9}{5}+\frac{11}{3}\\=\frac{-45}{60}-\frac{108}{60}+\frac{220}{60}\\=\frac{-45-108+220}{60}\\=\frac{67}{60}\)
8. \(-\left(\frac{9}{-7}\right) +\left(\frac{3}{9}\right) +\left(\frac{-8}{-7}\right)\\= \frac{9}{7}+ \frac{3}{9}+\frac{8}{7}\\=\frac{9}{7}+\frac{1}{3}+\frac{8}{7}\\=\frac{27}{21}+\frac{7}{21}+\frac{24}{21}\\=\frac{27+7+24}{21}\\=\frac{58}{21}\)
9. \(-\left(\frac{-6}{-7}\right) +\left(\frac{-8}{-3}\right) +\left(\frac{6}{7}\right)\\= \frac{-6}{7}+ \frac{8}{3}+\frac{6}{7}\\=\frac{-18}{21}+\frac{56}{21}+\frac{18}{21}\\=\frac{-18+56+18}{21}\\=\frac{56}{21}\\=\frac{8}{3}\)
10. \(+\left(\frac{9}{2}\right) -\left(\frac{10}{3}\right) +\left(\frac{-3}{-10}\right)\\= \frac{9}{2}- \frac{10}{3}+\frac{3}{10}\\=\frac{135}{30}-\frac{100}{30}+\frac{9}{30}\\=\frac{135-100+9}{30}\\=\frac{44}{30}\\=\frac{22}{15}\)
11. \(+\left(\frac{6}{5}\right) -\left(\frac{-8}{-9}\right) -\left(\frac{-7}{2}\right)\\= \frac{6}{5}- \frac{8}{9}+\frac{7}{2}\\=\frac{108}{90}-\frac{80}{90}+\frac{315}{90}\\=\frac{108-80+315}{90}\\=\frac{343}{90}\)
12. \(-\left(\frac{-5}{-6}\right) +\left(\frac{-8}{-4}\right) +\left(\frac{-9}{4}\right)\\= \frac{-5}{6}+ \frac{8}{4}-\frac{9}{4}\\=\frac{-5}{6}+\frac{2}{1}-\frac{9}{4}\\=\frac{-10}{12}+\frac{24}{12}-\frac{27}{12}\\=\frac{-10+24-27}{12}\\=\frac{-13}{12}\)