Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{10}{-7}\right) -\left(\frac{-6}{9}\right) -\left(\frac{3}{-7}\right)\\= \frac{-10}{7}+ \frac{6}{9}+\frac{3}{7}\\=\frac{-10}{7}+\frac{2}{3}+\frac{3}{7}\\=\frac{-30}{21}+\frac{14}{21}+\frac{9}{21}\\=\frac{-30+14+9}{21}\\=\frac{-7}{21}\\=\frac{-1}{3}\)
2. \(-\left(\frac{10}{-7}\right) -\left(\frac{-8}{-9}\right) -\left(\frac{-7}{-8}\right)\\= \frac{10}{7}- \frac{8}{9}-\frac{7}{8}\\=\frac{720}{504}-\frac{448}{504}-\frac{441}{504}\\=\frac{720-448-441}{504}\\=\frac{-169}{504}\)
3. \(-\left(\frac{7}{6}\right) -\left(\frac{-5}{6}\right) +\left(\frac{5}{-6}\right)\\= \frac{-7}{6}+ \frac{5}{6}-\frac{5}{6}\\=\frac{-7+5-5}{6}\\=\frac{-7}{6}\)
4. \(-\left(\frac{7}{8}\right) -\left(\frac{5}{5}\right) +\left(\frac{2}{3}\right)\\= \frac{-7}{8}- \frac{5}{5}+\frac{2}{3}\\=\frac{-7}{8}-\frac{1}{1}+\frac{2}{3}\\=\frac{-21}{24}-\frac{24}{24}+\frac{16}{24}\\=\frac{-21-24+16}{24}\\=\frac{-29}{24}\)
5. \(-\left(\frac{-9}{-5}\right) -\left(\frac{5}{6}\right) -\left(\frac{-6}{-3}\right)\\= \frac{-9}{5}- \frac{5}{6}-\frac{6}{3}\\=\frac{-9}{5}-\frac{5}{6}-\frac{2}{1}\\=\frac{-54}{30}-\frac{25}{30}-\frac{60}{30}\\=\frac{-54-25-60}{30}\\=\frac{-139}{30}\)
6. \(+\left(\frac{10}{-7}\right) -\left(\frac{6}{8}\right) -\left(\frac{-2}{10}\right)\\= \frac{-10}{7}- \frac{6}{8}+\frac{2}{10}\\=\frac{-10}{7}-\frac{3}{4}+\frac{1}{5}\\=\frac{-200}{140}-\frac{105}{140}+\frac{28}{140}\\=\frac{-200-105+28}{140}\\=\frac{-277}{140}\)
7. \(-\left(\frac{9}{-7}\right) +\left(\frac{10}{5}\right) -\left(\frac{-7}{-9}\right)\\= \frac{9}{7}+ \frac{10}{5}-\frac{7}{9}\\=\frac{9}{7}+\frac{2}{1}-\frac{7}{9}\\=\frac{81}{63}+\frac{126}{63}-\frac{49}{63}\\=\frac{81+126-49}{63}\\=\frac{158}{63}\)
8. \(-\left(\frac{-9}{-2}\right) +\left(\frac{8}{-10}\right) -\left(\frac{9}{9}\right)\\= \frac{-9}{2}- \frac{8}{10}-\frac{9}{9}\\=\frac{-9}{2}-\frac{4}{5}-\frac{1}{1}\\=\frac{-45}{10}-\frac{8}{10}-\frac{10}{10}\\=\frac{-45-8-10}{10}\\=\frac{-63}{10}\)
9. \(+\left(\frac{3}{4}\right) +\left(\frac{-6}{-2}\right) -\left(\frac{-8}{-7}\right)\\= \frac{3}{4}+ \frac{6}{2}-\frac{8}{7}\\=\frac{3}{4}+\frac{3}{1}-\frac{8}{7}\\=\frac{21}{28}+\frac{84}{28}-\frac{32}{28}\\=\frac{21+84-32}{28}\\=\frac{73}{28}\)
10. \(-\left(\frac{5}{7}\right) -\left(\frac{-10}{-4}\right) -\left(\frac{-5}{-11}\right)\\= \frac{-5}{7}- \frac{10}{4}-\frac{5}{11}\\=\frac{-5}{7}-\frac{5}{2}-\frac{5}{11}\\=\frac{-110}{154}-\frac{385}{154}-\frac{70}{154}\\=\frac{-110-385-70}{154}\\=\frac{-565}{154}\)
11. \(+\left(\frac{-3}{-4}\right) +\left(\frac{6}{4}\right) +\left(\frac{8}{-11}\right)\\= \frac{3}{4}+ \frac{6}{4}-\frac{8}{11}\\=\frac{3}{4}+\frac{3}{2}-\frac{8}{11}\\=\frac{33}{44}+\frac{66}{44}-\frac{32}{44}\\=\frac{33+66-32}{44}\\=\frac{67}{44}\)
12. \(-\left(\frac{-6}{5}\right) +\left(\frac{-4}{4}\right) -\left(\frac{-5}{4}\right)\\= \frac{6}{5}- \frac{4}{4}+\frac{5}{4}\\=\frac{6}{5}-\frac{1}{1}+\frac{5}{4}\\=\frac{24}{20}-\frac{20}{20}+\frac{25}{20}\\=\frac{24-20+25}{20}\\=\frac{29}{20}\)