Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-5}{-9}\right) +\left(\frac{-5}{8}\right) +\left(\frac{6}{3}\right)\\= \frac{5}{9}- \frac{5}{8}+\frac{6}{3}\\=\frac{5}{9}-\frac{5}{8}+\frac{2}{1}\\=\frac{40}{72}-\frac{45}{72}+\frac{144}{72}\\=\frac{40-45+144}{72}\\=\frac{139}{72}\)
2. \(-\left(\frac{-7}{6}\right) -\left(\frac{6}{-4}\right) +\left(\frac{-3}{11}\right)\\= \frac{7}{6}+ \frac{6}{4}-\frac{3}{11}\\=\frac{7}{6}+\frac{3}{2}-\frac{3}{11}\\=\frac{77}{66}+\frac{99}{66}-\frac{18}{66}\\=\frac{77+99-18}{66}\\=\frac{158}{66}\\=\frac{79}{33}\)
3. \(-\left(\frac{-6}{5}\right) +\left(\frac{9}{8}\right) +\left(\frac{-5}{3}\right)\\= \frac{6}{5}+ \frac{9}{8}-\frac{5}{3}\\=\frac{144}{120}+\frac{135}{120}-\frac{200}{120}\\=\frac{144+135-200}{120}\\=\frac{79}{120}\)
4. \(-\left(\frac{4}{7}\right) -\left(\frac{10}{-6}\right) +\left(\frac{-11}{2}\right)\\= \frac{-4}{7}+ \frac{10}{6}-\frac{11}{2}\\=\frac{-4}{7}+\frac{5}{3}-\frac{11}{2}\\=\frac{-24}{42}+\frac{70}{42}-\frac{231}{42}\\=\frac{-24+70-231}{42}\\=\frac{-185}{42}\)
5. \(-\left(\frac{6}{5}\right) -\left(\frac{2}{6}\right) -\left(\frac{-12}{4}\right)\\= \frac{-6}{5}- \frac{2}{6}+\frac{12}{4}\\=\frac{-6}{5}-\frac{1}{3}+\frac{3}{1}\\=\frac{-18}{15}-\frac{5}{15}+\frac{45}{15}\\=\frac{-18-5+45}{15}\\=\frac{22}{15}\)
6. \(+\left(\frac{-4}{-9}\right) -\left(\frac{-10}{7}\right) +\left(\frac{-5}{11}\right)\\= \frac{4}{9}+ \frac{10}{7}-\frac{5}{11}\\=\frac{308}{693}+\frac{990}{693}-\frac{315}{693}\\=\frac{308+990-315}{693}\\=\frac{983}{693}\)
7. \(-\left(\frac{-3}{-5}\right) -\left(\frac{-7}{-9}\right) -\left(\frac{7}{-10}\right)\\= \frac{-3}{5}- \frac{7}{9}+\frac{7}{10}\\=\frac{-54}{90}-\frac{70}{90}+\frac{63}{90}\\=\frac{-54-70+63}{90}\\=\frac{-61}{90}\)
8. \(+\left(\frac{7}{8}\right) +\left(\frac{2}{-8}\right) +\left(\frac{-6}{12}\right)\\= \frac{7}{8}- \frac{2}{8}-\frac{6}{12}\\=\frac{7}{8}-\frac{1}{4}-\frac{1}{2}\\=\frac{7-1-1}{8}\\=\frac{5}{8}\)
9. \(-\left(\frac{7}{-4}\right) -\left(\frac{-4}{-2}\right) +\left(\frac{2}{-11}\right)\\= \frac{7}{4}- \frac{4}{2}-\frac{2}{11}\\=\frac{7}{4}-\frac{2}{1}-\frac{2}{11}\\=\frac{77}{44}-\frac{88}{44}-\frac{8}{44}\\=\frac{77-88-8}{44}\\=\frac{-19}{44}\)
10. \(-\left(\frac{7}{2}\right) -\left(\frac{7}{-9}\right) +\left(\frac{10}{9}\right)\\= \frac{-7}{2}+ \frac{7}{9}+\frac{10}{9}\\=\frac{-63}{18}+\frac{14}{18}+\frac{20}{18}\\=\frac{-63+14+20}{18}\\=\frac{-29}{18}\)
11. \(+\left(\frac{-8}{3}\right) +\left(\frac{5}{-4}\right) +\left(\frac{-8}{5}\right)\\= \frac{-8}{3}- \frac{5}{4}-\frac{8}{5}\\=\frac{-160}{60}-\frac{75}{60}-\frac{96}{60}\\=\frac{-160-75-96}{60}\\=\frac{-331}{60}\)
12. \(-\left(\frac{5}{2}\right) -\left(\frac{-3}{-3}\right) -\left(\frac{-12}{4}\right)\\= \frac{-5}{2}- \frac{3}{3}+\frac{12}{4}\\=\frac{-5}{2}-\frac{1}{1}+\frac{3}{1}\\=\frac{-5-1+3}{2}\\=\frac{-3}{2}\)