Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-8}{9}\right) -\left(\frac{-9}{-7}\right) +\left(\frac{4}{8}\right)\\= \frac{-8}{9}- \frac{9}{7}+\frac{4}{8}\\=\frac{-8}{9}-\frac{9}{7}+\frac{1}{2}\\=\frac{-112}{126}-\frac{162}{126}+\frac{63}{126}\\=\frac{-112-162+63}{126}\\=\frac{-211}{126}\)
2. \(+\left(\frac{-6}{-5}\right) +\left(\frac{3}{10}\right) +\left(\frac{10}{-5}\right)\\= \frac{6}{5}+ \frac{3}{10}-\frac{10}{5}\\=\frac{6}{5}+\frac{3}{10}-\frac{2}{1}\\=\frac{12}{10}+\frac{3}{10}-\frac{20}{10}\\=\frac{12+3-20}{10}\\=\frac{-5}{10}\\=\frac{-1}{2}\)
3. \(-\left(\frac{-8}{5}\right) -\left(\frac{2}{-2}\right) +\left(\frac{11}{-10}\right)\\= \frac{8}{5}+ \frac{2}{2}-\frac{11}{10}\\=\frac{8}{5}+\frac{1}{1}-\frac{11}{10}\\=\frac{16}{10}+\frac{10}{10}-\frac{11}{10}\\=\frac{16+10-11}{10}\\=\frac{15}{10}\\=\frac{3}{2}\)
4. \(-\left(\frac{-8}{5}\right) -\left(\frac{3}{-6}\right) -\left(\frac{-11}{-5}\right)\\= \frac{8}{5}+ \frac{3}{6}-\frac{11}{5}\\=\frac{8}{5}+\frac{1}{2}-\frac{11}{5}\\=\frac{16}{10}+\frac{5}{10}-\frac{22}{10}\\=\frac{16+5-22}{10}\\=\frac{-1}{10}\)
5. \(+\left(\frac{6}{-7}\right) +\left(\frac{9}{6}\right) -\left(\frac{2}{-12}\right)\\= \frac{-6}{7}+ \frac{9}{6}+\frac{2}{12}\\=\frac{-6}{7}+\frac{3}{2}+\frac{1}{6}\\=\frac{-36}{42}+\frac{63}{42}+\frac{7}{42}\\=\frac{-36+63+7}{42}\\=\frac{34}{42}\\=\frac{17}{21}\)
6. \(-\left(\frac{-9}{-2}\right) +\left(\frac{-4}{-5}\right) +\left(\frac{3}{10}\right)\\= \frac{-9}{2}+ \frac{4}{5}+\frac{3}{10}\\=\frac{-45}{10}+\frac{8}{10}+\frac{3}{10}\\=\frac{-45+8+3}{10}\\=\frac{-34}{10}\\=\frac{-17}{5}\)
7. \(+\left(\frac{-5}{4}\right) -\left(\frac{10}{5}\right) -\left(\frac{-8}{-3}\right)\\= \frac{-5}{4}- \frac{10}{5}-\frac{8}{3}\\=\frac{-5}{4}-\frac{2}{1}-\frac{8}{3}\\=\frac{-15}{12}-\frac{24}{12}-\frac{32}{12}\\=\frac{-15-24-32}{12}\\=\frac{-71}{12}\)
8. \(-\left(\frac{-4}{9}\right) +\left(\frac{10}{-7}\right) +\left(\frac{-2}{-12}\right)\\= \frac{4}{9}- \frac{10}{7}+\frac{2}{12}\\=\frac{4}{9}-\frac{10}{7}+\frac{1}{6}\\=\frac{56}{126}-\frac{180}{126}+\frac{21}{126}\\=\frac{56-180+21}{126}\\=\frac{-103}{126}\)
9. \(-\left(\frac{-7}{-2}\right) +\left(\frac{-8}{-6}\right) -\left(\frac{-12}{9}\right)\\= \frac{-7}{2}+ \frac{8}{6}+\frac{12}{9}\\=\frac{-7}{2}+\frac{4}{3}+\frac{4}{3}\\=\frac{-21}{6}+\frac{8}{6}+\frac{8}{6}\\=\frac{-21+8+8}{6}\\=\frac{-5}{6}\)
10. \(-\left(\frac{-2}{7}\right) -\left(\frac{5}{10}\right) -\left(\frac{9}{11}\right)\\= \frac{2}{7}- \frac{5}{10}-\frac{9}{11}\\=\frac{2}{7}-\frac{1}{2}-\frac{9}{11}\\=\frac{44}{154}-\frac{77}{154}-\frac{126}{154}\\=\frac{44-77-126}{154}\\=\frac{-159}{154}\)
11. \(-\left(\frac{5}{9}\right) -\left(\frac{2}{7}\right) -\left(\frac{-8}{11}\right)\\= \frac{-5}{9}- \frac{2}{7}+\frac{8}{11}\\=\frac{-385}{693}-\frac{198}{693}+\frac{504}{693}\\=\frac{-385-198+504}{693}\\=\frac{-79}{693}\)
12. \(-\left(\frac{7}{-5}\right) +\left(\frac{-3}{10}\right) +\left(\frac{-11}{-10}\right)\\= \frac{7}{5}- \frac{3}{10}+\frac{11}{10}\\=\frac{14}{10}-\frac{3}{10}+\frac{11}{10}\\=\frac{14-3+11}{10}\\=\frac{22}{10}\\=\frac{11}{5}\)