Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-5}{8}\right) -\left(\frac{9}{2}\right) -\left(\frac{11}{9}\right)\\= \frac{5}{8}- \frac{9}{2}-\frac{11}{9}\\=\frac{45}{72}-\frac{324}{72}-\frac{88}{72}\\=\frac{45-324-88}{72}\\=\frac{-367}{72}\)
2. \(-\left(\frac{-6}{5}\right) -\left(\frac{-4}{6}\right) -\left(\frac{-11}{-3}\right)\\= \frac{6}{5}+ \frac{4}{6}-\frac{11}{3}\\=\frac{6}{5}+\frac{2}{3}-\frac{11}{3}\\=\frac{18}{15}+\frac{10}{15}-\frac{55}{15}\\=\frac{18+10-55}{15}\\=\frac{-27}{15}\\=\frac{-9}{5}\)
3. \(-\left(\frac{-10}{-7}\right) -\left(\frac{10}{7}\right) -\left(\frac{5}{7}\right)\\= \frac{-10}{7}- \frac{10}{7}-\frac{5}{7}\\=\frac{-10-10-5}{7}\\=\frac{-25}{7}\)
4. \(+\left(\frac{5}{4}\right) +\left(\frac{4}{2}\right) -\left(\frac{10}{4}\right)\\= \frac{5}{4}+ \frac{4}{2}-\frac{10}{4}\\=\frac{5}{4}+\frac{2}{1}-\frac{5}{2}\\=\frac{5+2-5}{4}\\=\frac{2}{4}\\=\frac{1}{2}\)
5. \(+\left(\frac{5}{-7}\right) +\left(\frac{-4}{7}\right) -\left(\frac{11}{-2}\right)\\= \frac{-5}{7}- \frac{4}{7}+\frac{11}{2}\\=\frac{-10}{14}-\frac{8}{14}+\frac{77}{14}\\=\frac{-10-8+77}{14}\\=\frac{59}{14}\)
6. \(+\left(\frac{3}{7}\right) +\left(\frac{5}{-2}\right) +\left(\frac{-4}{10}\right)\\= \frac{3}{7}- \frac{5}{2}-\frac{4}{10}\\=\frac{3}{7}-\frac{5}{2}-\frac{2}{5}\\=\frac{30}{70}-\frac{175}{70}-\frac{28}{70}\\=\frac{30-175-28}{70}\\=\frac{-173}{70}\)
7. \(-\left(\frac{7}{2}\right) +\left(\frac{-8}{9}\right) +\left(\frac{10}{11}\right)\\= \frac{-7}{2}- \frac{8}{9}+\frac{10}{11}\\=\frac{-693}{198}-\frac{176}{198}+\frac{180}{198}\\=\frac{-693-176+180}{198}\\=\frac{-689}{198}\)
8. \(-\left(\frac{9}{7}\right) +\left(\frac{9}{-9}\right) +\left(\frac{5}{10}\right)\\= \frac{-9}{7}- \frac{9}{9}+\frac{5}{10}\\=\frac{-9}{7}-\frac{1}{1}+\frac{1}{2}\\=\frac{-18}{14}-\frac{14}{14}+\frac{7}{14}\\=\frac{-18-14+7}{14}\\=\frac{-25}{14}\)
9. \(-\left(\frac{6}{-5}\right) +\left(\frac{4}{-10}\right) -\left(\frac{6}{11}\right)\\= \frac{6}{5}- \frac{4}{10}-\frac{6}{11}\\=\frac{6}{5}-\frac{2}{5}-\frac{6}{11}\\=\frac{66}{55}-\frac{22}{55}-\frac{30}{55}\\=\frac{66-22-30}{55}\\=\frac{14}{55}\)
10. \(-\left(\frac{-3}{2}\right) +\left(\frac{-4}{9}\right) +\left(\frac{-2}{-6}\right)\\= \frac{3}{2}- \frac{4}{9}+\frac{2}{6}\\=\frac{3}{2}-\frac{4}{9}+\frac{1}{3}\\=\frac{27}{18}-\frac{8}{18}+\frac{6}{18}\\=\frac{27-8+6}{18}\\=\frac{25}{18}\)
11. \(-\left(\frac{-6}{-5}\right) -\left(\frac{-4}{-6}\right) -\left(\frac{-4}{3}\right)\\= \frac{-6}{5}- \frac{4}{6}+\frac{4}{3}\\=\frac{-6}{5}-\frac{2}{3}+\frac{4}{3}\\=\frac{-18}{15}-\frac{10}{15}+\frac{20}{15}\\=\frac{-18-10+20}{15}\\=\frac{-8}{15}\)
12. \(+\left(\frac{4}{3}\right) +\left(\frac{8}{-3}\right) -\left(\frac{2}{11}\right)\\= \frac{4}{3}- \frac{8}{3}-\frac{2}{11}\\=\frac{44}{33}-\frac{88}{33}-\frac{6}{33}\\=\frac{44-88-6}{33}\\=\frac{-50}{33}\)