Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{6}{-7}\right) -\left(\frac{10}{10}\right) -\left(\frac{5}{10}\right)\\= \frac{-6}{7}- \frac{10}{10}-\frac{5}{10}\\=\frac{-6}{7}-\frac{1}{1}-\frac{1}{2}\\=\frac{-12}{14}-\frac{14}{14}-\frac{7}{14}\\=\frac{-12-14-7}{14}\\=\frac{-33}{14}\)
2. \(-\left(\frac{-9}{8}\right) -\left(\frac{-6}{9}\right) +\left(\frac{-11}{8}\right)\\= \frac{9}{8}+ \frac{6}{9}-\frac{11}{8}\\=\frac{9}{8}+\frac{2}{3}-\frac{11}{8}\\=\frac{27}{24}+\frac{16}{24}-\frac{33}{24}\\=\frac{27+16-33}{24}\\=\frac{10}{24}\\=\frac{5}{12}\)
3. \(+\left(\frac{4}{-9}\right) +\left(\frac{-3}{7}\right) -\left(\frac{8}{11}\right)\\= \frac{-4}{9}- \frac{3}{7}-\frac{8}{11}\\=\frac{-308}{693}-\frac{297}{693}-\frac{504}{693}\\=\frac{-308-297-504}{693}\\=\frac{-1109}{693}\)
4. \(-\left(\frac{2}{-7}\right) -\left(\frac{10}{-8}\right) -\left(\frac{2}{-5}\right)\\= \frac{2}{7}+ \frac{10}{8}+\frac{2}{5}\\=\frac{2}{7}+\frac{5}{4}+\frac{2}{5}\\=\frac{40}{140}+\frac{175}{140}+\frac{56}{140}\\=\frac{40+175+56}{140}\\=\frac{271}{140}\)
5. \(+\left(\frac{-5}{7}\right) -\left(\frac{-10}{-5}\right) +\left(\frac{-11}{11}\right)\\= \frac{-5}{7}- \frac{10}{5}-\frac{11}{11}\\=\frac{-5}{7}-\frac{2}{1}-\frac{1}{1}\\=\frac{-5-2-1}{7}\\=\frac{-8}{7}\)
6. \(-\left(\frac{-10}{9}\right) -\left(\frac{-9}{-6}\right) +\left(\frac{-9}{7}\right)\\= \frac{10}{9}- \frac{9}{6}-\frac{9}{7}\\=\frac{10}{9}-\frac{3}{2}-\frac{9}{7}\\=\frac{140}{126}-\frac{189}{126}-\frac{162}{126}\\=\frac{140-189-162}{126}\\=\frac{-211}{126}\)
7. \(-\left(\frac{6}{-5}\right) -\left(\frac{-10}{-2}\right) -\left(\frac{-11}{9}\right)\\= \frac{6}{5}- \frac{10}{2}+\frac{11}{9}\\=\frac{6}{5}-\frac{5}{1}+\frac{11}{9}\\=\frac{54}{45}-\frac{225}{45}+\frac{55}{45}\\=\frac{54-225+55}{45}\\=\frac{-116}{45}\)
8. \(-\left(\frac{4}{-3}\right) +\left(\frac{4}{-10}\right) -\left(\frac{11}{-5}\right)\\= \frac{4}{3}- \frac{4}{10}+\frac{11}{5}\\=\frac{4}{3}-\frac{2}{5}+\frac{11}{5}\\=\frac{20}{15}-\frac{6}{15}+\frac{33}{15}\\=\frac{20-6+33}{15}\\=\frac{47}{15}\)
9. \(-\left(\frac{7}{2}\right) +\left(\frac{-8}{9}\right) -\left(\frac{-12}{8}\right)\\= \frac{-7}{2}- \frac{8}{9}+\frac{12}{8}\\=\frac{-7}{2}-\frac{8}{9}+\frac{3}{2}\\=\frac{-63}{18}-\frac{16}{18}+\frac{27}{18}\\=\frac{-63-16+27}{18}\\=\frac{-52}{18}\\=\frac{-26}{9}\)
10. \(+\left(\frac{7}{-2}\right) -\left(\frac{-5}{-6}\right) +\left(\frac{8}{-10}\right)\\= \frac{-7}{2}- \frac{5}{6}-\frac{8}{10}\\=\frac{-7}{2}-\frac{5}{6}-\frac{4}{5}\\=\frac{-105}{30}-\frac{25}{30}-\frac{24}{30}\\=\frac{-105-25-24}{30}\\=\frac{-154}{30}\\=\frac{-77}{15}\)
11. \(-\left(\frac{-3}{2}\right) +\left(\frac{4}{4}\right) +\left(\frac{6}{-9}\right)\\= \frac{3}{2}+ \frac{4}{4}-\frac{6}{9}\\=\frac{3}{2}+\frac{1}{1}-\frac{2}{3}\\=\frac{9}{6}+\frac{6}{6}-\frac{4}{6}\\=\frac{9+6-4}{6}\\=\frac{11}{6}\)
12. \(-\left(\frac{-4}{-3}\right) -\left(\frac{-2}{9}\right) +\left(\frac{-4}{-3}\right)\\= \frac{-4}{3}+ \frac{2}{9}+\frac{4}{3}\\=\frac{-12}{9}+\frac{2}{9}+\frac{12}{9}\\=\frac{-12+2+12}{9}\\=\frac{2}{9}\)