Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{-9}\right) -\left(\frac{8}{-6}\right) +\left(\frac{-12}{-6}\right)\\= \frac{-10}{9}+ \frac{8}{6}+\frac{12}{6}\\=\frac{-10}{9}+\frac{4}{3}+\frac{2}{1}\\=\frac{-10+4+2}{9}\\=\frac{-4}{9}\)
2. \(-\left(\frac{-4}{-5}\right) -\left(\frac{8}{-2}\right) -\left(\frac{3}{12}\right)\\= \frac{-4}{5}+ \frac{8}{2}-\frac{3}{12}\\=\frac{-4}{5}+\frac{4}{1}-\frac{1}{4}\\=\frac{-16}{20}+\frac{80}{20}-\frac{5}{20}\\=\frac{-16+80-5}{20}\\=\frac{59}{20}\)
3. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-3}{-10}\right) +\left(\frac{-5}{5}\right)\\= \frac{6}{5}- \frac{3}{10}-\frac{5}{5}\\=\frac{6}{5}-\frac{3}{10}-\frac{1}{1}\\=\frac{12}{10}-\frac{3}{10}-\frac{10}{10}\\=\frac{12-3-10}{10}\\=\frac{-1}{10}\)
4. \(-\left(\frac{9}{2}\right) +\left(\frac{6}{6}\right) +\left(\frac{6}{12}\right)\\= \frac{-9}{2}+ \frac{6}{6}+\frac{6}{12}\\=\frac{-9}{2}+\frac{1}{1}+\frac{1}{2}\\=\frac{-9+1+1}{2}\\=\frac{-7}{2}\)
5. \(-\left(\frac{6}{5}\right) +\left(\frac{3}{8}\right) +\left(\frac{-8}{-4}\right)\\= \frac{-6}{5}+ \frac{3}{8}+\frac{8}{4}\\=\frac{-6}{5}+\frac{3}{8}+\frac{2}{1}\\=\frac{-48}{40}+\frac{15}{40}+\frac{80}{40}\\=\frac{-48+15+80}{40}\\=\frac{47}{40}\)
6. \(-\left(\frac{3}{-2}\right) -\left(\frac{-9}{-3}\right) +\left(\frac{-2}{9}\right)\\= \frac{3}{2}- \frac{9}{3}-\frac{2}{9}\\=\frac{3}{2}-\frac{3}{1}-\frac{2}{9}\\=\frac{27}{18}-\frac{54}{18}-\frac{4}{18}\\=\frac{27-54-4}{18}\\=\frac{-31}{18}\)
7. \(-\left(\frac{-2}{-7}\right) +\left(\frac{10}{4}\right) -\left(\frac{-2}{5}\right)\\= \frac{-2}{7}+ \frac{10}{4}+\frac{2}{5}\\=\frac{-2}{7}+\frac{5}{2}+\frac{2}{5}\\=\frac{-20}{70}+\frac{175}{70}+\frac{28}{70}\\=\frac{-20+175+28}{70}\\=\frac{183}{70}\)
8. \(+\left(\frac{6}{-7}\right) -\left(\frac{2}{-10}\right) -\left(\frac{4}{4}\right)\\= \frac{-6}{7}+ \frac{2}{10}-\frac{4}{4}\\=\frac{-6}{7}+\frac{1}{5}-\frac{1}{1}\\=\frac{-30}{35}+\frac{7}{35}-\frac{35}{35}\\=\frac{-30+7-35}{35}\\=\frac{-58}{35}\)
9. \(+\left(\frac{-4}{9}\right) -\left(\frac{10}{10}\right) -\left(\frac{-8}{5}\right)\\= \frac{-4}{9}- \frac{10}{10}+\frac{8}{5}\\=\frac{-4}{9}-\frac{1}{1}+\frac{8}{5}\\=\frac{-20}{45}-\frac{45}{45}+\frac{72}{45}\\=\frac{-20-45+72}{45}\\=\frac{7}{45}\)
10. \(-\left(\frac{-2}{-5}\right) +\left(\frac{-8}{-10}\right) +\left(\frac{-4}{-9}\right)\\= \frac{-2}{5}+ \frac{8}{10}+\frac{4}{9}\\=\frac{-2}{5}+\frac{4}{5}+\frac{4}{9}\\=\frac{-18}{45}+\frac{36}{45}+\frac{20}{45}\\=\frac{-18+36+20}{45}\\=\frac{38}{45}\)
11. \(-\left(\frac{-8}{-5}\right) +\left(\frac{-10}{7}\right) +\left(\frac{-9}{-8}\right)\\= \frac{-8}{5}- \frac{10}{7}+\frac{9}{8}\\=\frac{-448}{280}-\frac{400}{280}+\frac{315}{280}\\=\frac{-448-400+315}{280}\\=\frac{-533}{280}\)
12. \(-\left(\frac{8}{7}\right) +\left(\frac{4}{9}\right) +\left(\frac{6}{-12}\right)\\= \frac{-8}{7}+ \frac{4}{9}-\frac{6}{12}\\=\frac{-8}{7}+\frac{4}{9}-\frac{1}{2}\\=\frac{-144}{126}+\frac{56}{126}-\frac{63}{126}\\=\frac{-144+56-63}{126}\\=\frac{-151}{126}\)