Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{8}{-3}\right) -\left(\frac{6}{5}\right) -\left(\frac{-5}{9}\right)\\= \frac{-8}{3}- \frac{6}{5}+\frac{5}{9}\\=\frac{-120}{45}-\frac{54}{45}+\frac{25}{45}\\=\frac{-120-54+25}{45}\\=\frac{-149}{45}\)
2. \(+\left(\frac{-8}{-3}\right) -\left(\frac{10}{-5}\right) +\left(\frac{6}{6}\right)\\= \frac{8}{3}+ \frac{10}{5}+\frac{6}{6}\\=\frac{8}{3}+\frac{2}{1}+\frac{1}{1}\\=\frac{8+2+1}{3}\\=\frac{11}{3}\)
3. \(-\left(\frac{3}{2}\right) +\left(\frac{4}{10}\right) -\left(\frac{9}{9}\right)\\= \frac{-3}{2}+ \frac{4}{10}-\frac{9}{9}\\=\frac{-3}{2}+\frac{2}{5}-\frac{1}{1}\\=\frac{-15}{10}+\frac{4}{10}-\frac{10}{10}\\=\frac{-15+4-10}{10}\\=\frac{-21}{10}\)
4. \(-\left(\frac{6}{5}\right) -\left(\frac{-10}{9}\right) +\left(\frac{10}{-12}\right)\\= \frac{-6}{5}+ \frac{10}{9}-\frac{10}{12}\\=\frac{-6}{5}+\frac{10}{9}-\frac{5}{6}\\=\frac{-108}{90}+\frac{100}{90}-\frac{75}{90}\\=\frac{-108+100-75}{90}\\=\frac{-83}{90}\)
5. \(+\left(\frac{-2}{-5}\right) -\left(\frac{4}{8}\right) +\left(\frac{9}{8}\right)\\= \frac{2}{5}- \frac{4}{8}+\frac{9}{8}\\=\frac{2}{5}-\frac{1}{2}+\frac{9}{8}\\=\frac{16}{40}-\frac{20}{40}+\frac{45}{40}\\=\frac{16-20+45}{40}\\=\frac{41}{40}\)
6. \(-\left(\frac{-5}{-7}\right) -\left(\frac{5}{-9}\right) +\left(\frac{11}{-6}\right)\\= \frac{-5}{7}+ \frac{5}{9}-\frac{11}{6}\\=\frac{-90}{126}+\frac{70}{126}-\frac{231}{126}\\=\frac{-90+70-231}{126}\\=\frac{-251}{126}\)
7. \(-\left(\frac{2}{9}\right) -\left(\frac{-2}{6}\right) +\left(\frac{6}{5}\right)\\= \frac{-2}{9}+ \frac{2}{6}+\frac{6}{5}\\=\frac{-2}{9}+\frac{1}{3}+\frac{6}{5}\\=\frac{-10}{45}+\frac{15}{45}+\frac{54}{45}\\=\frac{-10+15+54}{45}\\=\frac{59}{45}\)
8. \(+\left(\frac{6}{5}\right) +\left(\frac{7}{-3}\right) +\left(\frac{-12}{12}\right)\\= \frac{6}{5}- \frac{7}{3}-\frac{12}{12}\\=\frac{6}{5}-\frac{7}{3}-\frac{1}{1}\\=\frac{18}{15}-\frac{35}{15}-\frac{15}{15}\\=\frac{18-35-15}{15}\\=\frac{-32}{15}\)
9. \(-\left(\frac{-10}{7}\right) +\left(\frac{-9}{-8}\right) -\left(\frac{-5}{12}\right)\\= \frac{10}{7}+ \frac{9}{8}+\frac{5}{12}\\=\frac{240}{168}+\frac{189}{168}+\frac{70}{168}\\=\frac{240+189+70}{168}\\=\frac{499}{168}\)
10. \(-\left(\frac{5}{-6}\right) +\left(\frac{3}{-6}\right) +\left(\frac{6}{11}\right)\\= \frac{5}{6}- \frac{3}{6}+\frac{6}{11}\\=\frac{5}{6}-\frac{1}{2}+\frac{6}{11}\\=\frac{55}{66}-\frac{33}{66}+\frac{36}{66}\\=\frac{55-33+36}{66}\\=\frac{58}{66}\\=\frac{29}{33}\)
11. \(+\left(\frac{-8}{-9}\right) -\left(\frac{2}{10}\right) -\left(\frac{9}{-6}\right)\\= \frac{8}{9}- \frac{2}{10}+\frac{9}{6}\\=\frac{8}{9}-\frac{1}{5}+\frac{3}{2}\\=\frac{80}{90}-\frac{18}{90}+\frac{135}{90}\\=\frac{80-18+135}{90}\\=\frac{197}{90}\)
12. \(-\left(\frac{10}{3}\right) -\left(\frac{-6}{-10}\right) -\left(\frac{9}{-4}\right)\\= \frac{-10}{3}- \frac{6}{10}+\frac{9}{4}\\=\frac{-10}{3}-\frac{3}{5}+\frac{9}{4}\\=\frac{-200}{60}-\frac{36}{60}+\frac{135}{60}\\=\frac{-200-36+135}{60}\\=\frac{-101}{60}\)