Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-2}{-9}\right) -\left(\frac{3}{8}\right) -\left(\frac{-12}{3}\right)\\= \frac{2}{9}- \frac{3}{8}+\frac{12}{3}\\=\frac{2}{9}-\frac{3}{8}+\frac{4}{1}\\=\frac{16}{72}-\frac{27}{72}+\frac{288}{72}\\=\frac{16-27+288}{72}\\=\frac{277}{72}\)
2. \(-\left(\frac{-5}{-9}\right) +\left(\frac{2}{-8}\right) +\left(\frac{-9}{9}\right)\\= \frac{-5}{9}- \frac{2}{8}-\frac{9}{9}\\=\frac{-5}{9}-\frac{1}{4}-\frac{1}{1}\\=\frac{-20}{36}-\frac{9}{36}-\frac{36}{36}\\=\frac{-20-9-36}{36}\\=\frac{-65}{36}\)
3. \(+\left(\frac{-4}{-7}\right) -\left(\frac{-10}{-10}\right) +\left(\frac{9}{-6}\right)\\= \frac{4}{7}- \frac{10}{10}-\frac{9}{6}\\=\frac{4}{7}-\frac{1}{1}-\frac{3}{2}\\=\frac{8}{14}-\frac{14}{14}-\frac{21}{14}\\=\frac{8-14-21}{14}\\=\frac{-27}{14}\)
4. \(-\left(\frac{10}{3}\right) -\left(\frac{-5}{-10}\right) +\left(\frac{-10}{-4}\right)\\= \frac{-10}{3}- \frac{5}{10}+\frac{10}{4}\\=\frac{-10}{3}-\frac{1}{2}+\frac{5}{2}\\=\frac{-20}{6}-\frac{3}{6}+\frac{15}{6}\\=\frac{-20-3+15}{6}\\=\frac{-8}{6}\\=\frac{-4}{3}\)
5. \(-\left(\frac{-2}{-9}\right) -\left(\frac{-9}{-5}\right) -\left(\frac{2}{-9}\right)\\= \frac{-2}{9}- \frac{9}{5}+\frac{2}{9}\\=\frac{-10}{45}-\frac{81}{45}+\frac{10}{45}\\=\frac{-10-81+10}{45}\\=\frac{-81}{45}\\=\frac{-9}{5}\)
6. \(+\left(\frac{-7}{6}\right) -\left(\frac{-9}{-4}\right) +\left(\frac{2}{6}\right)\\= \frac{-7}{6}- \frac{9}{4}+\frac{2}{6}\\=\frac{-7}{6}-\frac{9}{4}+\frac{1}{3}\\=\frac{-14}{12}-\frac{27}{12}+\frac{4}{12}\\=\frac{-14-27+4}{12}\\=\frac{-37}{12}\)
7. \(-\left(\frac{-9}{7}\right) +\left(\frac{3}{-8}\right) -\left(\frac{-2}{12}\right)\\= \frac{9}{7}- \frac{3}{8}+\frac{2}{12}\\=\frac{9}{7}-\frac{3}{8}+\frac{1}{6}\\=\frac{216}{168}-\frac{63}{168}+\frac{28}{168}\\=\frac{216-63+28}{168}\\=\frac{181}{168}\)
8. \(-\left(\frac{2}{5}\right) +\left(\frac{5}{-7}\right) -\left(\frac{-9}{-7}\right)\\= \frac{-2}{5}- \frac{5}{7}-\frac{9}{7}\\=\frac{-14}{35}-\frac{25}{35}-\frac{45}{35}\\=\frac{-14-25-45}{35}\\=\frac{-84}{35}\\=\frac{-12}{5}\)
9. \(+\left(\frac{9}{-2}\right) +\left(\frac{6}{10}\right) -\left(\frac{11}{-9}\right)\\= \frac{-9}{2}+ \frac{6}{10}+\frac{11}{9}\\=\frac{-9}{2}+\frac{3}{5}+\frac{11}{9}\\=\frac{-405}{90}+\frac{54}{90}+\frac{110}{90}\\=\frac{-405+54+110}{90}\\=\frac{-241}{90}\)
10. \(+\left(\frac{-9}{-7}\right) +\left(\frac{-10}{10}\right) -\left(\frac{-3}{-10}\right)\\= \frac{9}{7}- \frac{10}{10}-\frac{3}{10}\\=\frac{9}{7}-\frac{1}{1}-\frac{3}{10}\\=\frac{90}{70}-\frac{70}{70}-\frac{21}{70}\\=\frac{90-70-21}{70}\\=\frac{-1}{70}\)
11. \(+\left(\frac{-5}{-7}\right) -\left(\frac{-3}{7}\right) -\left(\frac{9}{8}\right)\\= \frac{5}{7}+ \frac{3}{7}-\frac{9}{8}\\=\frac{40}{56}+\frac{24}{56}-\frac{63}{56}\\=\frac{40+24-63}{56}\\=\frac{1}{56}\)
12. \(-\left(\frac{10}{3}\right) -\left(\frac{-4}{-5}\right) -\left(\frac{-6}{-3}\right)\\= \frac{-10}{3}- \frac{4}{5}-\frac{6}{3}\\=\frac{-10}{3}-\frac{4}{5}-\frac{2}{1}\\=\frac{-50}{15}-\frac{12}{15}-\frac{30}{15}\\=\frac{-50-12-30}{15}\\=\frac{-92}{15}\)