Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-2}{-9}\right) -\left(\frac{8}{8}\right) +\left(\frac{-7}{-5}\right)\\= \frac{-2}{9}- \frac{8}{8}+\frac{7}{5}\\=\frac{-2}{9}-\frac{1}{1}+\frac{7}{5}\\=\frac{-10}{45}-\frac{45}{45}+\frac{63}{45}\\=\frac{-10-45+63}{45}\\=\frac{8}{45}\)
2. \(-\left(\frac{-4}{3}\right) -\left(\frac{7}{-8}\right) -\left(\frac{-3}{3}\right)\\= \frac{4}{3}+ \frac{7}{8}+\frac{3}{3}\\=\frac{4}{3}+\frac{7}{8}+\frac{1}{1}\\=\frac{32}{24}+\frac{21}{24}+\frac{24}{24}\\=\frac{32+21+24}{24}\\=\frac{77}{24}\)
3. \(+\left(\frac{-7}{-2}\right) -\left(\frac{-4}{9}\right) -\left(\frac{8}{-4}\right)\\= \frac{7}{2}+ \frac{4}{9}+\frac{8}{4}\\=\frac{7}{2}+\frac{4}{9}+\frac{2}{1}\\=\frac{63}{18}+\frac{8}{18}+\frac{36}{18}\\=\frac{63+8+36}{18}\\=\frac{107}{18}\)
4. \(-\left(\frac{9}{5}\right) -\left(\frac{-6}{7}\right) +\left(\frac{-12}{10}\right)\\= \frac{-9}{5}+ \frac{6}{7}-\frac{12}{10}\\=\frac{-9}{5}+\frac{6}{7}-\frac{6}{5}\\=\frac{-63}{35}+\frac{30}{35}-\frac{42}{35}\\=\frac{-63+30-42}{35}\\=\frac{-75}{35}\\=\frac{-15}{7}\)
5. \(+\left(\frac{9}{7}\right) -\left(\frac{-6}{-6}\right) -\left(\frac{-7}{4}\right)\\= \frac{9}{7}- \frac{6}{6}+\frac{7}{4}\\=\frac{9}{7}-\frac{1}{1}+\frac{7}{4}\\=\frac{36}{28}-\frac{28}{28}+\frac{49}{28}\\=\frac{36-28+49}{28}\\=\frac{57}{28}\)
6. \(+\left(\frac{-3}{-2}\right) +\left(\frac{-7}{2}\right) -\left(\frac{11}{11}\right)\\= \frac{3}{2}- \frac{7}{2}-\frac{11}{11}\\=\frac{3}{2}-\frac{7}{2}-\frac{1}{1}\\=\frac{3-7-1}{2}\\=\frac{-5}{2}\)
7. \(+\left(\frac{3}{2}\right) +\left(\frac{-8}{-8}\right) +\left(\frac{12}{7}\right)\\= \frac{3}{2}+ \frac{8}{8}+\frac{12}{7}\\=\frac{3}{2}+\frac{1}{1}+\frac{12}{7}\\=\frac{21}{14}+\frac{14}{14}+\frac{24}{14}\\=\frac{21+14+24}{14}\\=\frac{59}{14}\)
8. \(-\left(\frac{-6}{5}\right) +\left(\frac{5}{-9}\right) +\left(\frac{-8}{12}\right)\\= \frac{6}{5}- \frac{5}{9}-\frac{8}{12}\\=\frac{6}{5}-\frac{5}{9}-\frac{2}{3}\\=\frac{54}{45}-\frac{25}{45}-\frac{30}{45}\\=\frac{54-25-30}{45}\\=\frac{-1}{45}\)
9. \(-\left(\frac{6}{5}\right) +\left(\frac{5}{10}\right) -\left(\frac{11}{10}\right)\\= \frac{-6}{5}+ \frac{5}{10}-\frac{11}{10}\\=\frac{-6}{5}+\frac{1}{2}-\frac{11}{10}\\=\frac{-12}{10}+\frac{5}{10}-\frac{11}{10}\\=\frac{-12+5-11}{10}\\=\frac{-18}{10}\\=\frac{-9}{5}\)
10. \(-\left(\frac{6}{7}\right) -\left(\frac{-10}{8}\right) +\left(\frac{-5}{12}\right)\\= \frac{-6}{7}+ \frac{10}{8}-\frac{5}{12}\\=\frac{-6}{7}+\frac{5}{4}-\frac{5}{12}\\=\frac{-72}{84}+\frac{105}{84}-\frac{35}{84}\\=\frac{-72+105-35}{84}\\=\frac{-2}{84}\\=\frac{-1}{42}\)
11. \(+\left(\frac{10}{7}\right) +\left(\frac{-9}{-5}\right) +\left(\frac{12}{12}\right)\\= \frac{10}{7}+ \frac{9}{5}+\frac{12}{12}\\=\frac{10}{7}+\frac{9}{5}+\frac{1}{1}\\=\frac{50}{35}+\frac{63}{35}+\frac{35}{35}\\=\frac{50+63+35}{35}\\=\frac{148}{35}\)
12. \(+\left(\frac{10}{7}\right) +\left(\frac{-9}{-3}\right) +\left(\frac{-5}{-6}\right)\\= \frac{10}{7}+ \frac{9}{3}+\frac{5}{6}\\=\frac{10}{7}+\frac{3}{1}+\frac{5}{6}\\=\frac{60}{42}+\frac{126}{42}+\frac{35}{42}\\=\frac{60+126+35}{42}\\=\frac{221}{42}\)