Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{3}\right) +\left(\frac{-6}{2}\right) -\left(\frac{8}{-12}\right)\\= \frac{-10}{3}- \frac{6}{2}+\frac{8}{12}\\=\frac{-10}{3}-\frac{3}{1}+\frac{2}{3}\\=\frac{-10-3+2}{3}\\=\frac{-11}{3}\)
2. \(-\left(\frac{8}{-3}\right) -\left(\frac{-8}{7}\right) -\left(\frac{-6}{-8}\right)\\= \frac{8}{3}+ \frac{8}{7}-\frac{6}{8}\\=\frac{8}{3}+\frac{8}{7}-\frac{3}{4}\\=\frac{224}{84}+\frac{96}{84}-\frac{63}{84}\\=\frac{224+96-63}{84}\\=\frac{257}{84}\)
3. \(+\left(\frac{-2}{-5}\right) -\left(\frac{-9}{-9}\right) -\left(\frac{10}{-8}\right)\\= \frac{2}{5}- \frac{9}{9}+\frac{10}{8}\\=\frac{2}{5}-\frac{1}{1}+\frac{5}{4}\\=\frac{8}{20}-\frac{20}{20}+\frac{25}{20}\\=\frac{8-20+25}{20}\\=\frac{13}{20}\)
4. \(+\left(\frac{-3}{-2}\right) +\left(\frac{-7}{-9}\right) -\left(\frac{-12}{-3}\right)\\= \frac{3}{2}+ \frac{7}{9}-\frac{12}{3}\\=\frac{3}{2}+\frac{7}{9}-\frac{4}{1}\\=\frac{27}{18}+\frac{14}{18}-\frac{72}{18}\\=\frac{27+14-72}{18}\\=\frac{-31}{18}\)
5. \(+\left(\frac{2}{-7}\right) +\left(\frac{10}{2}\right) -\left(\frac{-2}{-3}\right)\\= \frac{-2}{7}+ \frac{10}{2}-\frac{2}{3}\\=\frac{-2}{7}+\frac{5}{1}-\frac{2}{3}\\=\frac{-6}{21}+\frac{105}{21}-\frac{14}{21}\\=\frac{-6+105-14}{21}\\=\frac{85}{21}\)
6. \(-\left(\frac{-10}{-7}\right) -\left(\frac{6}{-4}\right) -\left(\frac{-3}{-12}\right)\\= \frac{-10}{7}+ \frac{6}{4}-\frac{3}{12}\\=\frac{-10}{7}+\frac{3}{2}-\frac{1}{4}\\=\frac{-40}{28}+\frac{42}{28}-\frac{7}{28}\\=\frac{-40+42-7}{28}\\=\frac{-5}{28}\)
7. \(-\left(\frac{9}{2}\right) +\left(\frac{-4}{-9}\right) -\left(\frac{-6}{4}\right)\\= \frac{-9}{2}+ \frac{4}{9}+\frac{6}{4}\\=\frac{-9}{2}+\frac{4}{9}+\frac{3}{2}\\=\frac{-81}{18}+\frac{8}{18}+\frac{27}{18}\\=\frac{-81+8+27}{18}\\=\frac{-46}{18}\\=\frac{-23}{9}\)
8. \(+\left(\frac{6}{5}\right) -\left(\frac{-3}{-4}\right) +\left(\frac{-3}{-10}\right)\\= \frac{6}{5}- \frac{3}{4}+\frac{3}{10}\\=\frac{24}{20}-\frac{15}{20}+\frac{6}{20}\\=\frac{24-15+6}{20}\\=\frac{15}{20}\\=\frac{3}{4}\)
9. \(-\left(\frac{9}{-2}\right) -\left(\frac{9}{6}\right) +\left(\frac{-12}{6}\right)\\= \frac{9}{2}- \frac{9}{6}-\frac{12}{6}\\=\frac{9}{2}-\frac{3}{2}-\frac{2}{1}\\=\frac{9-3-2}{2}\\=\frac{4}{2}\\=\frac{2}{1}\)
10. \(-\left(\frac{-10}{7}\right) -\left(\frac{10}{10}\right) +\left(\frac{10}{-4}\right)\\= \frac{10}{7}- \frac{10}{10}-\frac{10}{4}\\=\frac{10}{7}-\frac{1}{1}-\frac{5}{2}\\=\frac{20}{14}-\frac{14}{14}-\frac{35}{14}\\=\frac{20-14-35}{14}\\=\frac{-29}{14}\)
11. \(-\left(\frac{-6}{-5}\right) +\left(\frac{-4}{4}\right) +\left(\frac{12}{9}\right)\\= \frac{-6}{5}- \frac{4}{4}+\frac{12}{9}\\=\frac{-6}{5}-\frac{1}{1}+\frac{4}{3}\\=\frac{-18}{15}-\frac{15}{15}+\frac{20}{15}\\=\frac{-18-15+20}{15}\\=\frac{-13}{15}\)
12. \(+\left(\frac{-4}{5}\right) -\left(\frac{-6}{-7}\right) -\left(\frac{-10}{10}\right)\\= \frac{-4}{5}- \frac{6}{7}+\frac{10}{10}\\=\frac{-4}{5}-\frac{6}{7}+\frac{1}{1}\\=\frac{-28}{35}-\frac{30}{35}+\frac{35}{35}\\=\frac{-28-30+35}{35}\\=\frac{-23}{35}\)