Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{3}{2}\right) +\left(\frac{-8}{-9}\right) -\left(\frac{-5}{6}\right)\\= \frac{-3}{2}+ \frac{8}{9}+\frac{5}{6}\\=\frac{-27}{18}+\frac{16}{18}+\frac{15}{18}\\=\frac{-27+16+15}{18}\\=\frac{4}{18}\\=\frac{2}{9}\)
2. \(-\left(\frac{9}{2}\right) -\left(\frac{-8}{7}\right) -\left(\frac{-4}{8}\right)\\= \frac{-9}{2}+ \frac{8}{7}+\frac{4}{8}\\=\frac{-9}{2}+\frac{8}{7}+\frac{1}{2}\\=\frac{-63}{14}+\frac{16}{14}+\frac{7}{14}\\=\frac{-63+16+7}{14}\\=\frac{-40}{14}\\=\frac{-20}{7}\)
3. \(+\left(\frac{-5}{6}\right) -\left(\frac{-5}{10}\right) -\left(\frac{3}{-5}\right)\\= \frac{-5}{6}+ \frac{5}{10}+\frac{3}{5}\\=\frac{-5}{6}+\frac{1}{2}+\frac{3}{5}\\=\frac{-25}{30}+\frac{15}{30}+\frac{18}{30}\\=\frac{-25+15+18}{30}\\=\frac{8}{30}\\=\frac{4}{15}\)
4. \(+\left(\frac{-7}{2}\right) +\left(\frac{5}{-9}\right) -\left(\frac{-5}{10}\right)\\= \frac{-7}{2}- \frac{5}{9}+\frac{5}{10}\\=\frac{-7}{2}-\frac{5}{9}+\frac{1}{2}\\=\frac{-63}{18}-\frac{10}{18}+\frac{9}{18}\\=\frac{-63-10+9}{18}\\=\frac{-64}{18}\\=\frac{-32}{9}\)
5. \(+\left(\frac{6}{5}\right) +\left(\frac{5}{-3}\right) -\left(\frac{-3}{-11}\right)\\= \frac{6}{5}- \frac{5}{3}-\frac{3}{11}\\=\frac{198}{165}-\frac{275}{165}-\frac{45}{165}\\=\frac{198-275-45}{165}\\=\frac{-122}{165}\)
6. \(+\left(\frac{2}{9}\right) +\left(\frac{-4}{5}\right) -\left(\frac{7}{9}\right)\\= \frac{2}{9}- \frac{4}{5}-\frac{7}{9}\\=\frac{10}{45}-\frac{36}{45}-\frac{35}{45}\\=\frac{10-36-35}{45}\\=\frac{-61}{45}\)
7. \(-\left(\frac{6}{-5}\right) +\left(\frac{-10}{-10}\right) -\left(\frac{7}{4}\right)\\= \frac{6}{5}+ \frac{10}{10}-\frac{7}{4}\\=\frac{6}{5}+\frac{1}{1}-\frac{7}{4}\\=\frac{24}{20}+\frac{20}{20}-\frac{35}{20}\\=\frac{24+20-35}{20}\\=\frac{9}{20}\)
8. \(+\left(\frac{-5}{-6}\right) -\left(\frac{7}{3}\right) -\left(\frac{-9}{-9}\right)\\= \frac{5}{6}- \frac{7}{3}-\frac{9}{9}\\=\frac{5}{6}-\frac{7}{3}-\frac{1}{1}\\=\frac{5-7-1}{6}\\=\frac{-3}{6}\\=\frac{-1}{2}\)
9. \(+\left(\frac{8}{3}\right) +\left(\frac{10}{8}\right) +\left(\frac{-3}{4}\right)\\= \frac{8}{3}+ \frac{10}{8}-\frac{3}{4}\\=\frac{8}{3}+\frac{5}{4}-\frac{3}{4}\\=\frac{32}{12}+\frac{15}{12}-\frac{9}{12}\\=\frac{32+15-9}{12}\\=\frac{38}{12}\\=\frac{19}{6}\)
10. \(-\left(\frac{-9}{-4}\right) +\left(\frac{-6}{3}\right) -\left(\frac{4}{3}\right)\\= \frac{-9}{4}- \frac{6}{3}-\frac{4}{3}\\=\frac{-9}{4}-\frac{2}{1}-\frac{4}{3}\\=\frac{-27}{12}-\frac{24}{12}-\frac{16}{12}\\=\frac{-27-24-16}{12}\\=\frac{-67}{12}\)
11. \(-\left(\frac{-3}{2}\right) -\left(\frac{-10}{10}\right) -\left(\frac{-10}{12}\right)\\= \frac{3}{2}+ \frac{10}{10}+\frac{10}{12}\\=\frac{3}{2}+\frac{1}{1}+\frac{5}{6}\\=\frac{9}{6}+\frac{6}{6}+\frac{5}{6}\\=\frac{9+6+5}{6}\\=\frac{20}{6}\\=\frac{10}{3}\)
12. \(+\left(\frac{2}{5}\right) +\left(\frac{10}{7}\right) -\left(\frac{12}{7}\right)\\= \frac{2}{5}+ \frac{10}{7}-\frac{12}{7}\\=\frac{14}{35}+\frac{50}{35}-\frac{60}{35}\\=\frac{14+50-60}{35}\\=\frac{4}{35}\)