Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{4}{-3}\right) +\left(\frac{4}{-5}\right) -\left(\frac{-6}{12}\right)\\= \frac{-4}{3}- \frac{4}{5}+\frac{6}{12}\\=\frac{-4}{3}-\frac{4}{5}+\frac{1}{2}\\=\frac{-40}{30}-\frac{24}{30}+\frac{15}{30}\\=\frac{-40-24+15}{30}\\=\frac{-49}{30}\)
2. \(+\left(\frac{-6}{-5}\right) +\left(\frac{8}{-8}\right) -\left(\frac{-2}{-4}\right)\\= \frac{6}{5}- \frac{8}{8}-\frac{2}{4}\\=\frac{6}{5}-\frac{1}{1}-\frac{1}{2}\\=\frac{12}{10}-\frac{10}{10}-\frac{5}{10}\\=\frac{12-10-5}{10}\\=\frac{-3}{10}\)
3. \(+\left(\frac{-7}{-8}\right) +\left(\frac{3}{-2}\right) +\left(\frac{7}{8}\right)\\= \frac{7}{8}- \frac{3}{2}+\frac{7}{8}\\=\frac{7-3+7}{8}\\=\frac{11}{8}\)
4. \(-\left(\frac{-7}{-4}\right) +\left(\frac{-2}{10}\right) +\left(\frac{-2}{-7}\right)\\= \frac{-7}{4}- \frac{2}{10}+\frac{2}{7}\\=\frac{-7}{4}-\frac{1}{5}+\frac{2}{7}\\=\frac{-245}{140}-\frac{28}{140}+\frac{40}{140}\\=\frac{-245-28+40}{140}\\=\frac{-233}{140}\)
5. \(+\left(\frac{10}{9}\right) +\left(\frac{-9}{-8}\right) +\left(\frac{-3}{5}\right)\\= \frac{10}{9}+ \frac{9}{8}-\frac{3}{5}\\=\frac{400}{360}+\frac{405}{360}-\frac{216}{360}\\=\frac{400+405-216}{360}\\=\frac{589}{360}\)
6. \(+\left(\frac{5}{8}\right) -\left(\frac{-10}{-2}\right) +\left(\frac{-12}{5}\right)\\= \frac{5}{8}- \frac{10}{2}-\frac{12}{5}\\=\frac{5}{8}-\frac{5}{1}-\frac{12}{5}\\=\frac{25}{40}-\frac{200}{40}-\frac{96}{40}\\=\frac{25-200-96}{40}\\=\frac{-271}{40}\)
7. \(+\left(\frac{7}{-2}\right) +\left(\frac{-10}{5}\right) +\left(\frac{11}{-4}\right)\\= \frac{-7}{2}- \frac{10}{5}-\frac{11}{4}\\=\frac{-7}{2}-\frac{2}{1}-\frac{11}{4}\\=\frac{-14}{4}-\frac{8}{4}-\frac{11}{4}\\=\frac{-14-8-11}{4}\\=\frac{-33}{4}\)
8. \(+\left(\frac{7}{2}\right) -\left(\frac{10}{8}\right) +\left(\frac{-2}{2}\right)\\= \frac{7}{2}- \frac{10}{8}-\frac{2}{2}\\=\frac{7}{2}-\frac{5}{4}-\frac{1}{1}\\=\frac{14}{4}-\frac{5}{4}-\frac{4}{4}\\=\frac{14-5-4}{4}\\=\frac{5}{4}\)
9. \(+\left(\frac{3}{2}\right) +\left(\frac{2}{-5}\right) +\left(\frac{-6}{3}\right)\\= \frac{3}{2}- \frac{2}{5}-\frac{6}{3}\\=\frac{3}{2}-\frac{2}{5}-\frac{2}{1}\\=\frac{15}{10}-\frac{4}{10}-\frac{20}{10}\\=\frac{15-4-20}{10}\\=\frac{-9}{10}\)
10. \(+\left(\frac{-6}{5}\right) +\left(\frac{10}{6}\right) -\left(\frac{8}{6}\right)\\= \frac{-6}{5}+ \frac{10}{6}-\frac{8}{6}\\=\frac{-6}{5}+\frac{5}{3}-\frac{4}{3}\\=\frac{-18}{15}+\frac{25}{15}-\frac{20}{15}\\=\frac{-18+25-20}{15}\\=\frac{-13}{15}\)
11. \(-\left(\frac{5}{6}\right) -\left(\frac{-4}{-3}\right) -\left(\frac{-4}{-12}\right)\\= \frac{-5}{6}- \frac{4}{3}-\frac{4}{12}\\=\frac{-5}{6}-\frac{4}{3}-\frac{1}{3}\\=\frac{-5-4-1}{6}\\=\frac{-10}{6}\\=\frac{-5}{3}\)
12. \(-\left(\frac{-2}{5}\right) +\left(\frac{3}{6}\right) -\left(\frac{11}{-10}\right)\\= \frac{2}{5}+ \frac{3}{6}+\frac{11}{10}\\=\frac{2}{5}+\frac{1}{2}+\frac{11}{10}\\=\frac{4}{10}+\frac{5}{10}+\frac{11}{10}\\=\frac{4+5+11}{10}\\=\frac{20}{10}\\=\frac{2}{1}\)