Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-5}{2}\right) -\left(\frac{-2}{-10}\right) +\left(\frac{-5}{-6}\right)\\= \frac{5}{2}- \frac{2}{10}+\frac{5}{6}\\=\frac{5}{2}-\frac{1}{5}+\frac{5}{6}\\=\frac{75}{30}-\frac{6}{30}+\frac{25}{30}\\=\frac{75-6+25}{30}\\=\frac{94}{30}\\=\frac{47}{15}\)
2. \(-\left(\frac{-2}{3}\right) -\left(\frac{-10}{-2}\right) -\left(\frac{7}{12}\right)\\= \frac{2}{3}- \frac{10}{2}-\frac{7}{12}\\=\frac{2}{3}-\frac{5}{1}-\frac{7}{12}\\=\frac{8}{12}-\frac{60}{12}-\frac{7}{12}\\=\frac{8-60-7}{12}\\=\frac{-59}{12}\)
3. \(-\left(\frac{-6}{5}\right) -\left(\frac{4}{-9}\right) -\left(\frac{-10}{11}\right)\\= \frac{6}{5}+ \frac{4}{9}+\frac{10}{11}\\=\frac{594}{495}+\frac{220}{495}+\frac{450}{495}\\=\frac{594+220+450}{495}\\=\frac{1264}{495}\)
4. \(-\left(\frac{8}{3}\right) -\left(\frac{4}{9}\right) +\left(\frac{-12}{2}\right)\\= \frac{-8}{3}- \frac{4}{9}-\frac{12}{2}\\=\frac{-8}{3}-\frac{4}{9}-\frac{6}{1}\\=\frac{-24}{9}-\frac{4}{9}-\frac{54}{9}\\=\frac{-24-4-54}{9}\\=\frac{-82}{9}\)
5. \(-\left(\frac{7}{8}\right) +\left(\frac{-5}{3}\right) -\left(\frac{-4}{4}\right)\\= \frac{-7}{8}- \frac{5}{3}+\frac{4}{4}\\=\frac{-7}{8}-\frac{5}{3}+\frac{1}{1}\\=\frac{-21}{24}-\frac{40}{24}+\frac{24}{24}\\=\frac{-21-40+24}{24}\\=\frac{-37}{24}\)
6. \(+\left(\frac{9}{2}\right) -\left(\frac{-4}{-2}\right) +\left(\frac{-3}{-5}\right)\\= \frac{9}{2}- \frac{4}{2}+\frac{3}{5}\\=\frac{9}{2}-\frac{2}{1}+\frac{3}{5}\\=\frac{45}{10}-\frac{20}{10}+\frac{6}{10}\\=\frac{45-20+6}{10}\\=\frac{31}{10}\)
7. \(+\left(\frac{-9}{-2}\right) -\left(\frac{-7}{-2}\right) +\left(\frac{11}{-6}\right)\\= \frac{9}{2}- \frac{7}{2}-\frac{11}{6}\\=\frac{27}{6}-\frac{21}{6}-\frac{11}{6}\\=\frac{27-21-11}{6}\\=\frac{-5}{6}\)
8. \(+\left(\frac{10}{-7}\right) +\left(\frac{2}{-3}\right) -\left(\frac{-5}{-2}\right)\\= \frac{-10}{7}- \frac{2}{3}-\frac{5}{2}\\=\frac{-60}{42}-\frac{28}{42}-\frac{105}{42}\\=\frac{-60-28-105}{42}\\=\frac{-193}{42}\)
9. \(+\left(\frac{5}{-6}\right) -\left(\frac{-10}{-6}\right) -\left(\frac{10}{6}\right)\\= \frac{-5}{6}- \frac{10}{6}-\frac{10}{6}\\=\frac{-5}{6}-\frac{5}{3}-\frac{5}{3}\\=\frac{-5-5-5}{6}\\=\frac{-15}{6}\\=\frac{-5}{2}\)
10. \(-\left(\frac{8}{3}\right) -\left(\frac{-6}{9}\right) -\left(\frac{12}{4}\right)\\= \frac{-8}{3}+ \frac{6}{9}-\frac{12}{4}\\=\frac{-8}{3}+\frac{2}{3}-\frac{3}{1}\\=\frac{-8+2-3}{3}\\=\frac{-9}{3}\\=\frac{-3}{1}\)
11. \(-\left(\frac{9}{-5}\right) +\left(\frac{-5}{2}\right) -\left(\frac{-11}{-5}\right)\\= \frac{9}{5}- \frac{5}{2}-\frac{11}{5}\\=\frac{18}{10}-\frac{25}{10}-\frac{22}{10}\\=\frac{18-25-22}{10}\\=\frac{-29}{10}\)
12. \(+\left(\frac{4}{5}\right) +\left(\frac{9}{-5}\right) -\left(\frac{7}{-8}\right)\\= \frac{4}{5}- \frac{9}{5}+\frac{7}{8}\\=\frac{32}{40}-\frac{72}{40}+\frac{35}{40}\\=\frac{32-72+35}{40}\\=\frac{-5}{40}\\=\frac{-1}{8}\)