Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{2}{-3}\right) -\left(\frac{5}{-4}\right) -\left(\frac{-8}{-5}\right)\\= \frac{2}{3}+ \frac{5}{4}-\frac{8}{5}\\=\frac{40}{60}+\frac{75}{60}-\frac{96}{60}\\=\frac{40+75-96}{60}\\=\frac{19}{60}\)
2. \(-\left(\frac{5}{-8}\right) -\left(\frac{8}{6}\right) +\left(\frac{11}{7}\right)\\= \frac{5}{8}- \frac{8}{6}+\frac{11}{7}\\=\frac{5}{8}-\frac{4}{3}+\frac{11}{7}\\=\frac{105}{168}-\frac{224}{168}+\frac{264}{168}\\=\frac{105-224+264}{168}\\=\frac{145}{168}\)
3. \(-\left(\frac{3}{4}\right) -\left(\frac{5}{-4}\right) -\left(\frac{-7}{-12}\right)\\= \frac{-3}{4}+ \frac{5}{4}-\frac{7}{12}\\=\frac{-9}{12}+\frac{15}{12}-\frac{7}{12}\\=\frac{-9+15-7}{12}\\=\frac{-1}{12}\)
4. \(-\left(\frac{-3}{-5}\right) +\left(\frac{-5}{-10}\right) -\left(\frac{-10}{4}\right)\\= \frac{-3}{5}+ \frac{5}{10}+\frac{10}{4}\\=\frac{-3}{5}+\frac{1}{2}+\frac{5}{2}\\=\frac{-6}{10}+\frac{5}{10}+\frac{25}{10}\\=\frac{-6+5+25}{10}\\=\frac{24}{10}\\=\frac{12}{5}\)
5. \(+\left(\frac{8}{7}\right) +\left(\frac{8}{-6}\right) +\left(\frac{-12}{11}\right)\\= \frac{8}{7}- \frac{8}{6}-\frac{12}{11}\\=\frac{8}{7}-\frac{4}{3}-\frac{12}{11}\\=\frac{264}{231}-\frac{308}{231}-\frac{252}{231}\\=\frac{264-308-252}{231}\\=\frac{-296}{231}\)
6. \(+\left(\frac{7}{-8}\right) +\left(\frac{-4}{-7}\right) +\left(\frac{-3}{8}\right)\\= \frac{-7}{8}+ \frac{4}{7}-\frac{3}{8}\\=\frac{-49}{56}+\frac{32}{56}-\frac{21}{56}\\=\frac{-49+32-21}{56}\\=\frac{-38}{56}\\=\frac{-19}{28}\)
7. \(+\left(\frac{-9}{-7}\right) +\left(\frac{10}{-6}\right) +\left(\frac{-2}{9}\right)\\= \frac{9}{7}- \frac{10}{6}-\frac{2}{9}\\=\frac{9}{7}-\frac{5}{3}-\frac{2}{9}\\=\frac{81}{63}-\frac{105}{63}-\frac{14}{63}\\=\frac{81-105-14}{63}\\=\frac{-38}{63}\)
8. \(-\left(\frac{-5}{-8}\right) -\left(\frac{-4}{-5}\right) -\left(\frac{-5}{-10}\right)\\= \frac{-5}{8}- \frac{4}{5}-\frac{5}{10}\\=\frac{-5}{8}-\frac{4}{5}-\frac{1}{2}\\=\frac{-25}{40}-\frac{32}{40}-\frac{20}{40}\\=\frac{-25-32-20}{40}\\=\frac{-77}{40}\)
9. \(+\left(\frac{-4}{-7}\right) -\left(\frac{-6}{5}\right) +\left(\frac{-10}{-11}\right)\\= \frac{4}{7}+ \frac{6}{5}+\frac{10}{11}\\=\frac{220}{385}+\frac{462}{385}+\frac{350}{385}\\=\frac{220+462+350}{385}\\=\frac{1032}{385}\)
10. \(+\left(\frac{9}{-2}\right) +\left(\frac{-8}{2}\right) -\left(\frac{-9}{-6}\right)\\= \frac{-9}{2}- \frac{8}{2}-\frac{9}{6}\\=\frac{-9}{2}-\frac{4}{1}-\frac{3}{2}\\=\frac{-9-4-3}{2}\\=\frac{-16}{2}\\=\frac{-8}{1}\)
11. \(-\left(\frac{-4}{7}\right) -\left(\frac{-9}{-8}\right) +\left(\frac{-2}{-8}\right)\\= \frac{4}{7}- \frac{9}{8}+\frac{2}{8}\\=\frac{4}{7}-\frac{9}{8}+\frac{1}{4}\\=\frac{32}{56}-\frac{63}{56}+\frac{14}{56}\\=\frac{32-63+14}{56}\\=\frac{-17}{56}\)
12. \(+\left(\frac{-9}{5}\right) -\left(\frac{-8}{-8}\right) -\left(\frac{12}{10}\right)\\= \frac{-9}{5}- \frac{8}{8}-\frac{12}{10}\\=\frac{-9}{5}-\frac{1}{1}-\frac{6}{5}\\=\frac{-9-1-6}{5}\\=\frac{-16}{5}\)