Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{9}{4}\right) +\left(\frac{-8}{9}\right) -\left(\frac{11}{4}\right)\\= \frac{-9}{4}- \frac{8}{9}-\frac{11}{4}\\=\frac{-81}{36}-\frac{32}{36}-\frac{99}{36}\\=\frac{-81-32-99}{36}\\=\frac{-212}{36}\\=\frac{-53}{9}\)
2. \(+\left(\frac{-2}{-5}\right) -\left(\frac{5}{-2}\right) +\left(\frac{-6}{9}\right)\\= \frac{2}{5}+ \frac{5}{2}-\frac{6}{9}\\=\frac{2}{5}+\frac{5}{2}-\frac{2}{3}\\=\frac{12}{30}+\frac{75}{30}-\frac{20}{30}\\=\frac{12+75-20}{30}\\=\frac{67}{30}\)
3. \(+\left(\frac{-8}{-7}\right) +\left(\frac{-5}{-4}\right) +\left(\frac{-9}{6}\right)\\= \frac{8}{7}+ \frac{5}{4}-\frac{9}{6}\\=\frac{8}{7}+\frac{5}{4}-\frac{3}{2}\\=\frac{32}{28}+\frac{35}{28}-\frac{42}{28}\\=\frac{32+35-42}{28}\\=\frac{25}{28}\)
4. \(-\left(\frac{5}{9}\right) -\left(\frac{-2}{5}\right) -\left(\frac{-10}{10}\right)\\= \frac{-5}{9}+ \frac{2}{5}+\frac{10}{10}\\=\frac{-5}{9}+\frac{2}{5}+\frac{1}{1}\\=\frac{-25}{45}+\frac{18}{45}+\frac{45}{45}\\=\frac{-25+18+45}{45}\\=\frac{38}{45}\)
5. \(+\left(\frac{4}{7}\right) +\left(\frac{-10}{-3}\right) +\left(\frac{-5}{12}\right)\\= \frac{4}{7}+ \frac{10}{3}-\frac{5}{12}\\=\frac{48}{84}+\frac{280}{84}-\frac{35}{84}\\=\frac{48+280-35}{84}\\=\frac{293}{84}\)
6. \(-\left(\frac{-9}{-2}\right) +\left(\frac{-8}{9}\right) +\left(\frac{-6}{3}\right)\\= \frac{-9}{2}- \frac{8}{9}-\frac{6}{3}\\=\frac{-9}{2}-\frac{8}{9}-\frac{2}{1}\\=\frac{-81}{18}-\frac{16}{18}-\frac{36}{18}\\=\frac{-81-16-36}{18}\\=\frac{-133}{18}\)
7. \(-\left(\frac{10}{-7}\right) +\left(\frac{6}{8}\right) +\left(\frac{-2}{5}\right)\\= \frac{10}{7}+ \frac{6}{8}-\frac{2}{5}\\=\frac{10}{7}+\frac{3}{4}-\frac{2}{5}\\=\frac{200}{140}+\frac{105}{140}-\frac{56}{140}\\=\frac{200+105-56}{140}\\=\frac{249}{140}\)
8. \(+\left(\frac{-6}{-5}\right) -\left(\frac{2}{6}\right) -\left(\frac{7}{-9}\right)\\= \frac{6}{5}- \frac{2}{6}+\frac{7}{9}\\=\frac{6}{5}-\frac{1}{3}+\frac{7}{9}\\=\frac{54}{45}-\frac{15}{45}+\frac{35}{45}\\=\frac{54-15+35}{45}\\=\frac{74}{45}\)
9. \(+\left(\frac{-7}{-2}\right) +\left(\frac{-8}{-10}\right) -\left(\frac{5}{-3}\right)\\= \frac{7}{2}+ \frac{8}{10}+\frac{5}{3}\\=\frac{7}{2}+\frac{4}{5}+\frac{5}{3}\\=\frac{105}{30}+\frac{24}{30}+\frac{50}{30}\\=\frac{105+24+50}{30}\\=\frac{179}{30}\)
10. \(-\left(\frac{7}{8}\right) +\left(\frac{2}{6}\right) +\left(\frac{-5}{7}\right)\\= \frac{-7}{8}+ \frac{2}{6}-\frac{5}{7}\\=\frac{-7}{8}+\frac{1}{3}-\frac{5}{7}\\=\frac{-147}{168}+\frac{56}{168}-\frac{120}{168}\\=\frac{-147+56-120}{168}\\=\frac{-211}{168}\)
11. \(-\left(\frac{-8}{3}\right) -\left(\frac{-2}{-6}\right) -\left(\frac{-2}{-2}\right)\\= \frac{8}{3}- \frac{2}{6}-\frac{2}{2}\\=\frac{8}{3}-\frac{1}{3}-\frac{1}{1}\\=\frac{8-1-1}{3}\\=\frac{6}{3}\\=\frac{2}{1}\)
12. \(-\left(\frac{2}{-9}\right) -\left(\frac{-9}{-7}\right) +\left(\frac{-8}{2}\right)\\= \frac{2}{9}- \frac{9}{7}-\frac{8}{2}\\=\frac{2}{9}-\frac{9}{7}-\frac{4}{1}\\=\frac{14}{63}-\frac{81}{63}-\frac{252}{63}\\=\frac{14-81-252}{63}\\=\frac{-319}{63}\)