Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-8}{-3}\right) -\left(\frac{3}{-5}\right) +\left(\frac{4}{-6}\right)\\= \frac{8}{3}+ \frac{3}{5}-\frac{4}{6}\\=\frac{8}{3}+\frac{3}{5}-\frac{2}{3}\\=\frac{40}{15}+\frac{9}{15}-\frac{10}{15}\\=\frac{40+9-10}{15}\\=\frac{39}{15}\\=\frac{13}{5}\)
2. \(+\left(\frac{-8}{7}\right) -\left(\frac{-7}{-3}\right) +\left(\frac{-4}{-6}\right)\\= \frac{-8}{7}- \frac{7}{3}+\frac{4}{6}\\=\frac{-8}{7}-\frac{7}{3}+\frac{2}{3}\\=\frac{-24}{21}-\frac{49}{21}+\frac{14}{21}\\=\frac{-24-49+14}{21}\\=\frac{-59}{21}\)
3. \(+\left(\frac{8}{5}\right) +\left(\frac{5}{10}\right) +\left(\frac{9}{9}\right)\\= \frac{8}{5}+ \frac{5}{10}+\frac{9}{9}\\=\frac{8}{5}+\frac{1}{2}+\frac{1}{1}\\=\frac{16}{10}+\frac{5}{10}+\frac{10}{10}\\=\frac{16+5+10}{10}\\=\frac{31}{10}\)
4. \(-\left(\frac{7}{5}\right) -\left(\frac{-3}{3}\right) -\left(\frac{4}{2}\right)\\= \frac{-7}{5}+ \frac{3}{3}-\frac{4}{2}\\=\frac{-7}{5}+\frac{1}{1}-\frac{2}{1}\\=\frac{-7+1-2}{5}\\=\frac{-8}{5}\)
5. \(-\left(\frac{-5}{7}\right) +\left(\frac{-4}{-3}\right) +\left(\frac{-12}{3}\right)\\= \frac{5}{7}+ \frac{4}{3}-\frac{12}{3}\\=\frac{5}{7}+\frac{4}{3}-\frac{4}{1}\\=\frac{15}{21}+\frac{28}{21}-\frac{84}{21}\\=\frac{15+28-84}{21}\\=\frac{-41}{21}\)
6. \(+\left(\frac{3}{-2}\right) -\left(\frac{-2}{-9}\right) -\left(\frac{9}{-11}\right)\\= \frac{-3}{2}- \frac{2}{9}+\frac{9}{11}\\=\frac{-297}{198}-\frac{44}{198}+\frac{162}{198}\\=\frac{-297-44+162}{198}\\=\frac{-179}{198}\)
7. \(-\left(\frac{9}{2}\right) +\left(\frac{6}{-8}\right) -\left(\frac{-7}{12}\right)\\= \frac{-9}{2}- \frac{6}{8}+\frac{7}{12}\\=\frac{-9}{2}-\frac{3}{4}+\frac{7}{12}\\=\frac{-54}{12}-\frac{9}{12}+\frac{7}{12}\\=\frac{-54-9+7}{12}\\=\frac{-56}{12}\\=\frac{-14}{3}\)
8. \(-\left(\frac{5}{9}\right) +\left(\frac{-10}{-3}\right) -\left(\frac{5}{-6}\right)\\= \frac{-5}{9}+ \frac{10}{3}+\frac{5}{6}\\=\frac{-10}{18}+\frac{60}{18}+\frac{15}{18}\\=\frac{-10+60+15}{18}\\=\frac{65}{18}\)
9. \(+\left(\frac{4}{3}\right) +\left(\frac{-7}{-3}\right) -\left(\frac{-8}{10}\right)\\= \frac{4}{3}+ \frac{7}{3}+\frac{8}{10}\\=\frac{4}{3}+\frac{7}{3}+\frac{4}{5}\\=\frac{20}{15}+\frac{35}{15}+\frac{12}{15}\\=\frac{20+35+12}{15}\\=\frac{67}{15}\)
10. \(+\left(\frac{-4}{9}\right) +\left(\frac{-2}{7}\right) -\left(\frac{4}{-12}\right)\\= \frac{-4}{9}- \frac{2}{7}+\frac{4}{12}\\=\frac{-4}{9}-\frac{2}{7}+\frac{1}{3}\\=\frac{-28}{63}-\frac{18}{63}+\frac{21}{63}\\=\frac{-28-18+21}{63}\\=\frac{-25}{63}\)
11. \(+\left(\frac{-3}{5}\right) +\left(\frac{5}{-3}\right) -\left(\frac{8}{4}\right)\\= \frac{-3}{5}- \frac{5}{3}-\frac{8}{4}\\=\frac{-3}{5}-\frac{5}{3}-\frac{2}{1}\\=\frac{-9}{15}-\frac{25}{15}-\frac{30}{15}\\=\frac{-9-25-30}{15}\\=\frac{-64}{15}\)
12. \(+\left(\frac{4}{-7}\right) +\left(\frac{2}{2}\right) -\left(\frac{-3}{3}\right)\\= \frac{-4}{7}+ \frac{2}{2}+\frac{3}{3}\\=\frac{-4}{7}+\frac{1}{1}+\frac{1}{1}\\=\frac{-4+1+1}{7}\\=\frac{-2}{7}\)