Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{9}{-4}\right) +\left(\frac{-3}{-4}\right) +\left(\frac{2}{-12}\right)\\= \frac{9}{4}+ \frac{3}{4}-\frac{2}{12}\\=\frac{9}{4}+\frac{3}{4}-\frac{1}{6}\\=\frac{27}{12}+\frac{9}{12}-\frac{2}{12}\\=\frac{27+9-2}{12}\\=\frac{34}{12}\\=\frac{17}{6}\)
2. \(-\left(\frac{5}{6}\right) -\left(\frac{-9}{2}\right) +\left(\frac{10}{12}\right)\\= \frac{-5}{6}+ \frac{9}{2}+\frac{10}{12}\\=\frac{-5}{6}+\frac{9}{2}+\frac{5}{6}\\=\frac{-5+9+5}{6}\\=\frac{9}{6}\\=\frac{3}{2}\)
3. \(-\left(\frac{4}{5}\right) +\left(\frac{4}{-4}\right) +\left(\frac{-4}{6}\right)\\= \frac{-4}{5}- \frac{4}{4}-\frac{4}{6}\\=\frac{-4}{5}-\frac{1}{1}-\frac{2}{3}\\=\frac{-12}{15}-\frac{15}{15}-\frac{10}{15}\\=\frac{-12-15-10}{15}\\=\frac{-37}{15}\)
4. \(+\left(\frac{10}{7}\right) +\left(\frac{-7}{7}\right) +\left(\frac{8}{9}\right)\\= \frac{10}{7}- \frac{7}{7}+\frac{8}{9}\\=\frac{10}{7}-\frac{1}{1}+\frac{8}{9}\\=\frac{90}{63}-\frac{63}{63}+\frac{56}{63}\\=\frac{90-63+56}{63}\\=\frac{83}{63}\)
5. \(-\left(\frac{-8}{9}\right) -\left(\frac{-7}{3}\right) +\left(\frac{10}{5}\right)\\= \frac{8}{9}+ \frac{7}{3}+\frac{10}{5}\\=\frac{8}{9}+\frac{7}{3}+\frac{2}{1}\\=\frac{8+7+2}{9}\\=\frac{17}{9}\)
6. \(-\left(\frac{-5}{3}\right) +\left(\frac{-2}{6}\right) +\left(\frac{-9}{11}\right)\\= \frac{5}{3}- \frac{2}{6}-\frac{9}{11}\\=\frac{5}{3}-\frac{1}{3}-\frac{9}{11}\\=\frac{55}{33}-\frac{11}{33}-\frac{27}{33}\\=\frac{55-11-27}{33}\\=\frac{17}{33}\)
7. \(+\left(\frac{-6}{-5}\right) +\left(\frac{-6}{-6}\right) -\left(\frac{-9}{12}\right)\\= \frac{6}{5}+ \frac{6}{6}+\frac{9}{12}\\=\frac{6}{5}+\frac{1}{1}+\frac{3}{4}\\=\frac{24}{20}+\frac{20}{20}+\frac{15}{20}\\=\frac{24+20+15}{20}\\=\frac{59}{20}\)
8. \(+\left(\frac{-9}{2}\right) -\left(\frac{6}{9}\right) +\left(\frac{6}{9}\right)\\= \frac{-9}{2}- \frac{6}{9}+\frac{6}{9}\\=\frac{-9}{2}-\frac{2}{3}+\frac{2}{3}\\=\frac{-27}{6}-\frac{4}{6}+\frac{4}{6}\\=\frac{-27-4+4}{6}\\=\frac{-27}{6}\\=\frac{-9}{2}\)
9. \(+\left(\frac{-2}{-9}\right) -\left(\frac{-3}{9}\right) +\left(\frac{2}{7}\right)\\= \frac{2}{9}+ \frac{3}{9}+\frac{2}{7}\\=\frac{2}{9}+\frac{1}{3}+\frac{2}{7}\\=\frac{14}{63}+\frac{21}{63}+\frac{18}{63}\\=\frac{14+21+18}{63}\\=\frac{53}{63}\)
10. \(-\left(\frac{-2}{9}\right) -\left(\frac{-8}{9}\right) -\left(\frac{8}{-5}\right)\\= \frac{2}{9}+ \frac{8}{9}+\frac{8}{5}\\=\frac{10}{45}+\frac{40}{45}+\frac{72}{45}\\=\frac{10+40+72}{45}\\=\frac{122}{45}\)
11. \(+\left(\frac{-7}{2}\right) +\left(\frac{2}{10}\right) +\left(\frac{12}{-9}\right)\\= \frac{-7}{2}+ \frac{2}{10}-\frac{12}{9}\\=\frac{-7}{2}+\frac{1}{5}-\frac{4}{3}\\=\frac{-105}{30}+\frac{6}{30}-\frac{40}{30}\\=\frac{-105+6-40}{30}\\=\frac{-139}{30}\)
12. \(-\left(\frac{8}{3}\right) -\left(\frac{-8}{8}\right) -\left(\frac{9}{2}\right)\\= \frac{-8}{3}+ \frac{8}{8}-\frac{9}{2}\\=\frac{-8}{3}+\frac{1}{1}-\frac{9}{2}\\=\frac{-16}{6}+\frac{6}{6}-\frac{27}{6}\\=\frac{-16+6-27}{6}\\=\frac{-37}{6}\)