Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-4}{5}\right) +\left(\frac{10}{-6}\right) +\left(\frac{8}{-4}\right)\\= \frac{4}{5}- \frac{10}{6}-\frac{8}{4}\\=\frac{4}{5}-\frac{5}{3}-\frac{2}{1}\\=\frac{12}{15}-\frac{25}{15}-\frac{30}{15}\\=\frac{12-25-30}{15}\\=\frac{-43}{15}\)
2. \(-\left(\frac{-5}{3}\right) -\left(\frac{-10}{8}\right) +\left(\frac{-12}{12}\right)\\= \frac{5}{3}+ \frac{10}{8}-\frac{12}{12}\\=\frac{5}{3}+\frac{5}{4}-\frac{1}{1}\\=\frac{20}{12}+\frac{15}{12}-\frac{12}{12}\\=\frac{20+15-12}{12}\\=\frac{23}{12}\)
3. \(+\left(\frac{-9}{2}\right) -\left(\frac{9}{9}\right) +\left(\frac{-8}{-10}\right)\\= \frac{-9}{2}- \frac{9}{9}+\frac{8}{10}\\=\frac{-9}{2}-\frac{1}{1}+\frac{4}{5}\\=\frac{-45}{10}-\frac{10}{10}+\frac{8}{10}\\=\frac{-45-10+8}{10}\\=\frac{-47}{10}\)
4. \(+\left(\frac{-10}{-3}\right) +\left(\frac{-10}{3}\right) +\left(\frac{-5}{-5}\right)\\= \frac{10}{3}- \frac{10}{3}+\frac{5}{5}\\=\frac{10}{3}-\frac{10}{3}+\frac{1}{1}\\=\frac{10-10+1}{3}\\=\frac{1}{3}\)
5. \(+\left(\frac{2}{5}\right) +\left(\frac{9}{10}\right) +\left(\frac{-7}{3}\right)\\= \frac{2}{5}+ \frac{9}{10}-\frac{7}{3}\\=\frac{12}{30}+\frac{27}{30}-\frac{70}{30}\\=\frac{12+27-70}{30}\\=\frac{-31}{30}\)
6. \(-\left(\frac{9}{-2}\right) +\left(\frac{6}{6}\right) +\left(\frac{-5}{12}\right)\\= \frac{9}{2}+ \frac{6}{6}-\frac{5}{12}\\=\frac{9}{2}+\frac{1}{1}-\frac{5}{12}\\=\frac{54}{12}+\frac{12}{12}-\frac{5}{12}\\=\frac{54+12-5}{12}\\=\frac{61}{12}\)
7. \(-\left(\frac{-10}{3}\right) -\left(\frac{-5}{7}\right) -\left(\frac{11}{8}\right)\\= \frac{10}{3}+ \frac{5}{7}-\frac{11}{8}\\=\frac{560}{168}+\frac{120}{168}-\frac{231}{168}\\=\frac{560+120-231}{168}\\=\frac{449}{168}\)
8. \(-\left(\frac{-9}{-8}\right) +\left(\frac{9}{-9}\right) -\left(\frac{12}{11}\right)\\= \frac{-9}{8}- \frac{9}{9}-\frac{12}{11}\\=\frac{-9}{8}-\frac{1}{1}-\frac{12}{11}\\=\frac{-99}{88}-\frac{88}{88}-\frac{96}{88}\\=\frac{-99-88-96}{88}\\=\frac{-283}{88}\)
9. \(-\left(\frac{5}{-9}\right) -\left(\frac{-9}{3}\right) -\left(\frac{-6}{4}\right)\\= \frac{5}{9}+ \frac{9}{3}+\frac{6}{4}\\=\frac{5}{9}+\frac{3}{1}+\frac{3}{2}\\=\frac{10}{18}+\frac{54}{18}+\frac{27}{18}\\=\frac{10+54+27}{18}\\=\frac{91}{18}\)
10. \(+\left(\frac{-7}{-8}\right) +\left(\frac{5}{4}\right) +\left(\frac{-11}{-11}\right)\\= \frac{7}{8}+ \frac{5}{4}+\frac{11}{11}\\=\frac{7}{8}+\frac{5}{4}+\frac{1}{1}\\=\frac{7+5+1}{8}\\=\frac{13}{8}\)
11. \(-\left(\frac{-3}{7}\right) -\left(\frac{8}{-9}\right) +\left(\frac{-2}{-3}\right)\\= \frac{3}{7}+ \frac{8}{9}+\frac{2}{3}\\=\frac{27}{63}+\frac{56}{63}+\frac{42}{63}\\=\frac{27+56+42}{63}\\=\frac{125}{63}\)
12. \(-\left(\frac{-7}{8}\right) +\left(\frac{-10}{3}\right) +\left(\frac{-3}{-11}\right)\\= \frac{7}{8}- \frac{10}{3}+\frac{3}{11}\\=\frac{231}{264}-\frac{880}{264}+\frac{72}{264}\\=\frac{231-880+72}{264}\\=\frac{-577}{264}\)