Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-2}{3}\right) -\left(\frac{-3}{-2}\right) +\left(\frac{4}{-9}\right)\\= \frac{2}{3}- \frac{3}{2}-\frac{4}{9}\\=\frac{12}{18}-\frac{27}{18}-\frac{8}{18}\\=\frac{12-27-8}{18}\\=\frac{-23}{18}\)
2. \(-\left(\frac{-7}{9}\right) -\left(\frac{-2}{-10}\right) +\left(\frac{12}{2}\right)\\= \frac{7}{9}- \frac{2}{10}+\frac{12}{2}\\=\frac{7}{9}-\frac{1}{5}+\frac{6}{1}\\=\frac{35}{45}-\frac{9}{45}+\frac{270}{45}\\=\frac{35-9+270}{45}\\=\frac{296}{45}\)
3. \(-\left(\frac{2}{-3}\right) +\left(\frac{9}{9}\right) -\left(\frac{11}{-11}\right)\\= \frac{2}{3}+ \frac{9}{9}+\frac{11}{11}\\=\frac{2}{3}+\frac{1}{1}+\frac{1}{1}\\=\frac{2+1+1}{3}\\=\frac{4}{3}\)
4. \(-\left(\frac{-7}{-2}\right) +\left(\frac{-4}{6}\right) -\left(\frac{6}{-2}\right)\\= \frac{-7}{2}- \frac{4}{6}+\frac{6}{2}\\=\frac{-7}{2}-\frac{2}{3}+\frac{3}{1}\\=\frac{-21}{6}-\frac{4}{6}+\frac{18}{6}\\=\frac{-21-4+18}{6}\\=\frac{-7}{6}\)
5. \(-\left(\frac{-7}{-9}\right) +\left(\frac{-10}{9}\right) +\left(\frac{-7}{-5}\right)\\= \frac{-7}{9}- \frac{10}{9}+\frac{7}{5}\\=\frac{-35}{45}-\frac{50}{45}+\frac{63}{45}\\=\frac{-35-50+63}{45}\\=\frac{-22}{45}\)
6. \(-\left(\frac{-7}{-3}\right) +\left(\frac{8}{5}\right) +\left(\frac{3}{-6}\right)\\= \frac{-7}{3}+ \frac{8}{5}-\frac{3}{6}\\=\frac{-7}{3}+\frac{8}{5}-\frac{1}{2}\\=\frac{-70}{30}+\frac{48}{30}-\frac{15}{30}\\=\frac{-70+48-15}{30}\\=\frac{-37}{30}\)
7. \(+\left(\frac{-6}{-5}\right) +\left(\frac{3}{-9}\right) -\left(\frac{-8}{2}\right)\\= \frac{6}{5}- \frac{3}{9}+\frac{8}{2}\\=\frac{6}{5}-\frac{1}{3}+\frac{4}{1}\\=\frac{18}{15}-\frac{5}{15}+\frac{60}{15}\\=\frac{18-5+60}{15}\\=\frac{73}{15}\)
8. \(-\left(\frac{6}{7}\right) +\left(\frac{-8}{9}\right) +\left(\frac{9}{3}\right)\\= \frac{-6}{7}- \frac{8}{9}+\frac{9}{3}\\=\frac{-6}{7}-\frac{8}{9}+\frac{3}{1}\\=\frac{-54}{63}-\frac{56}{63}+\frac{189}{63}\\=\frac{-54-56+189}{63}\\=\frac{79}{63}\)
9. \(+\left(\frac{-2}{9}\right) -\left(\frac{-6}{-8}\right) +\left(\frac{10}{11}\right)\\= \frac{-2}{9}- \frac{6}{8}+\frac{10}{11}\\=\frac{-2}{9}-\frac{3}{4}+\frac{10}{11}\\=\frac{-88}{396}-\frac{297}{396}+\frac{360}{396}\\=\frac{-88-297+360}{396}\\=\frac{-25}{396}\)
10. \(-\left(\frac{-8}{3}\right) -\left(\frac{-8}{6}\right) -\left(\frac{-9}{5}\right)\\= \frac{8}{3}+ \frac{8}{6}+\frac{9}{5}\\=\frac{8}{3}+\frac{4}{3}+\frac{9}{5}\\=\frac{40}{15}+\frac{20}{15}+\frac{27}{15}\\=\frac{40+20+27}{15}\\=\frac{87}{15}\\=\frac{29}{5}\)
11. \(-\left(\frac{-10}{7}\right) -\left(\frac{5}{10}\right) -\left(\frac{9}{-2}\right)\\= \frac{10}{7}- \frac{5}{10}+\frac{9}{2}\\=\frac{10}{7}-\frac{1}{2}+\frac{9}{2}\\=\frac{20}{14}-\frac{7}{14}+\frac{63}{14}\\=\frac{20-7+63}{14}\\=\frac{76}{14}\\=\frac{38}{7}\)
12. \(+\left(\frac{5}{3}\right) +\left(\frac{3}{8}\right) -\left(\frac{-12}{8}\right)\\= \frac{5}{3}+ \frac{3}{8}+\frac{12}{8}\\=\frac{5}{3}+\frac{3}{8}+\frac{3}{2}\\=\frac{40}{24}+\frac{9}{24}+\frac{36}{24}\\=\frac{40+9+36}{24}\\=\frac{85}{24}\)