Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-5}{-6}\right) +\left(\frac{2}{-10}\right) -\left(\frac{-4}{7}\right)\\= \frac{5}{6}- \frac{2}{10}+\frac{4}{7}\\=\frac{5}{6}-\frac{1}{5}+\frac{4}{7}\\=\frac{175}{210}-\frac{42}{210}+\frac{120}{210}\\=\frac{175-42+120}{210}\\=\frac{253}{210}\)
2. \(-\left(\frac{-4}{-3}\right) -\left(\frac{-7}{7}\right) +\left(\frac{-6}{-5}\right)\\= \frac{-4}{3}+ \frac{7}{7}+\frac{6}{5}\\=\frac{-4}{3}+\frac{1}{1}+\frac{6}{5}\\=\frac{-20}{15}+\frac{15}{15}+\frac{18}{15}\\=\frac{-20+15+18}{15}\\=\frac{13}{15}\)
3. \(-\left(\frac{9}{-2}\right) -\left(\frac{-2}{9}\right) +\left(\frac{-5}{-9}\right)\\= \frac{9}{2}+ \frac{2}{9}+\frac{5}{9}\\=\frac{81}{18}+\frac{4}{18}+\frac{10}{18}\\=\frac{81+4+10}{18}\\=\frac{95}{18}\)
4. \(-\left(\frac{-9}{-7}\right) +\left(\frac{10}{3}\right) -\left(\frac{-3}{8}\right)\\= \frac{-9}{7}+ \frac{10}{3}+\frac{3}{8}\\=\frac{-216}{168}+\frac{560}{168}+\frac{63}{168}\\=\frac{-216+560+63}{168}\\=\frac{407}{168}\)
5. \(+\left(\frac{8}{3}\right) +\left(\frac{-3}{-7}\right) -\left(\frac{4}{-9}\right)\\= \frac{8}{3}+ \frac{3}{7}+\frac{4}{9}\\=\frac{168}{63}+\frac{27}{63}+\frac{28}{63}\\=\frac{168+27+28}{63}\\=\frac{223}{63}\)
6. \(-\left(\frac{-8}{7}\right) -\left(\frac{6}{2}\right) +\left(\frac{-4}{3}\right)\\= \frac{8}{7}- \frac{6}{2}-\frac{4}{3}\\=\frac{8}{7}-\frac{3}{1}-\frac{4}{3}\\=\frac{24}{21}-\frac{63}{21}-\frac{28}{21}\\=\frac{24-63-28}{21}\\=\frac{-67}{21}\)
7. \(+\left(\frac{9}{-2}\right) -\left(\frac{-8}{6}\right) +\left(\frac{8}{-10}\right)\\= \frac{-9}{2}+ \frac{8}{6}-\frac{8}{10}\\=\frac{-9}{2}+\frac{4}{3}-\frac{4}{5}\\=\frac{-135}{30}+\frac{40}{30}-\frac{24}{30}\\=\frac{-135+40-24}{30}\\=\frac{-119}{30}\)
8. \(-\left(\frac{-9}{7}\right) -\left(\frac{4}{4}\right) -\left(\frac{6}{5}\right)\\= \frac{9}{7}- \frac{4}{4}-\frac{6}{5}\\=\frac{9}{7}-\frac{1}{1}-\frac{6}{5}\\=\frac{45}{35}-\frac{35}{35}-\frac{42}{35}\\=\frac{45-35-42}{35}\\=\frac{-32}{35}\)
9. \(+\left(\frac{-8}{-5}\right) -\left(\frac{-10}{-10}\right) +\left(\frac{-9}{-7}\right)\\= \frac{8}{5}- \frac{10}{10}+\frac{9}{7}\\=\frac{8}{5}-\frac{1}{1}+\frac{9}{7}\\=\frac{56}{35}-\frac{35}{35}+\frac{45}{35}\\=\frac{56-35+45}{35}\\=\frac{66}{35}\)
10. \(-\left(\frac{-9}{2}\right) -\left(\frac{-7}{7}\right) -\left(\frac{-6}{8}\right)\\= \frac{9}{2}+ \frac{7}{7}+\frac{6}{8}\\=\frac{9}{2}+\frac{1}{1}+\frac{3}{4}\\=\frac{18}{4}+\frac{4}{4}+\frac{3}{4}\\=\frac{18+4+3}{4}\\=\frac{25}{4}\)
11. \(-\left(\frac{-9}{5}\right) -\left(\frac{2}{10}\right) -\left(\frac{4}{-5}\right)\\= \frac{9}{5}- \frac{2}{10}+\frac{4}{5}\\=\frac{9}{5}-\frac{1}{5}+\frac{4}{5}\\=\frac{9-1+4}{5}\\=\frac{12}{5}\)
12. \(+\left(\frac{9}{-2}\right) +\left(\frac{-4}{-9}\right) +\left(\frac{-5}{-6}\right)\\= \frac{-9}{2}+ \frac{4}{9}+\frac{5}{6}\\=\frac{-81}{18}+\frac{8}{18}+\frac{15}{18}\\=\frac{-81+8+15}{18}\\=\frac{-58}{18}\\=\frac{-29}{9}\)