Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-6}{5}\right) -\left(\frac{-3}{-7}\right) +\left(\frac{12}{11}\right)\\= \frac{6}{5}- \frac{3}{7}+\frac{12}{11}\\=\frac{462}{385}-\frac{165}{385}+\frac{420}{385}\\=\frac{462-165+420}{385}\\=\frac{717}{385}\)
2. \(-\left(\frac{4}{-9}\right) +\left(\frac{-5}{-8}\right) +\left(\frac{10}{10}\right)\\= \frac{4}{9}+ \frac{5}{8}+\frac{10}{10}\\=\frac{4}{9}+\frac{5}{8}+\frac{1}{1}\\=\frac{32}{72}+\frac{45}{72}+\frac{72}{72}\\=\frac{32+45+72}{72}\\=\frac{149}{72}\)
3. \(+\left(\frac{4}{-9}\right) +\left(\frac{-8}{7}\right) -\left(\frac{-11}{3}\right)\\= \frac{-4}{9}- \frac{8}{7}+\frac{11}{3}\\=\frac{-28}{63}-\frac{72}{63}+\frac{231}{63}\\=\frac{-28-72+231}{63}\\=\frac{131}{63}\)
4. \(+\left(\frac{-9}{8}\right) +\left(\frac{-4}{9}\right) +\left(\frac{4}{10}\right)\\= \frac{-9}{8}- \frac{4}{9}+\frac{4}{10}\\=\frac{-9}{8}-\frac{4}{9}+\frac{2}{5}\\=\frac{-405}{360}-\frac{160}{360}+\frac{144}{360}\\=\frac{-405-160+144}{360}\\=\frac{-421}{360}\)
5. \(+\left(\frac{9}{-2}\right) -\left(\frac{4}{9}\right) +\left(\frac{-6}{4}\right)\\= \frac{-9}{2}- \frac{4}{9}-\frac{6}{4}\\=\frac{-9}{2}-\frac{4}{9}-\frac{3}{2}\\=\frac{-81}{18}-\frac{8}{18}-\frac{27}{18}\\=\frac{-81-8-27}{18}\\=\frac{-116}{18}\\=\frac{-58}{9}\)
6. \(-\left(\frac{2}{9}\right) +\left(\frac{-7}{8}\right) -\left(\frac{-10}{11}\right)\\= \frac{-2}{9}- \frac{7}{8}+\frac{10}{11}\\=\frac{-176}{792}-\frac{693}{792}+\frac{720}{792}\\=\frac{-176-693+720}{792}\\=\frac{-149}{792}\)
7. \(-\left(\frac{4}{-7}\right) -\left(\frac{9}{2}\right) -\left(\frac{5}{-7}\right)\\= \frac{4}{7}- \frac{9}{2}+\frac{5}{7}\\=\frac{8}{14}-\frac{63}{14}+\frac{10}{14}\\=\frac{8-63+10}{14}\\=\frac{-45}{14}\)
8. \(+\left(\frac{9}{-2}\right) -\left(\frac{5}{-4}\right) -\left(\frac{-3}{-9}\right)\\= \frac{-9}{2}+ \frac{5}{4}-\frac{3}{9}\\=\frac{-9}{2}+\frac{5}{4}-\frac{1}{3}\\=\frac{-54}{12}+\frac{15}{12}-\frac{4}{12}\\=\frac{-54+15-4}{12}\\=\frac{-43}{12}\)
9. \(+\left(\frac{-9}{8}\right) +\left(\frac{-4}{-10}\right) +\left(\frac{4}{-8}\right)\\= \frac{-9}{8}+ \frac{4}{10}-\frac{4}{8}\\=\frac{-9}{8}+\frac{2}{5}-\frac{1}{2}\\=\frac{-45}{40}+\frac{16}{40}-\frac{20}{40}\\=\frac{-45+16-20}{40}\\=\frac{-49}{40}\)
10. \(-\left(\frac{-2}{7}\right) +\left(\frac{-2}{-10}\right) -\left(\frac{-11}{9}\right)\\= \frac{2}{7}+ \frac{2}{10}+\frac{11}{9}\\=\frac{2}{7}+\frac{1}{5}+\frac{11}{9}\\=\frac{90}{315}+\frac{63}{315}+\frac{385}{315}\\=\frac{90+63+385}{315}\\=\frac{538}{315}\)
11. \(+\left(\frac{-7}{2}\right) -\left(\frac{-10}{-5}\right) -\left(\frac{-3}{-11}\right)\\= \frac{-7}{2}- \frac{10}{5}-\frac{3}{11}\\=\frac{-7}{2}-\frac{2}{1}-\frac{3}{11}\\=\frac{-77}{22}-\frac{44}{22}-\frac{6}{22}\\=\frac{-77-44-6}{22}\\=\frac{-127}{22}\)
12. \(+\left(\frac{3}{8}\right) -\left(\frac{-2}{-5}\right) +\left(\frac{9}{-2}\right)\\= \frac{3}{8}- \frac{2}{5}-\frac{9}{2}\\=\frac{15}{40}-\frac{16}{40}-\frac{180}{40}\\=\frac{15-16-180}{40}\\=\frac{-181}{40}\)