Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{10}{-9}\right) +\left(\frac{-10}{3}\right) +\left(\frac{11}{11}\right)\\= \frac{-10}{9}- \frac{10}{3}+\frac{11}{11}\\=\frac{-10}{9}-\frac{10}{3}+\frac{1}{1}\\=\frac{-10-10+1}{9}\\=\frac{-19}{9}\)
2. \(+\left(\frac{4}{-7}\right) -\left(\frac{9}{9}\right) -\left(\frac{7}{6}\right)\\= \frac{-4}{7}- \frac{9}{9}-\frac{7}{6}\\=\frac{-4}{7}-\frac{1}{1}-\frac{7}{6}\\=\frac{-24}{42}-\frac{42}{42}-\frac{49}{42}\\=\frac{-24-42-49}{42}\\=\frac{-115}{42}\)
3. \(-\left(\frac{-5}{-6}\right) -\left(\frac{-9}{-9}\right) +\left(\frac{4}{2}\right)\\= \frac{-5}{6}- \frac{9}{9}+\frac{4}{2}\\=\frac{-5}{6}-\frac{1}{1}+\frac{2}{1}\\=\frac{-5-1+2}{6}\\=\frac{-4}{6}\\=\frac{-2}{3}\)
4. \(-\left(\frac{-9}{-2}\right) -\left(\frac{4}{6}\right) +\left(\frac{-6}{4}\right)\\= \frac{-9}{2}- \frac{4}{6}-\frac{6}{4}\\=\frac{-9}{2}-\frac{2}{3}-\frac{3}{2}\\=\frac{-27}{6}-\frac{4}{6}-\frac{9}{6}\\=\frac{-27-4-9}{6}\\=\frac{-40}{6}\\=\frac{-20}{3}\)
5. \(-\left(\frac{-3}{2}\right) +\left(\frac{-5}{-5}\right) -\left(\frac{-2}{9}\right)\\= \frac{3}{2}+ \frac{5}{5}+\frac{2}{9}\\=\frac{3}{2}+\frac{1}{1}+\frac{2}{9}\\=\frac{27}{18}+\frac{18}{18}+\frac{4}{18}\\=\frac{27+18+4}{18}\\=\frac{49}{18}\)
6. \(+\left(\frac{-9}{4}\right) +\left(\frac{-4}{2}\right) +\left(\frac{-10}{-2}\right)\\= \frac{-9}{4}- \frac{4}{2}+\frac{10}{2}\\=\frac{-9}{4}-\frac{2}{1}+\frac{5}{1}\\=\frac{-9-2+5}{4}\\=\frac{-6}{4}\\=\frac{-3}{2}\)
7. \(-\left(\frac{-5}{2}\right) -\left(\frac{-7}{8}\right) +\left(\frac{10}{12}\right)\\= \frac{5}{2}+ \frac{7}{8}+\frac{10}{12}\\=\frac{5}{2}+\frac{7}{8}+\frac{5}{6}\\=\frac{60}{24}+\frac{21}{24}+\frac{20}{24}\\=\frac{60+21+20}{24}\\=\frac{101}{24}\)
8. \(-\left(\frac{-7}{4}\right) +\left(\frac{6}{2}\right) +\left(\frac{11}{-5}\right)\\= \frac{7}{4}+ \frac{6}{2}-\frac{11}{5}\\=\frac{7}{4}+\frac{3}{1}-\frac{11}{5}\\=\frac{35}{20}+\frac{60}{20}-\frac{44}{20}\\=\frac{35+60-44}{20}\\=\frac{51}{20}\)
9. \(+\left(\frac{6}{-7}\right) +\left(\frac{8}{-9}\right) +\left(\frac{-9}{-9}\right)\\= \frac{-6}{7}- \frac{8}{9}+\frac{9}{9}\\=\frac{-6}{7}-\frac{8}{9}+\frac{1}{1}\\=\frac{-54}{63}-\frac{56}{63}+\frac{63}{63}\\=\frac{-54-56+63}{63}\\=\frac{-47}{63}\)
10. \(+\left(\frac{-10}{3}\right) -\left(\frac{4}{-6}\right) +\left(\frac{11}{-6}\right)\\= \frac{-10}{3}+ \frac{4}{6}-\frac{11}{6}\\=\frac{-10}{3}+\frac{2}{3}-\frac{11}{6}\\=\frac{-20}{6}+\frac{4}{6}-\frac{11}{6}\\=\frac{-20+4-11}{6}\\=\frac{-27}{6}\\=\frac{-9}{2}\)
11. \(+\left(\frac{-10}{7}\right) -\left(\frac{9}{10}\right) -\left(\frac{-5}{-9}\right)\\= \frac{-10}{7}- \frac{9}{10}-\frac{5}{9}\\=\frac{-900}{630}-\frac{567}{630}-\frac{350}{630}\\=\frac{-900-567-350}{630}\\=\frac{-1817}{630}\)
12. \(+\left(\frac{-5}{7}\right) -\left(\frac{6}{2}\right) -\left(\frac{2}{12}\right)\\= \frac{-5}{7}- \frac{6}{2}-\frac{2}{12}\\=\frac{-5}{7}-\frac{3}{1}-\frac{1}{6}\\=\frac{-30}{42}-\frac{126}{42}-\frac{7}{42}\\=\frac{-30-126-7}{42}\\=\frac{-163}{42}\)