Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{5}{-7}\right) +\left(\frac{4}{9}\right) -\left(\frac{-11}{3}\right)\\= \frac{5}{7}+ \frac{4}{9}+\frac{11}{3}\\=\frac{45}{63}+\frac{28}{63}+\frac{231}{63}\\=\frac{45+28+231}{63}\\=\frac{304}{63}\)
2. \(-\left(\frac{10}{3}\right) +\left(\frac{7}{-7}\right) +\left(\frac{-8}{8}\right)\\= \frac{-10}{3}- \frac{7}{7}-\frac{8}{8}\\=\frac{-10}{3}-\frac{1}{1}-\frac{1}{1}\\=\frac{-10-1-1}{3}\\=\frac{-12}{3}\\=\frac{-4}{1}\)
3. \(-\left(\frac{2}{-9}\right) -\left(\frac{5}{4}\right) -\left(\frac{-6}{2}\right)\\= \frac{2}{9}- \frac{5}{4}+\frac{6}{2}\\=\frac{2}{9}-\frac{5}{4}+\frac{3}{1}\\=\frac{8}{36}-\frac{45}{36}+\frac{108}{36}\\=\frac{8-45+108}{36}\\=\frac{71}{36}\)
4. \(-\left(\frac{9}{-4}\right) +\left(\frac{-3}{-6}\right) +\left(\frac{-11}{12}\right)\\= \frac{9}{4}+ \frac{3}{6}-\frac{11}{12}\\=\frac{9}{4}+\frac{1}{2}-\frac{11}{12}\\=\frac{27}{12}+\frac{6}{12}-\frac{11}{12}\\=\frac{27+6-11}{12}\\=\frac{22}{12}\\=\frac{11}{6}\)
5. \(+\left(\frac{6}{-5}\right) +\left(\frac{-2}{7}\right) -\left(\frac{9}{-2}\right)\\= \frac{-6}{5}- \frac{2}{7}+\frac{9}{2}\\=\frac{-84}{70}-\frac{20}{70}+\frac{315}{70}\\=\frac{-84-20+315}{70}\\=\frac{211}{70}\)
6. \(+\left(\frac{-6}{5}\right) +\left(\frac{8}{-7}\right) +\left(\frac{-5}{8}\right)\\= \frac{-6}{5}- \frac{8}{7}-\frac{5}{8}\\=\frac{-336}{280}-\frac{320}{280}-\frac{175}{280}\\=\frac{-336-320-175}{280}\\=\frac{-831}{280}\)
7. \(-\left(\frac{5}{7}\right) +\left(\frac{-5}{5}\right) +\left(\frac{-10}{4}\right)\\= \frac{-5}{7}- \frac{5}{5}-\frac{10}{4}\\=\frac{-5}{7}-\frac{1}{1}-\frac{5}{2}\\=\frac{-10}{14}-\frac{14}{14}-\frac{35}{14}\\=\frac{-10-14-35}{14}\\=\frac{-59}{14}\)
8. \(-\left(\frac{5}{2}\right) -\left(\frac{-7}{-9}\right) +\left(\frac{4}{8}\right)\\= \frac{-5}{2}- \frac{7}{9}+\frac{4}{8}\\=\frac{-5}{2}-\frac{7}{9}+\frac{1}{2}\\=\frac{-45}{18}-\frac{14}{18}+\frac{9}{18}\\=\frac{-45-14+9}{18}\\=\frac{-50}{18}\\=\frac{-25}{9}\)
9. \(+\left(\frac{6}{5}\right) -\left(\frac{2}{-6}\right) -\left(\frac{-8}{-2}\right)\\= \frac{6}{5}+ \frac{2}{6}-\frac{8}{2}\\=\frac{6}{5}+\frac{1}{3}-\frac{4}{1}\\=\frac{18}{15}+\frac{5}{15}-\frac{60}{15}\\=\frac{18+5-60}{15}\\=\frac{-37}{15}\)
10. \(+\left(\frac{5}{6}\right) -\left(\frac{4}{-9}\right) -\left(\frac{-7}{4}\right)\\= \frac{5}{6}+ \frac{4}{9}+\frac{7}{4}\\=\frac{30}{36}+\frac{16}{36}+\frac{63}{36}\\=\frac{30+16+63}{36}\\=\frac{109}{36}\)
11. \(+\left(\frac{-3}{8}\right) +\left(\frac{5}{7}\right) -\left(\frac{7}{8}\right)\\= \frac{-3}{8}+ \frac{5}{7}-\frac{7}{8}\\=\frac{-21}{56}+\frac{40}{56}-\frac{49}{56}\\=\frac{-21+40-49}{56}\\=\frac{-30}{56}\\=\frac{-15}{28}\)
12. \(+\left(\frac{4}{9}\right) -\left(\frac{-2}{7}\right) -\left(\frac{-5}{-7}\right)\\= \frac{4}{9}+ \frac{2}{7}-\frac{5}{7}\\=\frac{28}{63}+\frac{18}{63}-\frac{45}{63}\\=\frac{28+18-45}{63}\\=\frac{1}{63}\)