Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{5}{6}\right) +\left(\frac{-6}{7}\right) -\left(\frac{2}{12}\right)\\= \frac{-5}{6}- \frac{6}{7}-\frac{2}{12}\\=\frac{-5}{6}-\frac{6}{7}-\frac{1}{6}\\=\frac{-35}{42}-\frac{36}{42}-\frac{7}{42}\\=\frac{-35-36-7}{42}\\=\frac{-78}{42}\\=\frac{-13}{7}\)
2. \(+\left(\frac{-5}{8}\right) -\left(\frac{2}{9}\right) -\left(\frac{6}{5}\right)\\= \frac{-5}{8}- \frac{2}{9}-\frac{6}{5}\\=\frac{-225}{360}-\frac{80}{360}-\frac{432}{360}\\=\frac{-225-80-432}{360}\\=\frac{-737}{360}\)
3. \(-\left(\frac{2}{-5}\right) -\left(\frac{-2}{-7}\right) -\left(\frac{-11}{9}\right)\\= \frac{2}{5}- \frac{2}{7}+\frac{11}{9}\\=\frac{126}{315}-\frac{90}{315}+\frac{385}{315}\\=\frac{126-90+385}{315}\\=\frac{421}{315}\)
4. \(-\left(\frac{6}{-5}\right) +\left(\frac{2}{-6}\right) -\left(\frac{2}{2}\right)\\= \frac{6}{5}- \frac{2}{6}-\frac{2}{2}\\=\frac{6}{5}-\frac{1}{3}-\frac{1}{1}\\=\frac{18}{15}-\frac{5}{15}-\frac{15}{15}\\=\frac{18-5-15}{15}\\=\frac{-2}{15}\)
5. \(+\left(\frac{9}{7}\right) +\left(\frac{-6}{3}\right) -\left(\frac{8}{-8}\right)\\= \frac{9}{7}- \frac{6}{3}+\frac{8}{8}\\=\frac{9}{7}-\frac{2}{1}+\frac{1}{1}\\=\frac{9-2+1}{7}\\=\frac{8}{7}\)
6. \(-\left(\frac{4}{-5}\right) +\left(\frac{4}{-7}\right) -\left(\frac{2}{-5}\right)\\= \frac{4}{5}- \frac{4}{7}+\frac{2}{5}\\=\frac{28}{35}-\frac{20}{35}+\frac{14}{35}\\=\frac{28-20+14}{35}\\=\frac{22}{35}\)
7. \(-\left(\frac{-3}{-4}\right) +\left(\frac{-9}{7}\right) +\left(\frac{2}{-6}\right)\\= \frac{-3}{4}- \frac{9}{7}-\frac{2}{6}\\=\frac{-3}{4}-\frac{9}{7}-\frac{1}{3}\\=\frac{-63}{84}-\frac{108}{84}-\frac{28}{84}\\=\frac{-63-108-28}{84}\\=\frac{-199}{84}\)
8. \(+\left(\frac{4}{5}\right) +\left(\frac{-5}{9}\right) -\left(\frac{-7}{-3}\right)\\= \frac{4}{5}- \frac{5}{9}-\frac{7}{3}\\=\frac{36}{45}-\frac{25}{45}-\frac{105}{45}\\=\frac{36-25-105}{45}\\=\frac{-94}{45}\)
9. \(+\left(\frac{10}{-7}\right) +\left(\frac{-7}{-2}\right) -\left(\frac{-9}{4}\right)\\= \frac{-10}{7}+ \frac{7}{2}+\frac{9}{4}\\=\frac{-40}{28}+\frac{98}{28}+\frac{63}{28}\\=\frac{-40+98+63}{28}\\=\frac{121}{28}\)
10. \(-\left(\frac{3}{7}\right) +\left(\frac{-9}{8}\right) -\left(\frac{-4}{-12}\right)\\= \frac{-3}{7}- \frac{9}{8}-\frac{4}{12}\\=\frac{-3}{7}-\frac{9}{8}-\frac{1}{3}\\=\frac{-72}{168}-\frac{189}{168}-\frac{56}{168}\\=\frac{-72-189-56}{168}\\=\frac{-317}{168}\)
11. \(-\left(\frac{8}{-7}\right) +\left(\frac{2}{-2}\right) -\left(\frac{11}{-5}\right)\\= \frac{8}{7}- \frac{2}{2}+\frac{11}{5}\\=\frac{8}{7}-\frac{1}{1}+\frac{11}{5}\\=\frac{40}{35}-\frac{35}{35}+\frac{77}{35}\\=\frac{40-35+77}{35}\\=\frac{82}{35}\)
12. \(+\left(\frac{-3}{8}\right) -\left(\frac{6}{-9}\right) +\left(\frac{4}{2}\right)\\= \frac{-3}{8}+ \frac{6}{9}+\frac{4}{2}\\=\frac{-3}{8}+\frac{2}{3}+\frac{2}{1}\\=\frac{-9}{24}+\frac{16}{24}+\frac{48}{24}\\=\frac{-9+16+48}{24}\\=\frac{55}{24}\)