Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-3}{7}\right) -\left(\frac{-10}{-9}\right) -\left(\frac{4}{-3}\right)\\= \frac{-3}{7}- \frac{10}{9}+\frac{4}{3}\\=\frac{-27}{63}-\frac{70}{63}+\frac{84}{63}\\=\frac{-27-70+84}{63}\\=\frac{-13}{63}\)
2. \(-\left(\frac{8}{-5}\right) -\left(\frac{-6}{-2}\right) -\left(\frac{-6}{5}\right)\\= \frac{8}{5}- \frac{6}{2}+\frac{6}{5}\\=\frac{8}{5}-\frac{3}{1}+\frac{6}{5}\\=\frac{8-3+6}{5}\\=\frac{11}{5}\)
3. \(+\left(\frac{2}{3}\right) +\left(\frac{-6}{-4}\right) -\left(\frac{4}{11}\right)\\= \frac{2}{3}+ \frac{6}{4}-\frac{4}{11}\\=\frac{2}{3}+\frac{3}{2}-\frac{4}{11}\\=\frac{44}{66}+\frac{99}{66}-\frac{24}{66}\\=\frac{44+99-24}{66}\\=\frac{119}{66}\)
4. \(+\left(\frac{6}{5}\right) -\left(\frac{-9}{-3}\right) -\left(\frac{-8}{6}\right)\\= \frac{6}{5}- \frac{9}{3}+\frac{8}{6}\\=\frac{6}{5}-\frac{3}{1}+\frac{4}{3}\\=\frac{18}{15}-\frac{45}{15}+\frac{20}{15}\\=\frac{18-45+20}{15}\\=\frac{-7}{15}\)
5. \(-\left(\frac{3}{-8}\right) +\left(\frac{-6}{-8}\right) +\left(\frac{7}{-8}\right)\\= \frac{3}{8}+ \frac{6}{8}-\frac{7}{8}\\=\frac{3}{8}+\frac{3}{4}-\frac{7}{8}\\=\frac{3+3-7}{8}\\=\frac{-1}{8}\)
6. \(+\left(\frac{4}{9}\right) +\left(\frac{4}{-3}\right) +\left(\frac{-5}{-10}\right)\\= \frac{4}{9}- \frac{4}{3}+\frac{5}{10}\\=\frac{4}{9}-\frac{4}{3}+\frac{1}{2}\\=\frac{8}{18}-\frac{24}{18}+\frac{9}{18}\\=\frac{8-24+9}{18}\\=\frac{-7}{18}\)
7. \(+\left(\frac{-5}{3}\right) -\left(\frac{-7}{10}\right) -\left(\frac{-11}{-2}\right)\\= \frac{-5}{3}+ \frac{7}{10}-\frac{11}{2}\\=\frac{-50}{30}+\frac{21}{30}-\frac{165}{30}\\=\frac{-50+21-165}{30}\\=\frac{-194}{30}\\=\frac{-97}{15}\)
8. \(+\left(\frac{-7}{8}\right) +\left(\frac{-8}{-6}\right) +\left(\frac{11}{-11}\right)\\= \frac{-7}{8}+ \frac{8}{6}-\frac{11}{11}\\=\frac{-7}{8}+\frac{4}{3}-\frac{1}{1}\\=\frac{-21}{24}+\frac{32}{24}-\frac{24}{24}\\=\frac{-21+32-24}{24}\\=\frac{-13}{24}\)
9. \(+\left(\frac{6}{5}\right) +\left(\frac{-5}{-7}\right) -\left(\frac{-7}{-5}\right)\\= \frac{6}{5}+ \frac{5}{7}-\frac{7}{5}\\=\frac{42}{35}+\frac{25}{35}-\frac{49}{35}\\=\frac{42+25-49}{35}\\=\frac{18}{35}\)
10. \(+\left(\frac{3}{-2}\right) +\left(\frac{7}{-8}\right) -\left(\frac{3}{-2}\right)\\= \frac{-3}{2}- \frac{7}{8}+\frac{3}{2}\\=\frac{-12}{8}-\frac{7}{8}+\frac{12}{8}\\=\frac{-12-7+12}{8}\\=\frac{-7}{8}\)
11. \(+\left(\frac{3}{4}\right) -\left(\frac{4}{-3}\right) +\left(\frac{10}{-8}\right)\\= \frac{3}{4}+ \frac{4}{3}-\frac{10}{8}\\=\frac{3}{4}+\frac{4}{3}-\frac{5}{4}\\=\frac{9}{12}+\frac{16}{12}-\frac{15}{12}\\=\frac{9+16-15}{12}\\=\frac{10}{12}\\=\frac{5}{6}\)
12. \(-\left(\frac{3}{8}\right) +\left(\frac{5}{-7}\right) +\left(\frac{2}{-4}\right)\\= \frac{-3}{8}- \frac{5}{7}-\frac{2}{4}\\=\frac{-3}{8}-\frac{5}{7}-\frac{1}{2}\\=\frac{-21}{56}-\frac{40}{56}-\frac{28}{56}\\=\frac{-21-40-28}{56}\\=\frac{-89}{56}\)