Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{5}{2}\right) +\left(\frac{7}{3}\right) +\left(\frac{-3}{-11}\right)\\= \frac{-5}{2}+ \frac{7}{3}+\frac{3}{11}\\=\frac{-165}{66}+\frac{154}{66}+\frac{18}{66}\\=\frac{-165+154+18}{66}\\=\frac{7}{66}\)
2. \(-\left(\frac{10}{-7}\right) +\left(\frac{6}{-9}\right) -\left(\frac{-3}{9}\right)\\= \frac{10}{7}- \frac{6}{9}+\frac{3}{9}\\=\frac{10}{7}-\frac{2}{3}+\frac{1}{3}\\=\frac{30}{21}-\frac{14}{21}+\frac{7}{21}\\=\frac{30-14+7}{21}\\=\frac{23}{21}\)
3. \(-\left(\frac{3}{5}\right) -\left(\frac{-8}{4}\right) -\left(\frac{-2}{-4}\right)\\= \frac{-3}{5}+ \frac{8}{4}-\frac{2}{4}\\=\frac{-3}{5}+\frac{2}{1}-\frac{1}{2}\\=\frac{-6}{10}+\frac{20}{10}-\frac{5}{10}\\=\frac{-6+20-5}{10}\\=\frac{9}{10}\)
4. \(-\left(\frac{-9}{-4}\right) -\left(\frac{3}{-2}\right) -\left(\frac{-9}{-4}\right)\\= \frac{-9}{4}+ \frac{3}{2}-\frac{9}{4}\\=\frac{-9+3-9}{4}\\=\frac{-15}{4}\)
5. \(+\left(\frac{9}{4}\right) +\left(\frac{-8}{8}\right) +\left(\frac{3}{10}\right)\\= \frac{9}{4}- \frac{8}{8}+\frac{3}{10}\\=\frac{9}{4}-\frac{1}{1}+\frac{3}{10}\\=\frac{45}{20}-\frac{20}{20}+\frac{6}{20}\\=\frac{45-20+6}{20}\\=\frac{31}{20}\)
6. \(-\left(\frac{-6}{-7}\right) +\left(\frac{2}{-3}\right) -\left(\frac{-9}{6}\right)\\= \frac{-6}{7}- \frac{2}{3}+\frac{9}{6}\\=\frac{-6}{7}-\frac{2}{3}+\frac{3}{2}\\=\frac{-36}{42}-\frac{28}{42}+\frac{63}{42}\\=\frac{-36-28+63}{42}\\=\frac{-1}{42}\)
7. \(+\left(\frac{9}{7}\right) +\left(\frac{3}{-6}\right) +\left(\frac{11}{8}\right)\\= \frac{9}{7}- \frac{3}{6}+\frac{11}{8}\\=\frac{9}{7}-\frac{1}{2}+\frac{11}{8}\\=\frac{72}{56}-\frac{28}{56}+\frac{77}{56}\\=\frac{72-28+77}{56}\\=\frac{121}{56}\)
8. \(+\left(\frac{3}{2}\right) +\left(\frac{7}{-10}\right) -\left(\frac{-9}{8}\right)\\= \frac{3}{2}- \frac{7}{10}+\frac{9}{8}\\=\frac{60}{40}-\frac{28}{40}+\frac{45}{40}\\=\frac{60-28+45}{40}\\=\frac{77}{40}\)
9. \(-\left(\frac{-8}{9}\right) +\left(\frac{2}{9}\right) -\left(\frac{-10}{-5}\right)\\= \frac{8}{9}+ \frac{2}{9}-\frac{10}{5}\\=\frac{8}{9}+\frac{2}{9}-\frac{2}{1}\\=\frac{8+2-2}{9}\\=\frac{8}{9}\)
10. \(-\left(\frac{7}{-9}\right) +\left(\frac{-2}{2}\right) -\left(\frac{-5}{-2}\right)\\= \frac{7}{9}- \frac{2}{2}-\frac{5}{2}\\=\frac{7}{9}-\frac{1}{1}-\frac{5}{2}\\=\frac{14}{18}-\frac{18}{18}-\frac{45}{18}\\=\frac{14-18-45}{18}\\=\frac{-49}{18}\)
11. \(-\left(\frac{-2}{-7}\right) +\left(\frac{-9}{7}\right) +\left(\frac{6}{-10}\right)\\= \frac{-2}{7}- \frac{9}{7}-\frac{6}{10}\\=\frac{-2}{7}-\frac{9}{7}-\frac{3}{5}\\=\frac{-10}{35}-\frac{45}{35}-\frac{21}{35}\\=\frac{-10-45-21}{35}\\=\frac{-76}{35}\)
12. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-3}{-5}\right) +\left(\frac{-12}{3}\right)\\= \frac{6}{5}- \frac{3}{5}-\frac{12}{3}\\=\frac{6}{5}-\frac{3}{5}-\frac{4}{1}\\=\frac{6-3-4}{5}\\=\frac{-1}{5}\)