Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-5}{-8}\right) +\left(\frac{-8}{-5}\right) +\left(\frac{5}{-5}\right)\\= \frac{5}{8}+ \frac{8}{5}-\frac{5}{5}\\=\frac{5}{8}+\frac{8}{5}-\frac{1}{1}\\=\frac{25}{40}+\frac{64}{40}-\frac{40}{40}\\=\frac{25+64-40}{40}\\=\frac{49}{40}\)
2. \(-\left(\frac{7}{8}\right) -\left(\frac{8}{-10}\right) +\left(\frac{-8}{6}\right)\\= \frac{-7}{8}+ \frac{8}{10}-\frac{8}{6}\\=\frac{-7}{8}+\frac{4}{5}-\frac{4}{3}\\=\frac{-105}{120}+\frac{96}{120}-\frac{160}{120}\\=\frac{-105+96-160}{120}\\=\frac{-169}{120}\)
3. \(+\left(\frac{5}{-3}\right) -\left(\frac{8}{-7}\right) +\left(\frac{-12}{-2}\right)\\= \frac{-5}{3}+ \frac{8}{7}+\frac{12}{2}\\=\frac{-5}{3}+\frac{8}{7}+\frac{6}{1}\\=\frac{-35}{21}+\frac{24}{21}+\frac{126}{21}\\=\frac{-35+24+126}{21}\\=\frac{115}{21}\)
4. \(-\left(\frac{4}{-7}\right) -\left(\frac{-4}{-4}\right) -\left(\frac{-8}{12}\right)\\= \frac{4}{7}- \frac{4}{4}+\frac{8}{12}\\=\frac{4}{7}-\frac{1}{1}+\frac{2}{3}\\=\frac{12}{21}-\frac{21}{21}+\frac{14}{21}\\=\frac{12-21+14}{21}\\=\frac{5}{21}\)
5. \(+\left(\frac{-3}{2}\right) -\left(\frac{-8}{4}\right) +\left(\frac{2}{-9}\right)\\= \frac{-3}{2}+ \frac{8}{4}-\frac{2}{9}\\=\frac{-3}{2}+\frac{2}{1}-\frac{2}{9}\\=\frac{-27}{18}+\frac{36}{18}-\frac{4}{18}\\=\frac{-27+36-4}{18}\\=\frac{5}{18}\)
6. \(+\left(\frac{9}{2}\right) -\left(\frac{4}{8}\right) -\left(\frac{9}{10}\right)\\= \frac{9}{2}- \frac{4}{8}-\frac{9}{10}\\=\frac{9}{2}-\frac{1}{2}-\frac{9}{10}\\=\frac{45}{10}-\frac{5}{10}-\frac{9}{10}\\=\frac{45-5-9}{10}\\=\frac{31}{10}\)
7. \(-\left(\frac{5}{6}\right) -\left(\frac{-10}{-5}\right) +\left(\frac{3}{-7}\right)\\= \frac{-5}{6}- \frac{10}{5}-\frac{3}{7}\\=\frac{-5}{6}-\frac{2}{1}-\frac{3}{7}\\=\frac{-35}{42}-\frac{84}{42}-\frac{18}{42}\\=\frac{-35-84-18}{42}\\=\frac{-137}{42}\)
8. \(-\left(\frac{8}{5}\right) +\left(\frac{7}{10}\right) -\left(\frac{-7}{5}\right)\\= \frac{-8}{5}+ \frac{7}{10}+\frac{7}{5}\\=\frac{-16}{10}+\frac{7}{10}+\frac{14}{10}\\=\frac{-16+7+14}{10}\\=\frac{5}{10}\\=\frac{1}{2}\)
9. \(+\left(\frac{-6}{-7}\right) +\left(\frac{7}{-5}\right) +\left(\frac{-11}{-7}\right)\\= \frac{6}{7}- \frac{7}{5}+\frac{11}{7}\\=\frac{30}{35}-\frac{49}{35}+\frac{55}{35}\\=\frac{30-49+55}{35}\\=\frac{36}{35}\)
10. \(-\left(\frac{-2}{5}\right) +\left(\frac{3}{2}\right) +\left(\frac{-4}{-10}\right)\\= \frac{2}{5}+ \frac{3}{2}+\frac{4}{10}\\=\frac{2}{5}+\frac{3}{2}+\frac{2}{5}\\=\frac{4}{10}+\frac{15}{10}+\frac{4}{10}\\=\frac{4+15+4}{10}\\=\frac{23}{10}\)
11. \(-\left(\frac{4}{-5}\right) -\left(\frac{4}{5}\right) +\left(\frac{10}{4}\right)\\= \frac{4}{5}- \frac{4}{5}+\frac{10}{4}\\=\frac{4}{5}-\frac{4}{5}+\frac{5}{2}\\=\frac{8}{10}-\frac{8}{10}+\frac{25}{10}\\=\frac{8-8+25}{10}\\=\frac{25}{10}\\=\frac{5}{2}\)
12. \(+\left(\frac{8}{-9}\right) -\left(\frac{-6}{4}\right) +\left(\frac{5}{9}\right)\\= \frac{-8}{9}+ \frac{6}{4}+\frac{5}{9}\\=\frac{-8}{9}+\frac{3}{2}+\frac{5}{9}\\=\frac{-16}{18}+\frac{27}{18}+\frac{10}{18}\\=\frac{-16+27+10}{18}\\=\frac{21}{18}\\=\frac{7}{6}\)