Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-4}{-5}\right) -\left(\frac{7}{2}\right) -\left(\frac{7}{-2}\right)\\= \frac{4}{5}- \frac{7}{2}+\frac{7}{2}\\=\frac{8}{10}-\frac{35}{10}+\frac{35}{10}\\=\frac{8-35+35}{10}\\=\frac{8}{10}\\=\frac{4}{5}\)
2. \(+\left(\frac{-3}{-2}\right) -\left(\frac{4}{-5}\right) +\left(\frac{12}{11}\right)\\= \frac{3}{2}+ \frac{4}{5}+\frac{12}{11}\\=\frac{165}{110}+\frac{88}{110}+\frac{120}{110}\\=\frac{165+88+120}{110}\\=\frac{373}{110}\)
3. \(+\left(\frac{8}{5}\right) +\left(\frac{5}{8}\right) -\left(\frac{-10}{8}\right)\\= \frac{8}{5}+ \frac{5}{8}+\frac{10}{8}\\=\frac{8}{5}+\frac{5}{8}+\frac{5}{4}\\=\frac{64}{40}+\frac{25}{40}+\frac{50}{40}\\=\frac{64+25+50}{40}\\=\frac{139}{40}\)
4. \(+\left(\frac{7}{-4}\right) +\left(\frac{8}{7}\right) +\left(\frac{4}{-4}\right)\\= \frac{-7}{4}+ \frac{8}{7}-\frac{4}{4}\\=\frac{-7}{4}+\frac{8}{7}-\frac{1}{1}\\=\frac{-49}{28}+\frac{32}{28}-\frac{28}{28}\\=\frac{-49+32-28}{28}\\=\frac{-45}{28}\)
5. \(-\left(\frac{-6}{5}\right) -\left(\frac{2}{5}\right) +\left(\frac{-7}{10}\right)\\= \frac{6}{5}- \frac{2}{5}-\frac{7}{10}\\=\frac{12}{10}-\frac{4}{10}-\frac{7}{10}\\=\frac{12-4-7}{10}\\=\frac{1}{10}\)
6. \(-\left(\frac{8}{3}\right) -\left(\frac{9}{-4}\right) -\left(\frac{10}{-12}\right)\\= \frac{-8}{3}+ \frac{9}{4}+\frac{10}{12}\\=\frac{-8}{3}+\frac{9}{4}+\frac{5}{6}\\=\frac{-32}{12}+\frac{27}{12}+\frac{10}{12}\\=\frac{-32+27+10}{12}\\=\frac{5}{12}\)
7. \(-\left(\frac{-5}{2}\right) -\left(\frac{-10}{-9}\right) +\left(\frac{-2}{9}\right)\\= \frac{5}{2}- \frac{10}{9}-\frac{2}{9}\\=\frac{45}{18}-\frac{20}{18}-\frac{4}{18}\\=\frac{45-20-4}{18}\\=\frac{21}{18}\\=\frac{7}{6}\)
8. \(+\left(\frac{2}{9}\right) +\left(\frac{-5}{-8}\right) -\left(\frac{3}{-10}\right)\\= \frac{2}{9}+ \frac{5}{8}+\frac{3}{10}\\=\frac{80}{360}+\frac{225}{360}+\frac{108}{360}\\=\frac{80+225+108}{360}\\=\frac{413}{360}\)
9. \(-\left(\frac{-7}{2}\right) -\left(\frac{9}{6}\right) -\left(\frac{5}{8}\right)\\= \frac{7}{2}- \frac{9}{6}-\frac{5}{8}\\=\frac{7}{2}-\frac{3}{2}-\frac{5}{8}\\=\frac{28}{8}-\frac{12}{8}-\frac{5}{8}\\=\frac{28-12-5}{8}\\=\frac{11}{8}\)
10. \(-\left(\frac{2}{-7}\right) -\left(\frac{8}{2}\right) -\left(\frac{3}{-9}\right)\\= \frac{2}{7}- \frac{8}{2}+\frac{3}{9}\\=\frac{2}{7}-\frac{4}{1}+\frac{1}{3}\\=\frac{6}{21}-\frac{84}{21}+\frac{7}{21}\\=\frac{6-84+7}{21}\\=\frac{-71}{21}\)
11. \(+\left(\frac{-7}{2}\right) -\left(\frac{-2}{8}\right) -\left(\frac{-3}{10}\right)\\= \frac{-7}{2}+ \frac{2}{8}+\frac{3}{10}\\=\frac{-7}{2}+\frac{1}{4}+\frac{3}{10}\\=\frac{-70}{20}+\frac{5}{20}+\frac{6}{20}\\=\frac{-70+5+6}{20}\\=\frac{-59}{20}\)
12. \(+\left(\frac{9}{-7}\right) -\left(\frac{-3}{-8}\right) -\left(\frac{-11}{-3}\right)\\= \frac{-9}{7}- \frac{3}{8}-\frac{11}{3}\\=\frac{-216}{168}-\frac{63}{168}-\frac{616}{168}\\=\frac{-216-63-616}{168}\\=\frac{-895}{168}\)