Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{3}{-7}\right) +\left(\frac{2}{3}\right) +\left(\frac{-4}{4}\right)\\= \frac{-3}{7}+ \frac{2}{3}-\frac{4}{4}\\=\frac{-3}{7}+\frac{2}{3}-\frac{1}{1}\\=\frac{-9}{21}+\frac{14}{21}-\frac{21}{21}\\=\frac{-9+14-21}{21}\\=\frac{-16}{21}\)
2. \(+\left(\frac{7}{-2}\right) +\left(\frac{3}{-5}\right) +\left(\frac{-12}{11}\right)\\= \frac{-7}{2}- \frac{3}{5}-\frac{12}{11}\\=\frac{-385}{110}-\frac{66}{110}-\frac{120}{110}\\=\frac{-385-66-120}{110}\\=\frac{-571}{110}\)
3. \(-\left(\frac{-7}{6}\right) +\left(\frac{-8}{4}\right) -\left(\frac{-12}{-8}\right)\\= \frac{7}{6}- \frac{8}{4}-\frac{12}{8}\\=\frac{7}{6}-\frac{2}{1}-\frac{3}{2}\\=\frac{7-2-3}{6}\\=\frac{2}{6}\\=\frac{1}{3}\)
4. \(-\left(\frac{-10}{7}\right) +\left(\frac{2}{-2}\right) -\left(\frac{9}{-4}\right)\\= \frac{10}{7}- \frac{2}{2}+\frac{9}{4}\\=\frac{10}{7}-\frac{1}{1}+\frac{9}{4}\\=\frac{40}{28}-\frac{28}{28}+\frac{63}{28}\\=\frac{40-28+63}{28}\\=\frac{75}{28}\)
5. \(+\left(\frac{5}{6}\right) -\left(\frac{9}{10}\right) -\left(\frac{-5}{7}\right)\\= \frac{5}{6}- \frac{9}{10}+\frac{5}{7}\\=\frac{175}{210}-\frac{189}{210}+\frac{150}{210}\\=\frac{175-189+150}{210}\\=\frac{136}{210}\\=\frac{68}{105}\)
6. \(+\left(\frac{-6}{5}\right) -\left(\frac{6}{7}\right) +\left(\frac{-2}{9}\right)\\= \frac{-6}{5}- \frac{6}{7}-\frac{2}{9}\\=\frac{-378}{315}-\frac{270}{315}-\frac{70}{315}\\=\frac{-378-270-70}{315}\\=\frac{-718}{315}\)
7. \(+\left(\frac{6}{5}\right) -\left(\frac{6}{8}\right) +\left(\frac{-8}{-11}\right)\\= \frac{6}{5}- \frac{6}{8}+\frac{8}{11}\\=\frac{6}{5}-\frac{3}{4}+\frac{8}{11}\\=\frac{264}{220}-\frac{165}{220}+\frac{160}{220}\\=\frac{264-165+160}{220}\\=\frac{259}{220}\)
8. \(-\left(\frac{-9}{-7}\right) +\left(\frac{-5}{3}\right) +\left(\frac{-4}{5}\right)\\= \frac{-9}{7}- \frac{5}{3}-\frac{4}{5}\\=\frac{-135}{105}-\frac{175}{105}-\frac{84}{105}\\=\frac{-135-175-84}{105}\\=\frac{-394}{105}\)
9. \(+\left(\frac{-7}{3}\right) -\left(\frac{3}{-5}\right) -\left(\frac{-9}{10}\right)\\= \frac{-7}{3}+ \frac{3}{5}+\frac{9}{10}\\=\frac{-70}{30}+\frac{18}{30}+\frac{27}{30}\\=\frac{-70+18+27}{30}\\=\frac{-25}{30}\\=\frac{-5}{6}\)
10. \(+\left(\frac{-2}{7}\right) +\left(\frac{2}{-8}\right) -\left(\frac{-4}{-12}\right)\\= \frac{-2}{7}- \frac{2}{8}-\frac{4}{12}\\=\frac{-2}{7}-\frac{1}{4}-\frac{1}{3}\\=\frac{-24}{84}-\frac{21}{84}-\frac{28}{84}\\=\frac{-24-21-28}{84}\\=\frac{-73}{84}\)
11. \(+\left(\frac{10}{7}\right) -\left(\frac{7}{-8}\right) -\left(\frac{-9}{-5}\right)\\= \frac{10}{7}+ \frac{7}{8}-\frac{9}{5}\\=\frac{400}{280}+\frac{245}{280}-\frac{504}{280}\\=\frac{400+245-504}{280}\\=\frac{141}{280}\)
12. \(-\left(\frac{-4}{-9}\right) -\left(\frac{4}{9}\right) +\left(\frac{-3}{-7}\right)\\= \frac{-4}{9}- \frac{4}{9}+\frac{3}{7}\\=\frac{-28}{63}-\frac{28}{63}+\frac{27}{63}\\=\frac{-28-28+27}{63}\\=\frac{-29}{63}\)