Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{2}{-5}\right) -\left(\frac{-3}{-10}\right) +\left(\frac{2}{-3}\right)\\= \frac{2}{5}- \frac{3}{10}-\frac{2}{3}\\=\frac{12}{30}-\frac{9}{30}-\frac{20}{30}\\=\frac{12-9-20}{30}\\=\frac{-17}{30}\)
2. \(-\left(\frac{6}{-5}\right) -\left(\frac{5}{-8}\right) -\left(\frac{8}{-7}\right)\\= \frac{6}{5}+ \frac{5}{8}+\frac{8}{7}\\=\frac{336}{280}+\frac{175}{280}+\frac{320}{280}\\=\frac{336+175+320}{280}\\=\frac{831}{280}\)
3. \(+\left(\frac{-6}{-7}\right) +\left(\frac{-10}{8}\right) +\left(\frac{5}{-9}\right)\\= \frac{6}{7}- \frac{10}{8}-\frac{5}{9}\\=\frac{6}{7}-\frac{5}{4}-\frac{5}{9}\\=\frac{216}{252}-\frac{315}{252}-\frac{140}{252}\\=\frac{216-315-140}{252}\\=\frac{-239}{252}\)
4. \(-\left(\frac{-10}{-3}\right) -\left(\frac{4}{3}\right) -\left(\frac{-4}{-6}\right)\\= \frac{-10}{3}- \frac{4}{3}-\frac{4}{6}\\=\frac{-10}{3}-\frac{4}{3}-\frac{2}{3}\\=\frac{-10-4-2}{3}\\=\frac{-16}{3}\)
5. \(-\left(\frac{-4}{7}\right) +\left(\frac{7}{4}\right) +\left(\frac{-11}{7}\right)\\= \frac{4}{7}+ \frac{7}{4}-\frac{11}{7}\\=\frac{16}{28}+\frac{49}{28}-\frac{44}{28}\\=\frac{16+49-44}{28}\\=\frac{21}{28}\\=\frac{3}{4}\)
6. \(+\left(\frac{-5}{-2}\right) +\left(\frac{4}{-4}\right) -\left(\frac{-10}{-2}\right)\\= \frac{5}{2}- \frac{4}{4}-\frac{10}{2}\\=\frac{5}{2}-\frac{1}{1}-\frac{5}{1}\\=\frac{5-1-5}{2}\\=\frac{-1}{2}\)
7. \(-\left(\frac{9}{-8}\right) +\left(\frac{-3}{7}\right) +\left(\frac{11}{7}\right)\\= \frac{9}{8}- \frac{3}{7}+\frac{11}{7}\\=\frac{63}{56}-\frac{24}{56}+\frac{88}{56}\\=\frac{63-24+88}{56}\\=\frac{127}{56}\)
8. \(-\left(\frac{-3}{7}\right) -\left(\frac{2}{-6}\right) -\left(\frac{-8}{-12}\right)\\= \frac{3}{7}+ \frac{2}{6}-\frac{8}{12}\\=\frac{3}{7}+\frac{1}{3}-\frac{2}{3}\\=\frac{9}{21}+\frac{7}{21}-\frac{14}{21}\\=\frac{9+7-14}{21}\\=\frac{2}{21}\)
9. \(+\left(\frac{6}{7}\right) +\left(\frac{3}{-4}\right) +\left(\frac{5}{-11}\right)\\= \frac{6}{7}- \frac{3}{4}-\frac{5}{11}\\=\frac{264}{308}-\frac{231}{308}-\frac{140}{308}\\=\frac{264-231-140}{308}\\=\frac{-107}{308}\)
10. \(+\left(\frac{-8}{-5}\right) -\left(\frac{9}{5}\right) -\left(\frac{8}{-8}\right)\\= \frac{8}{5}- \frac{9}{5}+\frac{8}{8}\\=\frac{8}{5}-\frac{9}{5}+\frac{1}{1}\\=\frac{8-9+1}{5}\\=\frac{0}{5}\\=\frac{0}{1}\)
11. \(-\left(\frac{-7}{-2}\right) -\left(\frac{4}{-6}\right) -\left(\frac{-7}{11}\right)\\= \frac{-7}{2}+ \frac{4}{6}+\frac{7}{11}\\=\frac{-7}{2}+\frac{2}{3}+\frac{7}{11}\\=\frac{-231}{66}+\frac{44}{66}+\frac{42}{66}\\=\frac{-231+44+42}{66}\\=\frac{-145}{66}\)
12. \(-\left(\frac{-6}{-5}\right) +\left(\frac{-6}{7}\right) +\left(\frac{11}{4}\right)\\= \frac{-6}{5}- \frac{6}{7}+\frac{11}{4}\\=\frac{-168}{140}-\frac{120}{140}+\frac{385}{140}\\=\frac{-168-120+385}{140}\\=\frac{97}{140}\)