Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-6}{-7}\right) +\left(\frac{3}{-8}\right) -\left(\frac{6}{9}\right)\\= \frac{6}{7}- \frac{3}{8}-\frac{6}{9}\\=\frac{6}{7}-\frac{3}{8}-\frac{2}{3}\\=\frac{144}{168}-\frac{63}{168}-\frac{112}{168}\\=\frac{144-63-112}{168}\\=\frac{-31}{168}\)
2. \(+\left(\frac{3}{8}\right) +\left(\frac{10}{-9}\right) -\left(\frac{9}{-9}\right)\\= \frac{3}{8}- \frac{10}{9}+\frac{9}{9}\\=\frac{3}{8}-\frac{10}{9}+\frac{1}{1}\\=\frac{27}{72}-\frac{80}{72}+\frac{72}{72}\\=\frac{27-80+72}{72}\\=\frac{19}{72}\)
3. \(-\left(\frac{-10}{-7}\right) +\left(\frac{10}{4}\right) -\left(\frac{4}{7}\right)\\= \frac{-10}{7}+ \frac{10}{4}-\frac{4}{7}\\=\frac{-10}{7}+\frac{5}{2}-\frac{4}{7}\\=\frac{-20}{14}+\frac{35}{14}-\frac{8}{14}\\=\frac{-20+35-8}{14}\\=\frac{7}{14}\\=\frac{1}{2}\)
4. \(+\left(\frac{3}{-5}\right) +\left(\frac{2}{5}\right) +\left(\frac{-9}{-10}\right)\\= \frac{-3}{5}+ \frac{2}{5}-\frac{9}{10}\\=\frac{-6}{10}+\frac{4}{10}-\frac{9}{10}\\=\frac{-6+4-9}{10}\\=\frac{-11}{10}\)
5. \(+\left(\frac{-4}{7}\right) +\left(\frac{-9}{-7}\right) +\left(\frac{10}{-9}\right)\\= \frac{-4}{7}+ \frac{9}{7}+\frac{10}{9}\\=\frac{-36}{63}+\frac{81}{63}+\frac{70}{63}\\=\frac{-36+81+70}{63}\\=\frac{115}{63}\)
6. \(-\left(\frac{-3}{-2}\right) -\left(\frac{-4}{-2}\right) +\left(\frac{-7}{-3}\right)\\= \frac{-3}{2}- \frac{4}{2}+\frac{7}{3}\\=\frac{-3}{2}-\frac{2}{1}+\frac{7}{3}\\=\frac{-9}{6}-\frac{12}{6}+\frac{14}{6}\\=\frac{-9-12+14}{6}\\=\frac{-7}{6}\)
7. \(-\left(\frac{4}{7}\right) +\left(\frac{-9}{4}\right) +\left(\frac{-9}{-7}\right)\\= \frac{-4}{7}- \frac{9}{4}+\frac{9}{7}\\=\frac{-16}{28}-\frac{63}{28}+\frac{36}{28}\\=\frac{-16-63+36}{28}\\=\frac{-43}{28}\)
8. \(+\left(\frac{-10}{3}\right) -\left(\frac{6}{3}\right) +\left(\frac{10}{-7}\right)\\= \frac{-10}{3}- \frac{6}{3}-\frac{10}{7}\\=\frac{-10}{3}-\frac{2}{1}-\frac{10}{7}\\=\frac{-70}{21}-\frac{42}{21}-\frac{30}{21}\\=\frac{-70-42-30}{21}\\=\frac{-142}{21}\)
9. \(+\left(\frac{8}{7}\right) +\left(\frac{6}{-10}\right) +\left(\frac{-11}{-3}\right)\\= \frac{8}{7}- \frac{6}{10}-\frac{11}{3}\\=\frac{8}{7}-\frac{3}{5}-\frac{11}{3}\\=\frac{120}{105}-\frac{63}{105}-\frac{385}{105}\\=\frac{120-63-385}{105}\\=\frac{-328}{105}\)
10. \(-\left(\frac{-9}{-5}\right) -\left(\frac{-9}{10}\right) +\left(\frac{2}{10}\right)\\= \frac{-9}{5}+ \frac{9}{10}-\frac{2}{10}\\=\frac{-9}{5}+\frac{9}{10}-\frac{1}{5}\\=\frac{-18}{10}+\frac{9}{10}-\frac{2}{10}\\=\frac{-18+9-2}{10}\\=\frac{-11}{10}\)
11. \(-\left(\frac{-10}{7}\right) +\left(\frac{4}{-6}\right) -\left(\frac{-4}{10}\right)\\= \frac{10}{7}- \frac{4}{6}-\frac{4}{10}\\=\frac{10}{7}-\frac{2}{3}-\frac{2}{5}\\=\frac{150}{105}-\frac{70}{105}-\frac{42}{105}\\=\frac{150-70-42}{105}\\=\frac{38}{105}\)
12. \(-\left(\frac{-3}{10}\right) +\left(\frac{-6}{9}\right) -\left(\frac{-9}{-10}\right)\\= \frac{3}{10}- \frac{6}{9}-\frac{9}{10}\\=\frac{3}{10}-\frac{2}{3}-\frac{9}{10}\\=\frac{9}{30}-\frac{20}{30}-\frac{27}{30}\\=\frac{9-20-27}{30}\\=\frac{-38}{30}\\=\frac{-19}{15}\)