Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-5}{-7}\right) -\left(\frac{-5}{2}\right) -\left(\frac{7}{11}\right)\\= \frac{-5}{7}+ \frac{5}{2}-\frac{7}{11}\\=\frac{-110}{154}+\frac{385}{154}-\frac{98}{154}\\=\frac{-110+385-98}{154}\\=\frac{177}{154}\)
2. \(+\left(\frac{6}{-5}\right) -\left(\frac{-10}{-9}\right) +\left(\frac{9}{4}\right)\\= \frac{-6}{5}- \frac{10}{9}+\frac{9}{4}\\=\frac{-216}{180}-\frac{200}{180}+\frac{405}{180}\\=\frac{-216-200+405}{180}\\=\frac{-11}{180}\)
3. \(+\left(\frac{-9}{7}\right) +\left(\frac{-6}{7}\right) -\left(\frac{-4}{-4}\right)\\= \frac{-9}{7}- \frac{6}{7}-\frac{4}{4}\\=\frac{-9}{7}-\frac{6}{7}-\frac{1}{1}\\=\frac{-9-6-1}{7}\\=\frac{-16}{7}\)
4. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-5}{7}\right) +\left(\frac{12}{-2}\right)\\= \frac{6}{5}+ \frac{5}{7}-\frac{12}{2}\\=\frac{6}{5}+\frac{5}{7}-\frac{6}{1}\\=\frac{42}{35}+\frac{25}{35}-\frac{210}{35}\\=\frac{42+25-210}{35}\\=\frac{-143}{35}\)
5. \(+\left(\frac{4}{3}\right) -\left(\frac{-9}{-3}\right) +\left(\frac{-11}{11}\right)\\= \frac{4}{3}- \frac{9}{3}-\frac{11}{11}\\=\frac{4}{3}-\frac{3}{1}-\frac{1}{1}\\=\frac{4-3-1}{3}\\=\frac{0}{3}\\=\frac{0}{1}\)
6. \(-\left(\frac{-10}{-7}\right) +\left(\frac{-5}{6}\right) -\left(\frac{-11}{-10}\right)\\= \frac{-10}{7}- \frac{5}{6}-\frac{11}{10}\\=\frac{-300}{210}-\frac{175}{210}-\frac{231}{210}\\=\frac{-300-175-231}{210}\\=\frac{-706}{210}\\=\frac{-353}{105}\)
7. \(+\left(\frac{-8}{-9}\right) +\left(\frac{-3}{8}\right) +\left(\frac{-2}{7}\right)\\= \frac{8}{9}- \frac{3}{8}-\frac{2}{7}\\=\frac{448}{504}-\frac{189}{504}-\frac{144}{504}\\=\frac{448-189-144}{504}\\=\frac{115}{504}\)
8. \(+\left(\frac{-4}{-3}\right) -\left(\frac{-8}{6}\right) +\left(\frac{4}{8}\right)\\= \frac{4}{3}+ \frac{8}{6}+\frac{4}{8}\\=\frac{4}{3}+\frac{4}{3}+\frac{1}{2}\\=\frac{8}{6}+\frac{8}{6}+\frac{3}{6}\\=\frac{8+8+3}{6}\\=\frac{19}{6}\)
9. \(+\left(\frac{10}{3}\right) +\left(\frac{-5}{-6}\right) -\left(\frac{-10}{-10}\right)\\= \frac{10}{3}+ \frac{5}{6}-\frac{10}{10}\\=\frac{10}{3}+\frac{5}{6}-\frac{1}{1}\\=\frac{20}{6}+\frac{5}{6}-\frac{6}{6}\\=\frac{20+5-6}{6}\\=\frac{19}{6}\)
10. \(-\left(\frac{-3}{-4}\right) -\left(\frac{5}{7}\right) +\left(\frac{10}{8}\right)\\= \frac{-3}{4}- \frac{5}{7}+\frac{10}{8}\\=\frac{-3}{4}-\frac{5}{7}+\frac{5}{4}\\=\frac{-21}{28}-\frac{20}{28}+\frac{35}{28}\\=\frac{-21-20+35}{28}\\=\frac{-6}{28}\\=\frac{-3}{14}\)
11. \(-\left(\frac{4}{-7}\right) +\left(\frac{-6}{-7}\right) +\left(\frac{-5}{-11}\right)\\= \frac{4}{7}+ \frac{6}{7}+\frac{5}{11}\\=\frac{44}{77}+\frac{66}{77}+\frac{35}{77}\\=\frac{44+66+35}{77}\\=\frac{145}{77}\)
12. \(+\left(\frac{10}{7}\right) +\left(\frac{-5}{3}\right) +\left(\frac{-2}{-10}\right)\\= \frac{10}{7}- \frac{5}{3}+\frac{2}{10}\\=\frac{10}{7}-\frac{5}{3}+\frac{1}{5}\\=\frac{150}{105}-\frac{175}{105}+\frac{21}{105}\\=\frac{150-175+21}{105}\\=\frac{-4}{105}\)