Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{4}{7}\right) -\left(\frac{-6}{7}\right) +\left(\frac{-12}{-5}\right)\\= \frac{-4}{7}+ \frac{6}{7}+\frac{12}{5}\\=\frac{-20}{35}+\frac{30}{35}+\frac{84}{35}\\=\frac{-20+30+84}{35}\\=\frac{94}{35}\)
2. \(-\left(\frac{3}{2}\right) +\left(\frac{7}{-6}\right) -\left(\frac{-8}{12}\right)\\= \frac{-3}{2}- \frac{7}{6}+\frac{8}{12}\\=\frac{-3}{2}-\frac{7}{6}+\frac{2}{3}\\=\frac{-9}{6}-\frac{7}{6}+\frac{4}{6}\\=\frac{-9-7+4}{6}\\=\frac{-12}{6}\\=\frac{-2}{1}\)
3. \(+\left(\frac{-10}{-7}\right) -\left(\frac{2}{-7}\right) +\left(\frac{12}{-3}\right)\\= \frac{10}{7}+ \frac{2}{7}-\frac{12}{3}\\=\frac{10}{7}+\frac{2}{7}-\frac{4}{1}\\=\frac{10+2-4}{7}\\=\frac{8}{7}\)
4. \(-\left(\frac{-4}{5}\right) +\left(\frac{3}{-3}\right) +\left(\frac{11}{5}\right)\\= \frac{4}{5}- \frac{3}{3}+\frac{11}{5}\\=\frac{4}{5}-\frac{1}{1}+\frac{11}{5}\\=\frac{4-1+11}{5}\\=\frac{14}{5}\)
5. \(-\left(\frac{-3}{-2}\right) -\left(\frac{4}{-8}\right) -\left(\frac{-11}{-2}\right)\\= \frac{-3}{2}+ \frac{4}{8}-\frac{11}{2}\\=\frac{-3}{2}+\frac{1}{2}-\frac{11}{2}\\=\frac{-3+1-11}{2}\\=\frac{-13}{2}\)
6. \(-\left(\frac{9}{7}\right) +\left(\frac{-8}{-3}\right) +\left(\frac{2}{-10}\right)\\= \frac{-9}{7}+ \frac{8}{3}-\frac{2}{10}\\=\frac{-9}{7}+\frac{8}{3}-\frac{1}{5}\\=\frac{-135}{105}+\frac{280}{105}-\frac{21}{105}\\=\frac{-135+280-21}{105}\\=\frac{124}{105}\)
7. \(-\left(\frac{10}{7}\right) +\left(\frac{-9}{6}\right) +\left(\frac{-12}{12}\right)\\= \frac{-10}{7}- \frac{9}{6}-\frac{12}{12}\\=\frac{-10}{7}-\frac{3}{2}-\frac{1}{1}\\=\frac{-20}{14}-\frac{21}{14}-\frac{14}{14}\\=\frac{-20-21-14}{14}\\=\frac{-55}{14}\)
8. \(-\left(\frac{10}{-7}\right) -\left(\frac{7}{5}\right) -\left(\frac{6}{8}\right)\\= \frac{10}{7}- \frac{7}{5}-\frac{6}{8}\\=\frac{10}{7}-\frac{7}{5}-\frac{3}{4}\\=\frac{200}{140}-\frac{196}{140}-\frac{105}{140}\\=\frac{200-196-105}{140}\\=\frac{-101}{140}\)
9. \(-\left(\frac{-8}{3}\right) -\left(\frac{-3}{-9}\right) -\left(\frac{-10}{9}\right)\\= \frac{8}{3}- \frac{3}{9}+\frac{10}{9}\\=\frac{8}{3}-\frac{1}{3}+\frac{10}{9}\\=\frac{24}{9}-\frac{3}{9}+\frac{10}{9}\\=\frac{24-3+10}{9}\\=\frac{31}{9}\)
10. \(+\left(\frac{4}{7}\right) +\left(\frac{-6}{3}\right) +\left(\frac{-3}{2}\right)\\= \frac{4}{7}- \frac{6}{3}-\frac{3}{2}\\=\frac{4}{7}-\frac{2}{1}-\frac{3}{2}\\=\frac{8}{14}-\frac{28}{14}-\frac{21}{14}\\=\frac{8-28-21}{14}\\=\frac{-41}{14}\)
11. \(+\left(\frac{-7}{-6}\right) +\left(\frac{3}{-7}\right) -\left(\frac{-4}{-12}\right)\\= \frac{7}{6}- \frac{3}{7}-\frac{4}{12}\\=\frac{7}{6}-\frac{3}{7}-\frac{1}{3}\\=\frac{49}{42}-\frac{18}{42}-\frac{14}{42}\\=\frac{49-18-14}{42}\\=\frac{17}{42}\)
12. \(-\left(\frac{-9}{-7}\right) +\left(\frac{2}{-10}\right) -\left(\frac{-11}{4}\right)\\= \frac{-9}{7}- \frac{2}{10}+\frac{11}{4}\\=\frac{-9}{7}-\frac{1}{5}+\frac{11}{4}\\=\frac{-180}{140}-\frac{28}{140}+\frac{385}{140}\\=\frac{-180-28+385}{140}\\=\frac{177}{140}\)