Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-2}{-7}\right) +\left(\frac{7}{-2}\right) -\left(\frac{-12}{-8}\right)\\= \frac{-2}{7}- \frac{7}{2}-\frac{12}{8}\\=\frac{-2}{7}-\frac{7}{2}-\frac{3}{2}\\=\frac{-4}{14}-\frac{49}{14}-\frac{21}{14}\\=\frac{-4-49-21}{14}\\=\frac{-74}{14}\\=\frac{-37}{7}\)
2. \(+\left(\frac{-4}{-9}\right) -\left(\frac{-5}{-5}\right) -\left(\frac{5}{-3}\right)\\= \frac{4}{9}- \frac{5}{5}+\frac{5}{3}\\=\frac{4}{9}-\frac{1}{1}+\frac{5}{3}\\=\frac{4-1+5}{9}\\=\frac{8}{9}\)
3. \(-\left(\frac{8}{3}\right) +\left(\frac{-3}{7}\right) +\left(\frac{-8}{-5}\right)\\= \frac{-8}{3}- \frac{3}{7}+\frac{8}{5}\\=\frac{-280}{105}-\frac{45}{105}+\frac{168}{105}\\=\frac{-280-45+168}{105}\\=\frac{-157}{105}\)
4. \(-\left(\frac{-4}{7}\right) -\left(\frac{-2}{-7}\right) -\left(\frac{-11}{-11}\right)\\= \frac{4}{7}- \frac{2}{7}-\frac{11}{11}\\=\frac{4}{7}-\frac{2}{7}-\frac{1}{1}\\=\frac{4-2-1}{7}\\=\frac{1}{7}\)
5. \(+\left(\frac{-2}{3}\right) -\left(\frac{-10}{7}\right) -\left(\frac{11}{2}\right)\\= \frac{-2}{3}+ \frac{10}{7}-\frac{11}{2}\\=\frac{-28}{42}+\frac{60}{42}-\frac{231}{42}\\=\frac{-28+60-231}{42}\\=\frac{-199}{42}\)
6. \(-\left(\frac{-9}{2}\right) -\left(\frac{-3}{2}\right) +\left(\frac{11}{-12}\right)\\= \frac{9}{2}+ \frac{3}{2}-\frac{11}{12}\\=\frac{54}{12}+\frac{18}{12}-\frac{11}{12}\\=\frac{54+18-11}{12}\\=\frac{61}{12}\)
7. \(+\left(\frac{6}{-5}\right) -\left(\frac{5}{9}\right) +\left(\frac{8}{-10}\right)\\= \frac{-6}{5}- \frac{5}{9}-\frac{8}{10}\\=\frac{-6}{5}-\frac{5}{9}-\frac{4}{5}\\=\frac{-54}{45}-\frac{25}{45}-\frac{36}{45}\\=\frac{-54-25-36}{45}\\=\frac{-115}{45}\\=\frac{-23}{9}\)
8. \(+\left(\frac{2}{9}\right) +\left(\frac{-6}{9}\right) -\left(\frac{8}{-6}\right)\\= \frac{2}{9}- \frac{6}{9}+\frac{8}{6}\\=\frac{2}{9}-\frac{2}{3}+\frac{4}{3}\\=\frac{2-2+4}{9}\\=\frac{4}{9}\)
9. \(+\left(\frac{2}{9}\right) -\left(\frac{2}{10}\right) -\left(\frac{3}{7}\right)\\= \frac{2}{9}- \frac{2}{10}-\frac{3}{7}\\=\frac{2}{9}-\frac{1}{5}-\frac{3}{7}\\=\frac{70}{315}-\frac{63}{315}-\frac{135}{315}\\=\frac{70-63-135}{315}\\=\frac{-128}{315}\)
10. \(-\left(\frac{4}{-5}\right) +\left(\frac{-2}{8}\right) +\left(\frac{8}{-12}\right)\\= \frac{4}{5}- \frac{2}{8}-\frac{8}{12}\\=\frac{4}{5}-\frac{1}{4}-\frac{2}{3}\\=\frac{48}{60}-\frac{15}{60}-\frac{40}{60}\\=\frac{48-15-40}{60}\\=\frac{-7}{60}\)
11. \(-\left(\frac{6}{-5}\right) -\left(\frac{9}{-9}\right) +\left(\frac{-3}{2}\right)\\= \frac{6}{5}+ \frac{9}{9}-\frac{3}{2}\\=\frac{6}{5}+\frac{1}{1}-\frac{3}{2}\\=\frac{12}{10}+\frac{10}{10}-\frac{15}{10}\\=\frac{12+10-15}{10}\\=\frac{7}{10}\)
12. \(-\left(\frac{-7}{5}\right) +\left(\frac{2}{-4}\right) +\left(\frac{-11}{-4}\right)\\= \frac{7}{5}- \frac{2}{4}+\frac{11}{4}\\=\frac{7}{5}-\frac{1}{2}+\frac{11}{4}\\=\frac{28}{20}-\frac{10}{20}+\frac{55}{20}\\=\frac{28-10+55}{20}\\=\frac{73}{20}\)