Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-6}{-7}\right) +\left(\frac{8}{-8}\right) +\left(\frac{-4}{9}\right)\\= \frac{-6}{7}- \frac{8}{8}-\frac{4}{9}\\=\frac{-6}{7}-\frac{1}{1}-\frac{4}{9}\\=\frac{-54}{63}-\frac{63}{63}-\frac{28}{63}\\=\frac{-54-63-28}{63}\\=\frac{-145}{63}\)
2. \(+\left(\frac{10}{3}\right) -\left(\frac{2}{6}\right) +\left(\frac{7}{-9}\right)\\= \frac{10}{3}- \frac{2}{6}-\frac{7}{9}\\=\frac{10}{3}-\frac{1}{3}-\frac{7}{9}\\=\frac{30}{9}-\frac{3}{9}-\frac{7}{9}\\=\frac{30-3-7}{9}\\=\frac{20}{9}\)
3. \(-\left(\frac{-6}{7}\right) -\left(\frac{-3}{-10}\right) +\left(\frac{5}{-11}\right)\\= \frac{6}{7}- \frac{3}{10}-\frac{5}{11}\\=\frac{660}{770}-\frac{231}{770}-\frac{350}{770}\\=\frac{660-231-350}{770}\\=\frac{79}{770}\)
4. \(+\left(\frac{-7}{4}\right) +\left(\frac{-6}{-10}\right) +\left(\frac{-10}{5}\right)\\= \frac{-7}{4}+ \frac{6}{10}-\frac{10}{5}\\=\frac{-7}{4}+\frac{3}{5}-\frac{2}{1}\\=\frac{-35}{20}+\frac{12}{20}-\frac{40}{20}\\=\frac{-35+12-40}{20}\\=\frac{-63}{20}\)
5. \(+\left(\frac{-4}{-7}\right) -\left(\frac{-6}{3}\right) -\left(\frac{3}{5}\right)\\= \frac{4}{7}+ \frac{6}{3}-\frac{3}{5}\\=\frac{4}{7}+\frac{2}{1}-\frac{3}{5}\\=\frac{20}{35}+\frac{70}{35}-\frac{21}{35}\\=\frac{20+70-21}{35}\\=\frac{69}{35}\)
6. \(-\left(\frac{-2}{-5}\right) +\left(\frac{10}{-9}\right) -\left(\frac{6}{-3}\right)\\= \frac{-2}{5}- \frac{10}{9}+\frac{6}{3}\\=\frac{-2}{5}-\frac{10}{9}+\frac{2}{1}\\=\frac{-18}{45}-\frac{50}{45}+\frac{90}{45}\\=\frac{-18-50+90}{45}\\=\frac{22}{45}\)
7. \(+\left(\frac{-9}{2}\right) +\left(\frac{2}{3}\right) +\left(\frac{12}{8}\right)\\= \frac{-9}{2}+ \frac{2}{3}+\frac{12}{8}\\=\frac{-9}{2}+\frac{2}{3}+\frac{3}{2}\\=\frac{-27}{6}+\frac{4}{6}+\frac{9}{6}\\=\frac{-27+4+9}{6}\\=\frac{-14}{6}\\=\frac{-7}{3}\)
8. \(+\left(\frac{-8}{-3}\right) -\left(\frac{4}{3}\right) -\left(\frac{-5}{5}\right)\\= \frac{8}{3}- \frac{4}{3}+\frac{5}{5}\\=\frac{8}{3}-\frac{4}{3}+\frac{1}{1}\\=\frac{8-4+1}{3}\\=\frac{5}{3}\)
9. \(+\left(\frac{-6}{-7}\right) +\left(\frac{9}{-9}\right) -\left(\frac{-5}{-11}\right)\\= \frac{6}{7}- \frac{9}{9}-\frac{5}{11}\\=\frac{6}{7}-\frac{1}{1}-\frac{5}{11}\\=\frac{66}{77}-\frac{77}{77}-\frac{35}{77}\\=\frac{66-77-35}{77}\\=\frac{-46}{77}\)
10. \(-\left(\frac{-7}{-5}\right) -\left(\frac{9}{-2}\right) +\left(\frac{2}{-9}\right)\\= \frac{-7}{5}+ \frac{9}{2}-\frac{2}{9}\\=\frac{-126}{90}+\frac{405}{90}-\frac{20}{90}\\=\frac{-126+405-20}{90}\\=\frac{259}{90}\)
11. \(-\left(\frac{7}{2}\right) -\left(\frac{-9}{-7}\right) -\left(\frac{4}{6}\right)\\= \frac{-7}{2}- \frac{9}{7}-\frac{4}{6}\\=\frac{-7}{2}-\frac{9}{7}-\frac{2}{3}\\=\frac{-147}{42}-\frac{54}{42}-\frac{28}{42}\\=\frac{-147-54-28}{42}\\=\frac{-229}{42}\)
12. \(-\left(\frac{-10}{-9}\right) +\left(\frac{8}{-5}\right) +\left(\frac{-8}{-4}\right)\\= \frac{-10}{9}- \frac{8}{5}+\frac{8}{4}\\=\frac{-10}{9}-\frac{8}{5}+\frac{2}{1}\\=\frac{-50}{45}-\frac{72}{45}+\frac{90}{45}\\=\frac{-50-72+90}{45}\\=\frac{-32}{45}\)