Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-6}{7}\right) +\left(\frac{3}{-7}\right) +\left(\frac{12}{2}\right)\\= \frac{-6}{7}- \frac{3}{7}+\frac{12}{2}\\=\frac{-6}{7}-\frac{3}{7}+\frac{6}{1}\\=\frac{-6-3+6}{7}\\=\frac{-3}{7}\)
2. \(+\left(\frac{2}{5}\right) +\left(\frac{7}{-6}\right) -\left(\frac{-4}{6}\right)\\= \frac{2}{5}- \frac{7}{6}+\frac{4}{6}\\=\frac{2}{5}-\frac{7}{6}+\frac{2}{3}\\=\frac{12}{30}-\frac{35}{30}+\frac{20}{30}\\=\frac{12-35+20}{30}\\=\frac{-3}{30}\\=\frac{-1}{10}\)
3. \(+\left(\frac{-2}{9}\right) +\left(\frac{-5}{-9}\right) +\left(\frac{11}{-9}\right)\\= \frac{-2}{9}+ \frac{5}{9}-\frac{11}{9}\\=\frac{-2+5-11}{9}\\=\frac{-8}{9}\)
4. \(+\left(\frac{-8}{3}\right) -\left(\frac{-9}{7}\right) +\left(\frac{-4}{-9}\right)\\= \frac{-8}{3}+ \frac{9}{7}+\frac{4}{9}\\=\frac{-168}{63}+\frac{81}{63}+\frac{28}{63}\\=\frac{-168+81+28}{63}\\=\frac{-59}{63}\)
5. \(+\left(\frac{9}{7}\right) -\left(\frac{-10}{4}\right) -\left(\frac{-11}{-2}\right)\\= \frac{9}{7}+ \frac{10}{4}-\frac{11}{2}\\=\frac{9}{7}+\frac{5}{2}-\frac{11}{2}\\=\frac{18}{14}+\frac{35}{14}-\frac{77}{14}\\=\frac{18+35-77}{14}\\=\frac{-24}{14}\\=\frac{-12}{7}\)
6. \(+\left(\frac{-3}{2}\right) +\left(\frac{7}{-7}\right) -\left(\frac{8}{-9}\right)\\= \frac{-3}{2}- \frac{7}{7}+\frac{8}{9}\\=\frac{-3}{2}-\frac{1}{1}+\frac{8}{9}\\=\frac{-27}{18}-\frac{18}{18}+\frac{16}{18}\\=\frac{-27-18+16}{18}\\=\frac{-29}{18}\)
7. \(-\left(\frac{4}{3}\right) +\left(\frac{-7}{-5}\right) +\left(\frac{7}{-8}\right)\\= \frac{-4}{3}+ \frac{7}{5}-\frac{7}{8}\\=\frac{-160}{120}+\frac{168}{120}-\frac{105}{120}\\=\frac{-160+168-105}{120}\\=\frac{-97}{120}\)
8. \(+\left(\frac{-2}{-3}\right) -\left(\frac{8}{-4}\right) +\left(\frac{4}{-9}\right)\\= \frac{2}{3}+ \frac{8}{4}-\frac{4}{9}\\=\frac{2}{3}+\frac{2}{1}-\frac{4}{9}\\=\frac{6}{9}+\frac{18}{9}-\frac{4}{9}\\=\frac{6+18-4}{9}\\=\frac{20}{9}\)
9. \(-\left(\frac{4}{-5}\right) -\left(\frac{2}{4}\right) -\left(\frac{3}{5}\right)\\= \frac{4}{5}- \frac{2}{4}-\frac{3}{5}\\=\frac{4}{5}-\frac{1}{2}-\frac{3}{5}\\=\frac{8}{10}-\frac{5}{10}-\frac{6}{10}\\=\frac{8-5-6}{10}\\=\frac{-3}{10}\)
10. \(-\left(\frac{8}{-3}\right) -\left(\frac{6}{9}\right) -\left(\frac{-2}{-3}\right)\\= \frac{8}{3}- \frac{6}{9}-\frac{2}{3}\\=\frac{8}{3}-\frac{2}{3}-\frac{2}{3}\\=\frac{8-2-2}{3}\\=\frac{4}{3}\)
11. \(-\left(\frac{9}{-5}\right) -\left(\frac{3}{9}\right) -\left(\frac{-11}{-10}\right)\\= \frac{9}{5}- \frac{3}{9}-\frac{11}{10}\\=\frac{9}{5}-\frac{1}{3}-\frac{11}{10}\\=\frac{54}{30}-\frac{10}{30}-\frac{33}{30}\\=\frac{54-10-33}{30}\\=\frac{11}{30}\)
12. \(-\left(\frac{-3}{-4}\right) -\left(\frac{3}{-2}\right) +\left(\frac{-11}{3}\right)\\= \frac{-3}{4}+ \frac{3}{2}-\frac{11}{3}\\=\frac{-9}{12}+\frac{18}{12}-\frac{44}{12}\\=\frac{-9+18-44}{12}\\=\frac{-35}{12}\)