Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{9}{2}\right) +\left(\frac{-10}{-3}\right) +\left(\frac{10}{-2}\right)\\= \frac{9}{2}+ \frac{10}{3}-\frac{10}{2}\\=\frac{9}{2}+\frac{10}{3}-\frac{5}{1}\\=\frac{27}{6}+\frac{20}{6}-\frac{30}{6}\\=\frac{27+20-30}{6}\\=\frac{17}{6}\)
2. \(-\left(\frac{10}{-3}\right) -\left(\frac{10}{-4}\right) +\left(\frac{-6}{-4}\right)\\= \frac{10}{3}+ \frac{10}{4}+\frac{6}{4}\\=\frac{10}{3}+\frac{5}{2}+\frac{3}{2}\\=\frac{20}{6}+\frac{15}{6}+\frac{9}{6}\\=\frac{20+15+9}{6}\\=\frac{44}{6}\\=\frac{22}{3}\)
3. \(-\left(\frac{-10}{-3}\right) +\left(\frac{3}{-2}\right) +\left(\frac{11}{-3}\right)\\= \frac{-10}{3}- \frac{3}{2}-\frac{11}{3}\\=\frac{-20}{6}-\frac{9}{6}-\frac{22}{6}\\=\frac{-20-9-22}{6}\\=\frac{-51}{6}\\=\frac{-17}{2}\)
4. \(+\left(\frac{2}{9}\right) -\left(\frac{-8}{6}\right) +\left(\frac{2}{11}\right)\\= \frac{2}{9}+ \frac{8}{6}+\frac{2}{11}\\=\frac{2}{9}+\frac{4}{3}+\frac{2}{11}\\=\frac{22}{99}+\frac{132}{99}+\frac{18}{99}\\=\frac{22+132+18}{99}\\=\frac{172}{99}\)
5. \(+\left(\frac{-10}{-3}\right) +\left(\frac{-6}{3}\right) -\left(\frac{-4}{-9}\right)\\= \frac{10}{3}- \frac{6}{3}-\frac{4}{9}\\=\frac{10}{3}-\frac{2}{1}-\frac{4}{9}\\=\frac{30}{9}-\frac{18}{9}-\frac{4}{9}\\=\frac{30-18-4}{9}\\=\frac{8}{9}\)
6. \(+\left(\frac{8}{-3}\right) -\left(\frac{5}{-3}\right) +\left(\frac{12}{-9}\right)\\= \frac{-8}{3}+ \frac{5}{3}-\frac{12}{9}\\=\frac{-8}{3}+\frac{5}{3}-\frac{4}{3}\\=\frac{-8+5-4}{3}\\=\frac{-7}{3}\)
7. \(-\left(\frac{-3}{-8}\right) -\left(\frac{8}{10}\right) +\left(\frac{-5}{-5}\right)\\= \frac{-3}{8}- \frac{8}{10}+\frac{5}{5}\\=\frac{-3}{8}-\frac{4}{5}+\frac{1}{1}\\=\frac{-15}{40}-\frac{32}{40}+\frac{40}{40}\\=\frac{-15-32+40}{40}\\=\frac{-7}{40}\)
8. \(-\left(\frac{-4}{-3}\right) +\left(\frac{-3}{4}\right) +\left(\frac{2}{-4}\right)\\= \frac{-4}{3}- \frac{3}{4}-\frac{2}{4}\\=\frac{-4}{3}-\frac{3}{4}-\frac{1}{2}\\=\frac{-16}{12}-\frac{9}{12}-\frac{6}{12}\\=\frac{-16-9-6}{12}\\=\frac{-31}{12}\)
9. \(+\left(\frac{3}{-7}\right) +\left(\frac{-4}{-6}\right) -\left(\frac{5}{-10}\right)\\= \frac{-3}{7}+ \frac{4}{6}+\frac{5}{10}\\=\frac{-3}{7}+\frac{2}{3}+\frac{1}{2}\\=\frac{-18}{42}+\frac{28}{42}+\frac{21}{42}\\=\frac{-18+28+21}{42}\\=\frac{31}{42}\)
10. \(+\left(\frac{-7}{3}\right) -\left(\frac{-4}{-2}\right) -\left(\frac{-3}{9}\right)\\= \frac{-7}{3}- \frac{4}{2}+\frac{3}{9}\\=\frac{-7}{3}-\frac{2}{1}+\frac{1}{3}\\=\frac{-7-2+1}{3}\\=\frac{-8}{3}\)
11. \(+\left(\frac{-9}{4}\right) +\left(\frac{4}{-8}\right) +\left(\frac{-10}{5}\right)\\= \frac{-9}{4}- \frac{4}{8}-\frac{10}{5}\\=\frac{-9}{4}-\frac{1}{2}-\frac{2}{1}\\=\frac{-9-1-2}{4}\\=\frac{-12}{4}\\=\frac{-3}{1}\)
12. \(-\left(\frac{10}{-3}\right) +\left(\frac{3}{6}\right) -\left(\frac{6}{10}\right)\\= \frac{10}{3}+ \frac{3}{6}-\frac{6}{10}\\=\frac{10}{3}+\frac{1}{2}-\frac{3}{5}\\=\frac{100}{30}+\frac{15}{30}-\frac{18}{30}\\=\frac{100+15-18}{30}\\=\frac{97}{30}\)