Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{6}{5}\right) +\left(\frac{-2}{-3}\right) +\left(\frac{-10}{-12}\right)\\= \frac{6}{5}+ \frac{2}{3}+\frac{10}{12}\\=\frac{6}{5}+\frac{2}{3}+\frac{5}{6}\\=\frac{36}{30}+\frac{20}{30}+\frac{25}{30}\\=\frac{36+20+25}{30}\\=\frac{81}{30}\\=\frac{27}{10}\)
2. \(-\left(\frac{-9}{-4}\right) -\left(\frac{8}{5}\right) -\left(\frac{12}{-7}\right)\\= \frac{-9}{4}- \frac{8}{5}+\frac{12}{7}\\=\frac{-315}{140}-\frac{224}{140}+\frac{240}{140}\\=\frac{-315-224+240}{140}\\=\frac{-299}{140}\)
3. \(-\left(\frac{9}{-5}\right) -\left(\frac{-6}{6}\right) +\left(\frac{7}{11}\right)\\= \frac{9}{5}+ \frac{6}{6}+\frac{7}{11}\\=\frac{9}{5}+\frac{1}{1}+\frac{7}{11}\\=\frac{99}{55}+\frac{55}{55}+\frac{35}{55}\\=\frac{99+55+35}{55}\\=\frac{189}{55}\)
4. \(-\left(\frac{5}{-8}\right) +\left(\frac{-5}{-5}\right) -\left(\frac{-5}{2}\right)\\= \frac{5}{8}+ \frac{5}{5}+\frac{5}{2}\\=\frac{5}{8}+\frac{1}{1}+\frac{5}{2}\\=\frac{5+1+5}{8}\\=\frac{11}{8}\)
5. \(+\left(\frac{-8}{-7}\right) +\left(\frac{6}{7}\right) +\left(\frac{9}{-6}\right)\\= \frac{8}{7}+ \frac{6}{7}-\frac{9}{6}\\=\frac{8}{7}+\frac{6}{7}-\frac{3}{2}\\=\frac{16}{14}+\frac{12}{14}-\frac{21}{14}\\=\frac{16+12-21}{14}\\=\frac{7}{14}\\=\frac{1}{2}\)
6. \(+\left(\frac{9}{2}\right) -\left(\frac{6}{7}\right) +\left(\frac{9}{11}\right)\\= \frac{9}{2}- \frac{6}{7}+\frac{9}{11}\\=\frac{693}{154}-\frac{132}{154}+\frac{126}{154}\\=\frac{693-132+126}{154}\\=\frac{687}{154}\)
7. \(-\left(\frac{9}{-4}\right) -\left(\frac{-3}{-3}\right) +\left(\frac{-5}{8}\right)\\= \frac{9}{4}- \frac{3}{3}-\frac{5}{8}\\=\frac{9}{4}-\frac{1}{1}-\frac{5}{8}\\=\frac{18}{8}-\frac{8}{8}-\frac{5}{8}\\=\frac{18-8-5}{8}\\=\frac{5}{8}\)
8. \(+\left(\frac{-10}{7}\right) -\left(\frac{-7}{-2}\right) -\left(\frac{-2}{-2}\right)\\= \frac{-10}{7}- \frac{7}{2}-\frac{2}{2}\\=\frac{-10}{7}-\frac{7}{2}-\frac{1}{1}\\=\frac{-20}{14}-\frac{49}{14}-\frac{14}{14}\\=\frac{-20-49-14}{14}\\=\frac{-83}{14}\)
9. \(-\left(\frac{10}{-3}\right) -\left(\frac{10}{4}\right) -\left(\frac{12}{-12}\right)\\= \frac{10}{3}- \frac{10}{4}+\frac{12}{12}\\=\frac{10}{3}-\frac{5}{2}+\frac{1}{1}\\=\frac{20}{6}-\frac{15}{6}+\frac{6}{6}\\=\frac{20-15+6}{6}\\=\frac{11}{6}\)
10. \(-\left(\frac{-3}{-2}\right) -\left(\frac{-5}{10}\right) -\left(\frac{-5}{7}\right)\\= \frac{-3}{2}+ \frac{5}{10}+\frac{5}{7}\\=\frac{-3}{2}+\frac{1}{2}+\frac{5}{7}\\=\frac{-21}{14}+\frac{7}{14}+\frac{10}{14}\\=\frac{-21+7+10}{14}\\=\frac{-4}{14}\\=\frac{-2}{7}\)
11. \(+\left(\frac{-6}{-5}\right) +\left(\frac{-10}{-10}\right) -\left(\frac{-2}{-9}\right)\\= \frac{6}{5}+ \frac{10}{10}-\frac{2}{9}\\=\frac{6}{5}+\frac{1}{1}-\frac{2}{9}\\=\frac{54}{45}+\frac{45}{45}-\frac{10}{45}\\=\frac{54+45-10}{45}\\=\frac{89}{45}\)
12. \(-\left(\frac{6}{-7}\right) +\left(\frac{-10}{7}\right) +\left(\frac{3}{9}\right)\\= \frac{6}{7}- \frac{10}{7}+\frac{3}{9}\\=\frac{6}{7}-\frac{10}{7}+\frac{1}{3}\\=\frac{18}{21}-\frac{30}{21}+\frac{7}{21}\\=\frac{18-30+7}{21}\\=\frac{-5}{21}\)