Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{8}{-3}\right) -\left(\frac{-8}{9}\right) +\left(\frac{-2}{5}\right)\\= \frac{8}{3}+ \frac{8}{9}-\frac{2}{5}\\=\frac{120}{45}+\frac{40}{45}-\frac{18}{45}\\=\frac{120+40-18}{45}\\=\frac{142}{45}\)
2. \(+\left(\frac{-10}{9}\right) +\left(\frac{-4}{3}\right) +\left(\frac{-8}{-4}\right)\\= \frac{-10}{9}- \frac{4}{3}+\frac{8}{4}\\=\frac{-10}{9}-\frac{4}{3}+\frac{2}{1}\\=\frac{-10-4+2}{9}\\=\frac{-12}{9}\\=\frac{-4}{3}\)
3. \(-\left(\frac{2}{-3}\right) -\left(\frac{-7}{9}\right) +\left(\frac{-4}{8}\right)\\= \frac{2}{3}+ \frac{7}{9}-\frac{4}{8}\\=\frac{2}{3}+\frac{7}{9}-\frac{1}{2}\\=\frac{12}{18}+\frac{14}{18}-\frac{9}{18}\\=\frac{12+14-9}{18}\\=\frac{17}{18}\)
4. \(-\left(\frac{-4}{7}\right) -\left(\frac{6}{2}\right) +\left(\frac{-6}{-4}\right)\\= \frac{4}{7}- \frac{6}{2}+\frac{6}{4}\\=\frac{4}{7}-\frac{3}{1}+\frac{3}{2}\\=\frac{8}{14}-\frac{42}{14}+\frac{21}{14}\\=\frac{8-42+21}{14}\\=\frac{-13}{14}\)
5. \(-\left(\frac{10}{-3}\right) -\left(\frac{8}{4}\right) -\left(\frac{-6}{-7}\right)\\= \frac{10}{3}- \frac{8}{4}-\frac{6}{7}\\=\frac{10}{3}-\frac{2}{1}-\frac{6}{7}\\=\frac{70}{21}-\frac{42}{21}-\frac{18}{21}\\=\frac{70-42-18}{21}\\=\frac{10}{21}\)
6. \(+\left(\frac{10}{-7}\right) -\left(\frac{5}{4}\right) -\left(\frac{-3}{-10}\right)\\= \frac{-10}{7}- \frac{5}{4}-\frac{3}{10}\\=\frac{-200}{140}-\frac{175}{140}-\frac{42}{140}\\=\frac{-200-175-42}{140}\\=\frac{-417}{140}\)
7. \(+\left(\frac{8}{3}\right) -\left(\frac{3}{2}\right) -\left(\frac{9}{-4}\right)\\= \frac{8}{3}- \frac{3}{2}+\frac{9}{4}\\=\frac{32}{12}-\frac{18}{12}+\frac{27}{12}\\=\frac{32-18+27}{12}\\=\frac{41}{12}\)
8. \(+\left(\frac{-8}{3}\right) +\left(\frac{-10}{-10}\right) -\left(\frac{10}{2}\right)\\= \frac{-8}{3}+ \frac{10}{10}-\frac{10}{2}\\=\frac{-8}{3}+\frac{1}{1}-\frac{5}{1}\\=\frac{-8+1-5}{3}\\=\frac{-12}{3}\\=\frac{-4}{1}\)
9. \(+\left(\frac{9}{-2}\right) +\left(\frac{-2}{2}\right) +\left(\frac{-8}{2}\right)\\= \frac{-9}{2}- \frac{2}{2}-\frac{8}{2}\\=\frac{-9}{2}-\frac{1}{1}-\frac{4}{1}\\=\frac{-9-1-4}{2}\\=\frac{-14}{2}\\=\frac{-7}{1}\)
10. \(-\left(\frac{-6}{5}\right) -\left(\frac{8}{6}\right) -\left(\frac{5}{-4}\right)\\= \frac{6}{5}- \frac{8}{6}+\frac{5}{4}\\=\frac{6}{5}-\frac{4}{3}+\frac{5}{4}\\=\frac{72}{60}-\frac{80}{60}+\frac{75}{60}\\=\frac{72-80+75}{60}\\=\frac{67}{60}\)
11. \(+\left(\frac{-5}{-9}\right) -\left(\frac{9}{-10}\right) +\left(\frac{2}{3}\right)\\= \frac{5}{9}+ \frac{9}{10}+\frac{2}{3}\\=\frac{50}{90}+\frac{81}{90}+\frac{60}{90}\\=\frac{50+81+60}{90}\\=\frac{191}{90}\)
12. \(-\left(\frac{9}{5}\right) +\left(\frac{9}{-3}\right) +\left(\frac{7}{11}\right)\\= \frac{-9}{5}- \frac{9}{3}+\frac{7}{11}\\=\frac{-9}{5}-\frac{3}{1}+\frac{7}{11}\\=\frac{-99}{55}-\frac{165}{55}+\frac{35}{55}\\=\frac{-99-165+35}{55}\\=\frac{-229}{55}\)