Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{4}{-3}\right) -\left(\frac{7}{-10}\right) +\left(\frac{6}{-10}\right)\\= \frac{4}{3}+ \frac{7}{10}-\frac{6}{10}\\=\frac{4}{3}+\frac{7}{10}-\frac{3}{5}\\=\frac{40}{30}+\frac{21}{30}-\frac{18}{30}\\=\frac{40+21-18}{30}\\=\frac{43}{30}\)
2. \(-\left(\frac{-8}{3}\right) -\left(\frac{2}{-7}\right) +\left(\frac{-8}{9}\right)\\= \frac{8}{3}+ \frac{2}{7}-\frac{8}{9}\\=\frac{168}{63}+\frac{18}{63}-\frac{56}{63}\\=\frac{168+18-56}{63}\\=\frac{130}{63}\)
3. \(-\left(\frac{4}{-3}\right) -\left(\frac{-10}{4}\right) +\left(\frac{-5}{12}\right)\\= \frac{4}{3}+ \frac{10}{4}-\frac{5}{12}\\=\frac{4}{3}+\frac{5}{2}-\frac{5}{12}\\=\frac{16}{12}+\frac{30}{12}-\frac{5}{12}\\=\frac{16+30-5}{12}\\=\frac{41}{12}\)
4. \(+\left(\frac{5}{-7}\right) -\left(\frac{-3}{-7}\right) -\left(\frac{6}{-11}\right)\\= \frac{-5}{7}- \frac{3}{7}+\frac{6}{11}\\=\frac{-55}{77}-\frac{33}{77}+\frac{42}{77}\\=\frac{-55-33+42}{77}\\=\frac{-46}{77}\)
5. \(+\left(\frac{8}{-3}\right) -\left(\frac{8}{6}\right) -\left(\frac{-4}{8}\right)\\= \frac{-8}{3}- \frac{8}{6}+\frac{4}{8}\\=\frac{-8}{3}-\frac{4}{3}+\frac{1}{2}\\=\frac{-16}{6}-\frac{8}{6}+\frac{3}{6}\\=\frac{-16-8+3}{6}\\=\frac{-21}{6}\\=\frac{-7}{2}\)
6. \(-\left(\frac{-5}{6}\right) +\left(\frac{-6}{8}\right) +\left(\frac{-9}{12}\right)\\= \frac{5}{6}- \frac{6}{8}-\frac{9}{12}\\=\frac{5}{6}-\frac{3}{4}-\frac{3}{4}\\=\frac{10}{12}-\frac{9}{12}-\frac{9}{12}\\=\frac{10-9-9}{12}\\=\frac{-8}{12}\\=\frac{-2}{3}\)
7. \(+\left(\frac{8}{-3}\right) +\left(\frac{-6}{10}\right) +\left(\frac{6}{4}\right)\\= \frac{-8}{3}- \frac{6}{10}+\frac{6}{4}\\=\frac{-8}{3}-\frac{3}{5}+\frac{3}{2}\\=\frac{-80}{30}-\frac{18}{30}+\frac{45}{30}\\=\frac{-80-18+45}{30}\\=\frac{-53}{30}\)
8. \(+\left(\frac{8}{-7}\right) -\left(\frac{-8}{-3}\right) +\left(\frac{-10}{5}\right)\\= \frac{-8}{7}- \frac{8}{3}-\frac{10}{5}\\=\frac{-8}{7}-\frac{8}{3}-\frac{2}{1}\\=\frac{-24}{21}-\frac{56}{21}-\frac{42}{21}\\=\frac{-24-56-42}{21}\\=\frac{-122}{21}\)
9. \(-\left(\frac{6}{5}\right) +\left(\frac{-5}{4}\right) +\left(\frac{-6}{11}\right)\\= \frac{-6}{5}- \frac{5}{4}-\frac{6}{11}\\=\frac{-264}{220}-\frac{275}{220}-\frac{120}{220}\\=\frac{-264-275-120}{220}\\=\frac{-659}{220}\)
10. \(-\left(\frac{5}{6}\right) +\left(\frac{-7}{-6}\right) +\left(\frac{2}{-3}\right)\\= \frac{-5}{6}+ \frac{7}{6}-\frac{2}{3}\\=\frac{-5+7-2}{6}\\=\frac{0}{6}\\=\frac{0}{1}\)
11. \(+\left(\frac{-6}{-5}\right) +\left(\frac{-4}{-6}\right) +\left(\frac{11}{-10}\right)\\= \frac{6}{5}+ \frac{4}{6}-\frac{11}{10}\\=\frac{6}{5}+\frac{2}{3}-\frac{11}{10}\\=\frac{36}{30}+\frac{20}{30}-\frac{33}{30}\\=\frac{36+20-33}{30}\\=\frac{23}{30}\)
12. \(+\left(\frac{7}{5}\right) -\left(\frac{-3}{2}\right) -\left(\frac{6}{-4}\right)\\= \frac{7}{5}+ \frac{3}{2}+\frac{6}{4}\\=\frac{7}{5}+\frac{3}{2}+\frac{3}{2}\\=\frac{14}{10}+\frac{15}{10}+\frac{15}{10}\\=\frac{14+15+15}{10}\\=\frac{44}{10}\\=\frac{22}{5}\)