Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-6}{5}\right) -\left(\frac{7}{-5}\right) +\left(\frac{-12}{-12}\right)\\= \frac{-6}{5}+ \frac{7}{5}+\frac{12}{12}\\=\frac{-6}{5}+\frac{7}{5}+\frac{1}{1}\\=\frac{-6+7+1}{5}\\=\frac{2}{5}\)
2. \(+\left(\frac{7}{-9}\right) +\left(\frac{10}{2}\right) +\left(\frac{2}{-4}\right)\\= \frac{-7}{9}+ \frac{10}{2}-\frac{2}{4}\\=\frac{-7}{9}+\frac{5}{1}-\frac{1}{2}\\=\frac{-14}{18}+\frac{90}{18}-\frac{9}{18}\\=\frac{-14+90-9}{18}\\=\frac{67}{18}\)
3. \(+\left(\frac{3}{2}\right) +\left(\frac{3}{-7}\right) -\left(\frac{10}{5}\right)\\= \frac{3}{2}- \frac{3}{7}-\frac{10}{5}\\=\frac{3}{2}-\frac{3}{7}-\frac{2}{1}\\=\frac{21}{14}-\frac{6}{14}-\frac{28}{14}\\=\frac{21-6-28}{14}\\=\frac{-13}{14}\)
4. \(-\left(\frac{6}{-5}\right) +\left(\frac{-2}{-8}\right) +\left(\frac{7}{-3}\right)\\= \frac{6}{5}+ \frac{2}{8}-\frac{7}{3}\\=\frac{6}{5}+\frac{1}{4}-\frac{7}{3}\\=\frac{72}{60}+\frac{15}{60}-\frac{140}{60}\\=\frac{72+15-140}{60}\\=\frac{-53}{60}\)
5. \(+\left(\frac{8}{9}\right) -\left(\frac{-5}{4}\right) +\left(\frac{2}{4}\right)\\= \frac{8}{9}+ \frac{5}{4}+\frac{2}{4}\\=\frac{8}{9}+\frac{5}{4}+\frac{1}{2}\\=\frac{32}{36}+\frac{45}{36}+\frac{18}{36}\\=\frac{32+45+18}{36}\\=\frac{95}{36}\)
6. \(-\left(\frac{-8}{-7}\right) +\left(\frac{8}{2}\right) -\left(\frac{-9}{6}\right)\\= \frac{-8}{7}+ \frac{8}{2}+\frac{9}{6}\\=\frac{-8}{7}+\frac{4}{1}+\frac{3}{2}\\=\frac{-16}{14}+\frac{56}{14}+\frac{21}{14}\\=\frac{-16+56+21}{14}\\=\frac{61}{14}\)
7. \(-\left(\frac{-9}{-8}\right) +\left(\frac{9}{-10}\right) -\left(\frac{12}{-11}\right)\\= \frac{-9}{8}- \frac{9}{10}+\frac{12}{11}\\=\frac{-495}{440}-\frac{396}{440}+\frac{480}{440}\\=\frac{-495-396+480}{440}\\=\frac{-411}{440}\)
8. \(+\left(\frac{-2}{-9}\right) +\left(\frac{-8}{9}\right) +\left(\frac{-9}{-2}\right)\\= \frac{2}{9}- \frac{8}{9}+\frac{9}{2}\\=\frac{4}{18}-\frac{16}{18}+\frac{81}{18}\\=\frac{4-16+81}{18}\\=\frac{69}{18}\\=\frac{23}{6}\)
9. \(+\left(\frac{-8}{-3}\right) +\left(\frac{-5}{7}\right) -\left(\frac{8}{-3}\right)\\= \frac{8}{3}- \frac{5}{7}+\frac{8}{3}\\=\frac{56}{21}-\frac{15}{21}+\frac{56}{21}\\=\frac{56-15+56}{21}\\=\frac{97}{21}\)
10. \(-\left(\frac{-9}{-7}\right) -\left(\frac{6}{5}\right) -\left(\frac{5}{3}\right)\\= \frac{-9}{7}- \frac{6}{5}-\frac{5}{3}\\=\frac{-135}{105}-\frac{126}{105}-\frac{175}{105}\\=\frac{-135-126-175}{105}\\=\frac{-436}{105}\)
11. \(+\left(\frac{6}{-5}\right) -\left(\frac{3}{9}\right) +\left(\frac{7}{-12}\right)\\= \frac{-6}{5}- \frac{3}{9}-\frac{7}{12}\\=\frac{-6}{5}-\frac{1}{3}-\frac{7}{12}\\=\frac{-72}{60}-\frac{20}{60}-\frac{35}{60}\\=\frac{-72-20-35}{60}\\=\frac{-127}{60}\)
12. \(+\left(\frac{5}{-8}\right) -\left(\frac{-10}{-5}\right) -\left(\frac{8}{-8}\right)\\= \frac{-5}{8}- \frac{10}{5}+\frac{8}{8}\\=\frac{-5}{8}-\frac{2}{1}+\frac{1}{1}\\=\frac{-5-2+1}{8}\\=\frac{-6}{8}\\=\frac{-3}{4}\)