Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{10}{9}\right) -\left(\frac{2}{4}\right) +\left(\frac{2}{2}\right)\\= \frac{-10}{9}- \frac{2}{4}+\frac{2}{2}\\=\frac{-10}{9}-\frac{1}{2}+\frac{1}{1}\\=\frac{-20}{18}-\frac{9}{18}+\frac{18}{18}\\=\frac{-20-9+18}{18}\\=\frac{-11}{18}\)
2. \(-\left(\frac{-2}{-3}\right) -\left(\frac{-4}{-8}\right) +\left(\frac{4}{12}\right)\\= \frac{-2}{3}- \frac{4}{8}+\frac{4}{12}\\=\frac{-2}{3}-\frac{1}{2}+\frac{1}{3}\\=\frac{-4}{6}-\frac{3}{6}+\frac{2}{6}\\=\frac{-4-3+2}{6}\\=\frac{-5}{6}\)
3. \(-\left(\frac{3}{5}\right) +\left(\frac{-7}{3}\right) +\left(\frac{9}{10}\right)\\= \frac{-3}{5}- \frac{7}{3}+\frac{9}{10}\\=\frac{-18}{30}-\frac{70}{30}+\frac{27}{30}\\=\frac{-18-70+27}{30}\\=\frac{-61}{30}\)
4. \(-\left(\frac{6}{5}\right) -\left(\frac{-3}{4}\right) -\left(\frac{-4}{-11}\right)\\= \frac{-6}{5}+ \frac{3}{4}-\frac{4}{11}\\=\frac{-264}{220}+\frac{165}{220}-\frac{80}{220}\\=\frac{-264+165-80}{220}\\=\frac{-179}{220}\)
5. \(+\left(\frac{4}{3}\right) -\left(\frac{9}{-8}\right) +\left(\frac{7}{-7}\right)\\= \frac{4}{3}+ \frac{9}{8}-\frac{7}{7}\\=\frac{4}{3}+\frac{9}{8}-\frac{1}{1}\\=\frac{32}{24}+\frac{27}{24}-\frac{24}{24}\\=\frac{32+27-24}{24}\\=\frac{35}{24}\)
6. \(+\left(\frac{-9}{4}\right) +\left(\frac{6}{-9}\right) +\left(\frac{3}{-4}\right)\\= \frac{-9}{4}- \frac{6}{9}-\frac{3}{4}\\=\frac{-9}{4}-\frac{2}{3}-\frac{3}{4}\\=\frac{-27}{12}-\frac{8}{12}-\frac{9}{12}\\=\frac{-27-8-9}{12}\\=\frac{-44}{12}\\=\frac{-11}{3}\)
7. \(-\left(\frac{-9}{4}\right) +\left(\frac{-9}{4}\right) -\left(\frac{-5}{-4}\right)\\= \frac{9}{4}- \frac{9}{4}-\frac{5}{4}\\=\frac{9-9-5}{4}\\=\frac{-5}{4}\)
8. \(+\left(\frac{-7}{-8}\right) +\left(\frac{7}{-3}\right) +\left(\frac{12}{3}\right)\\= \frac{7}{8}- \frac{7}{3}+\frac{12}{3}\\=\frac{7}{8}-\frac{7}{3}+\frac{4}{1}\\=\frac{21}{24}-\frac{56}{24}+\frac{96}{24}\\=\frac{21-56+96}{24}\\=\frac{61}{24}\)
9. \(-\left(\frac{-10}{3}\right) +\left(\frac{-9}{-3}\right) -\left(\frac{-10}{3}\right)\\= \frac{10}{3}+ \frac{9}{3}+\frac{10}{3}\\=\frac{10}{3}+\frac{3}{1}+\frac{10}{3}\\=\frac{10+3+10}{3}\\=\frac{23}{3}\)
10. \(-\left(\frac{-3}{4}\right) +\left(\frac{-9}{-2}\right) -\left(\frac{-5}{3}\right)\\= \frac{3}{4}+ \frac{9}{2}+\frac{5}{3}\\=\frac{9}{12}+\frac{54}{12}+\frac{20}{12}\\=\frac{9+54+20}{12}\\=\frac{83}{12}\)
11. \(-\left(\frac{3}{7}\right) -\left(\frac{4}{-2}\right) +\left(\frac{-6}{12}\right)\\= \frac{-3}{7}+ \frac{4}{2}-\frac{6}{12}\\=\frac{-3}{7}+\frac{2}{1}-\frac{1}{2}\\=\frac{-6}{14}+\frac{28}{14}-\frac{7}{14}\\=\frac{-6+28-7}{14}\\=\frac{15}{14}\)
12. \(-\left(\frac{4}{3}\right) +\left(\frac{5}{-6}\right) -\left(\frac{-6}{-9}\right)\\= \frac{-4}{3}- \frac{5}{6}-\frac{6}{9}\\=\frac{-4}{3}-\frac{5}{6}-\frac{2}{3}\\=\frac{-8}{6}-\frac{5}{6}-\frac{4}{6}\\=\frac{-8-5-4}{6}\\=\frac{-17}{6}\)