Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-3}{-4}\right) -\left(\frac{-5}{-2}\right) +\left(\frac{-9}{-11}\right)\\= \frac{-3}{4}- \frac{5}{2}+\frac{9}{11}\\=\frac{-33}{44}-\frac{110}{44}+\frac{36}{44}\\=\frac{-33-110+36}{44}\\=\frac{-107}{44}\)
2. \(+\left(\frac{4}{-9}\right) +\left(\frac{7}{3}\right) +\left(\frac{7}{8}\right)\\= \frac{-4}{9}+ \frac{7}{3}+\frac{7}{8}\\=\frac{-32}{72}+\frac{168}{72}+\frac{63}{72}\\=\frac{-32+168+63}{72}\\=\frac{199}{72}\)
3. \(-\left(\frac{-8}{-7}\right) -\left(\frac{-9}{2}\right) +\left(\frac{6}{10}\right)\\= \frac{-8}{7}+ \frac{9}{2}+\frac{6}{10}\\=\frac{-8}{7}+\frac{9}{2}+\frac{3}{5}\\=\frac{-80}{70}+\frac{315}{70}+\frac{42}{70}\\=\frac{-80+315+42}{70}\\=\frac{277}{70}\)
4. \(-\left(\frac{-4}{-3}\right) -\left(\frac{-7}{-9}\right) +\left(\frac{-5}{-10}\right)\\= \frac{-4}{3}- \frac{7}{9}+\frac{5}{10}\\=\frac{-4}{3}-\frac{7}{9}+\frac{1}{2}\\=\frac{-24}{18}-\frac{14}{18}+\frac{9}{18}\\=\frac{-24-14+9}{18}\\=\frac{-29}{18}\)
5. \(-\left(\frac{-3}{-4}\right) -\left(\frac{-2}{10}\right) -\left(\frac{2}{3}\right)\\= \frac{-3}{4}+ \frac{2}{10}-\frac{2}{3}\\=\frac{-3}{4}+\frac{1}{5}-\frac{2}{3}\\=\frac{-45}{60}+\frac{12}{60}-\frac{40}{60}\\=\frac{-45+12-40}{60}\\=\frac{-73}{60}\)
6. \(+\left(\frac{5}{-9}\right) -\left(\frac{-5}{2}\right) -\left(\frac{2}{6}\right)\\= \frac{-5}{9}+ \frac{5}{2}-\frac{2}{6}\\=\frac{-5}{9}+\frac{5}{2}-\frac{1}{3}\\=\frac{-10}{18}+\frac{45}{18}-\frac{6}{18}\\=\frac{-10+45-6}{18}\\=\frac{29}{18}\)
7. \(-\left(\frac{-8}{-5}\right) -\left(\frac{-8}{3}\right) +\left(\frac{5}{7}\right)\\= \frac{-8}{5}+ \frac{8}{3}+\frac{5}{7}\\=\frac{-168}{105}+\frac{280}{105}+\frac{75}{105}\\=\frac{-168+280+75}{105}\\=\frac{187}{105}\)
8. \(-\left(\frac{7}{-2}\right) -\left(\frac{-9}{8}\right) -\left(\frac{-7}{2}\right)\\= \frac{7}{2}+ \frac{9}{8}+\frac{7}{2}\\=\frac{28}{8}+\frac{9}{8}+\frac{28}{8}\\=\frac{28+9+28}{8}\\=\frac{65}{8}\)
9. \(+\left(\frac{-7}{-3}\right) -\left(\frac{9}{-2}\right) -\left(\frac{-12}{-7}\right)\\= \frac{7}{3}+ \frac{9}{2}-\frac{12}{7}\\=\frac{98}{42}+\frac{189}{42}-\frac{72}{42}\\=\frac{98+189-72}{42}\\=\frac{215}{42}\)
10. \(+\left(\frac{8}{5}\right) -\left(\frac{-10}{5}\right) -\left(\frac{3}{11}\right)\\= \frac{8}{5}+ \frac{10}{5}-\frac{3}{11}\\=\frac{8}{5}+\frac{2}{1}-\frac{3}{11}\\=\frac{88}{55}+\frac{110}{55}-\frac{15}{55}\\=\frac{88+110-15}{55}\\=\frac{183}{55}\)
11. \(-\left(\frac{9}{2}\right) -\left(\frac{-4}{6}\right) -\left(\frac{-9}{-12}\right)\\= \frac{-9}{2}+ \frac{4}{6}-\frac{9}{12}\\=\frac{-9}{2}+\frac{2}{3}-\frac{3}{4}\\=\frac{-54}{12}+\frac{8}{12}-\frac{9}{12}\\=\frac{-54+8-9}{12}\\=\frac{-55}{12}\)
12. \(-\left(\frac{-3}{5}\right) +\left(\frac{-7}{4}\right) -\left(\frac{8}{11}\right)\\= \frac{3}{5}- \frac{7}{4}-\frac{8}{11}\\=\frac{132}{220}-\frac{385}{220}-\frac{160}{220}\\=\frac{132-385-160}{220}\\=\frac{-413}{220}\)