Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{-7}\right) +\left(\frac{-8}{2}\right) -\left(\frac{-5}{5}\right)\\= \frac{-9}{7}- \frac{8}{2}+\frac{5}{5}\\=\frac{-9}{7}-\frac{4}{1}+\frac{1}{1}\\=\frac{-9-4+1}{7}\\=\frac{-12}{7}\)
2. \(-\left(\frac{-4}{-5}\right) -\left(\frac{10}{-4}\right) +\left(\frac{9}{-2}\right)\\= \frac{-4}{5}+ \frac{10}{4}-\frac{9}{2}\\=\frac{-4}{5}+\frac{5}{2}-\frac{9}{2}\\=\frac{-8}{10}+\frac{25}{10}-\frac{45}{10}\\=\frac{-8+25-45}{10}\\=\frac{-28}{10}\\=\frac{-14}{5}\)
3. \(+\left(\frac{6}{5}\right) -\left(\frac{-2}{-6}\right) +\left(\frac{-4}{-9}\right)\\= \frac{6}{5}- \frac{2}{6}+\frac{4}{9}\\=\frac{6}{5}-\frac{1}{3}+\frac{4}{9}\\=\frac{54}{45}-\frac{15}{45}+\frac{20}{45}\\=\frac{54-15+20}{45}\\=\frac{59}{45}\)
4. \(+\left(\frac{3}{-5}\right) +\left(\frac{-2}{8}\right) -\left(\frac{8}{12}\right)\\= \frac{-3}{5}- \frac{2}{8}-\frac{8}{12}\\=\frac{-3}{5}-\frac{1}{4}-\frac{2}{3}\\=\frac{-36}{60}-\frac{15}{60}-\frac{40}{60}\\=\frac{-36-15-40}{60}\\=\frac{-91}{60}\)
5. \(-\left(\frac{-5}{-6}\right) -\left(\frac{6}{10}\right) +\left(\frac{4}{-11}\right)\\= \frac{-5}{6}- \frac{6}{10}-\frac{4}{11}\\=\frac{-5}{6}-\frac{3}{5}-\frac{4}{11}\\=\frac{-275}{330}-\frac{198}{330}-\frac{120}{330}\\=\frac{-275-198-120}{330}\\=\frac{-593}{330}\)
6. \(-\left(\frac{-2}{7}\right) -\left(\frac{5}{-2}\right) +\left(\frac{-9}{-5}\right)\\= \frac{2}{7}+ \frac{5}{2}+\frac{9}{5}\\=\frac{20}{70}+\frac{175}{70}+\frac{126}{70}\\=\frac{20+175+126}{70}\\=\frac{321}{70}\)
7. \(+\left(\frac{6}{5}\right) +\left(\frac{-3}{-7}\right) -\left(\frac{5}{-3}\right)\\= \frac{6}{5}+ \frac{3}{7}+\frac{5}{3}\\=\frac{126}{105}+\frac{45}{105}+\frac{175}{105}\\=\frac{126+45+175}{105}\\=\frac{346}{105}\)
8. \(+\left(\frac{4}{-5}\right) -\left(\frac{-5}{6}\right) -\left(\frac{-12}{-12}\right)\\= \frac{-4}{5}+ \frac{5}{6}-\frac{12}{12}\\=\frac{-4}{5}+\frac{5}{6}-\frac{1}{1}\\=\frac{-24}{30}+\frac{25}{30}-\frac{30}{30}\\=\frac{-24+25-30}{30}\\=\frac{-29}{30}\)
9. \(-\left(\frac{5}{2}\right) +\left(\frac{-6}{-9}\right) +\left(\frac{5}{-3}\right)\\= \frac{-5}{2}+ \frac{6}{9}-\frac{5}{3}\\=\frac{-5}{2}+\frac{2}{3}-\frac{5}{3}\\=\frac{-15}{6}+\frac{4}{6}-\frac{10}{6}\\=\frac{-15+4-10}{6}\\=\frac{-21}{6}\\=\frac{-7}{2}\)
10. \(+\left(\frac{-7}{-5}\right) -\left(\frac{-9}{5}\right) -\left(\frac{12}{9}\right)\\= \frac{7}{5}+ \frac{9}{5}-\frac{12}{9}\\=\frac{7}{5}+\frac{9}{5}-\frac{4}{3}\\=\frac{21}{15}+\frac{27}{15}-\frac{20}{15}\\=\frac{21+27-20}{15}\\=\frac{28}{15}\)
11. \(-\left(\frac{-4}{-3}\right) -\left(\frac{4}{5}\right) +\left(\frac{-3}{-9}\right)\\= \frac{-4}{3}- \frac{4}{5}+\frac{3}{9}\\=\frac{-4}{3}-\frac{4}{5}+\frac{1}{3}\\=\frac{-20}{15}-\frac{12}{15}+\frac{5}{15}\\=\frac{-20-12+5}{15}\\=\frac{-27}{15}\\=\frac{-9}{5}\)
12. \(+\left(\frac{-9}{-2}\right) +\left(\frac{-9}{-3}\right) -\left(\frac{5}{12}\right)\\= \frac{9}{2}+ \frac{9}{3}-\frac{5}{12}\\=\frac{9}{2}+\frac{3}{1}-\frac{5}{12}\\=\frac{54}{12}+\frac{36}{12}-\frac{5}{12}\\=\frac{54+36-5}{12}\\=\frac{85}{12}\)