Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{8}{-7}\right) +\left(\frac{7}{-10}\right) -\left(\frac{-11}{6}\right)\\= \frac{8}{7}- \frac{7}{10}+\frac{11}{6}\\=\frac{240}{210}-\frac{147}{210}+\frac{385}{210}\\=\frac{240-147+385}{210}\\=\frac{478}{210}\\=\frac{239}{105}\)
2. \(-\left(\frac{4}{9}\right) -\left(\frac{-3}{-9}\right) -\left(\frac{2}{-10}\right)\\= \frac{-4}{9}- \frac{3}{9}+\frac{2}{10}\\=\frac{-4}{9}-\frac{1}{3}+\frac{1}{5}\\=\frac{-20}{45}-\frac{15}{45}+\frac{9}{45}\\=\frac{-20-15+9}{45}\\=\frac{-26}{45}\)
3. \(+\left(\frac{-4}{-7}\right) +\left(\frac{-9}{-4}\right) +\left(\frac{7}{-8}\right)\\= \frac{4}{7}+ \frac{9}{4}-\frac{7}{8}\\=\frac{32}{56}+\frac{126}{56}-\frac{49}{56}\\=\frac{32+126-49}{56}\\=\frac{109}{56}\)
4. \(-\left(\frac{-7}{6}\right) -\left(\frac{9}{5}\right) +\left(\frac{2}{-6}\right)\\= \frac{7}{6}- \frac{9}{5}-\frac{2}{6}\\=\frac{7}{6}-\frac{9}{5}-\frac{1}{3}\\=\frac{35}{30}-\frac{54}{30}-\frac{10}{30}\\=\frac{35-54-10}{30}\\=\frac{-29}{30}\)
5. \(+\left(\frac{8}{3}\right) -\left(\frac{5}{-3}\right) +\left(\frac{-11}{12}\right)\\= \frac{8}{3}+ \frac{5}{3}-\frac{11}{12}\\=\frac{32}{12}+\frac{20}{12}-\frac{11}{12}\\=\frac{32+20-11}{12}\\=\frac{41}{12}\)
6. \(-\left(\frac{-4}{-9}\right) -\left(\frac{-2}{-2}\right) +\left(\frac{8}{-7}\right)\\= \frac{-4}{9}- \frac{2}{2}-\frac{8}{7}\\=\frac{-4}{9}-\frac{1}{1}-\frac{8}{7}\\=\frac{-28}{63}-\frac{63}{63}-\frac{72}{63}\\=\frac{-28-63-72}{63}\\=\frac{-163}{63}\)
7. \(-\left(\frac{4}{5}\right) -\left(\frac{6}{-10}\right) -\left(\frac{-3}{4}\right)\\= \frac{-4}{5}+ \frac{6}{10}+\frac{3}{4}\\=\frac{-4}{5}+\frac{3}{5}+\frac{3}{4}\\=\frac{-16}{20}+\frac{12}{20}+\frac{15}{20}\\=\frac{-16+12+15}{20}\\=\frac{11}{20}\)
8. \(-\left(\frac{9}{-7}\right) +\left(\frac{9}{-7}\right) -\left(\frac{5}{11}\right)\\= \frac{9}{7}- \frac{9}{7}-\frac{5}{11}\\=\frac{99}{77}-\frac{99}{77}-\frac{35}{77}\\=\frac{99-99-35}{77}\\=\frac{-35}{77}\\=\frac{-5}{11}\)
9. \(+\left(\frac{7}{6}\right) +\left(\frac{9}{2}\right) -\left(\frac{-7}{-10}\right)\\= \frac{7}{6}+ \frac{9}{2}-\frac{7}{10}\\=\frac{35}{30}+\frac{135}{30}-\frac{21}{30}\\=\frac{35+135-21}{30}\\=\frac{149}{30}\)
10. \(+\left(\frac{9}{-4}\right) +\left(\frac{-6}{-4}\right) +\left(\frac{-5}{-9}\right)\\= \frac{-9}{4}+ \frac{6}{4}+\frac{5}{9}\\=\frac{-9}{4}+\frac{3}{2}+\frac{5}{9}\\=\frac{-81}{36}+\frac{54}{36}+\frac{20}{36}\\=\frac{-81+54+20}{36}\\=\frac{-7}{36}\)
11. \(+\left(\frac{8}{5}\right) +\left(\frac{3}{9}\right) +\left(\frac{6}{4}\right)\\= \frac{8}{5}+ \frac{3}{9}+\frac{6}{4}\\=\frac{8}{5}+\frac{1}{3}+\frac{3}{2}\\=\frac{48}{30}+\frac{10}{30}+\frac{45}{30}\\=\frac{48+10+45}{30}\\=\frac{103}{30}\)
12. \(-\left(\frac{9}{4}\right) +\left(\frac{-2}{-3}\right) +\left(\frac{-11}{-4}\right)\\= \frac{-9}{4}+ \frac{2}{3}+\frac{11}{4}\\=\frac{-27}{12}+\frac{8}{12}+\frac{33}{12}\\=\frac{-27+8+33}{12}\\=\frac{14}{12}\\=\frac{7}{6}\)