Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{5}{-3}\right) +\left(\frac{2}{3}\right) +\left(\frac{-2}{8}\right)\\= \frac{5}{3}+ \frac{2}{3}-\frac{2}{8}\\=\frac{5}{3}+\frac{2}{3}-\frac{1}{4}\\=\frac{20}{12}+\frac{8}{12}-\frac{3}{12}\\=\frac{20+8-3}{12}\\=\frac{25}{12}\)
2. \(+\left(\frac{-5}{2}\right) -\left(\frac{8}{4}\right) +\left(\frac{11}{-7}\right)\\= \frac{-5}{2}- \frac{8}{4}-\frac{11}{7}\\=\frac{-5}{2}-\frac{2}{1}-\frac{11}{7}\\=\frac{-35}{14}-\frac{28}{14}-\frac{22}{14}\\=\frac{-35-28-22}{14}\\=\frac{-85}{14}\)
3. \(+\left(\frac{6}{5}\right) +\left(\frac{-8}{7}\right) +\left(\frac{-5}{-12}\right)\\= \frac{6}{5}- \frac{8}{7}+\frac{5}{12}\\=\frac{504}{420}-\frac{480}{420}+\frac{175}{420}\\=\frac{504-480+175}{420}\\=\frac{199}{420}\)
4. \(+\left(\frac{8}{9}\right) -\left(\frac{7}{9}\right) +\left(\frac{4}{-7}\right)\\= \frac{8}{9}- \frac{7}{9}-\frac{4}{7}\\=\frac{56}{63}-\frac{49}{63}-\frac{36}{63}\\=\frac{56-49-36}{63}\\=\frac{-29}{63}\)
5. \(-\left(\frac{5}{7}\right) -\left(\frac{5}{-2}\right) +\left(\frac{-9}{-5}\right)\\= \frac{-5}{7}+ \frac{5}{2}+\frac{9}{5}\\=\frac{-50}{70}+\frac{175}{70}+\frac{126}{70}\\=\frac{-50+175+126}{70}\\=\frac{251}{70}\)
6. \(-\left(\frac{6}{5}\right) +\left(\frac{-9}{6}\right) -\left(\frac{-8}{-12}\right)\\= \frac{-6}{5}- \frac{9}{6}-\frac{8}{12}\\=\frac{-6}{5}-\frac{3}{2}-\frac{2}{3}\\=\frac{-36}{30}-\frac{45}{30}-\frac{20}{30}\\=\frac{-36-45-20}{30}\\=\frac{-101}{30}\)
7. \(-\left(\frac{-8}{-3}\right) -\left(\frac{3}{-6}\right) +\left(\frac{-6}{4}\right)\\= \frac{-8}{3}+ \frac{3}{6}-\frac{6}{4}\\=\frac{-8}{3}+\frac{1}{2}-\frac{3}{2}\\=\frac{-16}{6}+\frac{3}{6}-\frac{9}{6}\\=\frac{-16+3-9}{6}\\=\frac{-22}{6}\\=\frac{-11}{3}\)
8. \(-\left(\frac{-4}{-3}\right) -\left(\frac{8}{-7}\right) +\left(\frac{-9}{5}\right)\\= \frac{-4}{3}+ \frac{8}{7}-\frac{9}{5}\\=\frac{-140}{105}+\frac{120}{105}-\frac{189}{105}\\=\frac{-140+120-189}{105}\\=\frac{-209}{105}\)
9. \(-\left(\frac{5}{-4}\right) +\left(\frac{7}{8}\right) +\left(\frac{10}{-9}\right)\\= \frac{5}{4}+ \frac{7}{8}-\frac{10}{9}\\=\frac{90}{72}+\frac{63}{72}-\frac{80}{72}\\=\frac{90+63-80}{72}\\=\frac{73}{72}\)
10. \(+\left(\frac{5}{3}\right) -\left(\frac{5}{-3}\right) +\left(\frac{-9}{-7}\right)\\= \frac{5}{3}+ \frac{5}{3}+\frac{9}{7}\\=\frac{35}{21}+\frac{35}{21}+\frac{27}{21}\\=\frac{35+35+27}{21}\\=\frac{97}{21}\)
11. \(+\left(\frac{6}{-5}\right) +\left(\frac{-8}{8}\right) -\left(\frac{7}{-5}\right)\\= \frac{-6}{5}- \frac{8}{8}+\frac{7}{5}\\=\frac{-6}{5}-\frac{1}{1}+\frac{7}{5}\\=\frac{-6-1+7}{5}\\=\frac{0}{5}\\=\frac{0}{1}\)
12. \(-\left(\frac{-8}{-3}\right) +\left(\frac{-9}{8}\right) -\left(\frac{4}{-2}\right)\\= \frac{-8}{3}- \frac{9}{8}+\frac{4}{2}\\=\frac{-8}{3}-\frac{9}{8}+\frac{2}{1}\\=\frac{-64}{24}-\frac{27}{24}+\frac{48}{24}\\=\frac{-64-27+48}{24}\\=\frac{-43}{24}\)