Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-2}{-9}\right) +\left(\frac{3}{4}\right) -\left(\frac{11}{-12}\right)\\= \frac{-2}{9}+ \frac{3}{4}+\frac{11}{12}\\=\frac{-8}{36}+\frac{27}{36}+\frac{33}{36}\\=\frac{-8+27+33}{36}\\=\frac{52}{36}\\=\frac{13}{9}\)
2. \(+\left(\frac{-6}{5}\right) +\left(\frac{-8}{-5}\right) -\left(\frac{-4}{-4}\right)\\= \frac{-6}{5}+ \frac{8}{5}-\frac{4}{4}\\=\frac{-6}{5}+\frac{8}{5}-\frac{1}{1}\\=\frac{-6+8-1}{5}\\=\frac{1}{5}\)
3. \(-\left(\frac{-3}{-7}\right) -\left(\frac{-2}{3}\right) -\left(\frac{-11}{2}\right)\\= \frac{-3}{7}+ \frac{2}{3}+\frac{11}{2}\\=\frac{-18}{42}+\frac{28}{42}+\frac{231}{42}\\=\frac{-18+28+231}{42}\\=\frac{241}{42}\)
4. \(+\left(\frac{-8}{-7}\right) +\left(\frac{-8}{-5}\right) +\left(\frac{12}{4}\right)\\= \frac{8}{7}+ \frac{8}{5}+\frac{12}{4}\\=\frac{8}{7}+\frac{8}{5}+\frac{3}{1}\\=\frac{40}{35}+\frac{56}{35}+\frac{105}{35}\\=\frac{40+56+105}{35}\\=\frac{201}{35}\)
5. \(-\left(\frac{10}{3}\right) -\left(\frac{5}{-8}\right) +\left(\frac{-7}{-9}\right)\\= \frac{-10}{3}+ \frac{5}{8}+\frac{7}{9}\\=\frac{-240}{72}+\frac{45}{72}+\frac{56}{72}\\=\frac{-240+45+56}{72}\\=\frac{-139}{72}\)
6. \(-\left(\frac{7}{-4}\right) +\left(\frac{-2}{7}\right) -\left(\frac{-10}{7}\right)\\= \frac{7}{4}- \frac{2}{7}+\frac{10}{7}\\=\frac{49}{28}-\frac{8}{28}+\frac{40}{28}\\=\frac{49-8+40}{28}\\=\frac{81}{28}\)
7. \(+\left(\frac{6}{-5}\right) -\left(\frac{-5}{-7}\right) +\left(\frac{5}{-8}\right)\\= \frac{-6}{5}- \frac{5}{7}-\frac{5}{8}\\=\frac{-336}{280}-\frac{200}{280}-\frac{175}{280}\\=\frac{-336-200-175}{280}\\=\frac{-711}{280}\)
8. \(-\left(\frac{6}{5}\right) -\left(\frac{6}{4}\right) -\left(\frac{-3}{11}\right)\\= \frac{-6}{5}- \frac{6}{4}+\frac{3}{11}\\=\frac{-6}{5}-\frac{3}{2}+\frac{3}{11}\\=\frac{-132}{110}-\frac{165}{110}+\frac{30}{110}\\=\frac{-132-165+30}{110}\\=\frac{-267}{110}\)
9. \(-\left(\frac{-7}{-4}\right) -\left(\frac{-4}{6}\right) -\left(\frac{8}{3}\right)\\= \frac{-7}{4}+ \frac{4}{6}-\frac{8}{3}\\=\frac{-7}{4}+\frac{2}{3}-\frac{8}{3}\\=\frac{-21}{12}+\frac{8}{12}-\frac{32}{12}\\=\frac{-21+8-32}{12}\\=\frac{-45}{12}\\=\frac{-15}{4}\)
10. \(-\left(\frac{9}{4}\right) -\left(\frac{-8}{6}\right) -\left(\frac{-3}{-12}\right)\\= \frac{-9}{4}+ \frac{8}{6}-\frac{3}{12}\\=\frac{-9}{4}+\frac{4}{3}-\frac{1}{4}\\=\frac{-27}{12}+\frac{16}{12}-\frac{3}{12}\\=\frac{-27+16-3}{12}\\=\frac{-14}{12}\\=\frac{-7}{6}\)
11. \(+\left(\frac{2}{3}\right) +\left(\frac{-7}{6}\right) -\left(\frac{9}{-5}\right)\\= \frac{2}{3}- \frac{7}{6}+\frac{9}{5}\\=\frac{20}{30}-\frac{35}{30}+\frac{54}{30}\\=\frac{20-35+54}{30}\\=\frac{39}{30}\\=\frac{13}{10}\)
12. \(+\left(\frac{9}{-5}\right) -\left(\frac{-7}{8}\right) +\left(\frac{8}{-9}\right)\\= \frac{-9}{5}+ \frac{7}{8}-\frac{8}{9}\\=\frac{-648}{360}+\frac{315}{360}-\frac{320}{360}\\=\frac{-648+315-320}{360}\\=\frac{-653}{360}\)