Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{4}{7}\right) +\left(\frac{6}{7}\right) +\left(\frac{-5}{-7}\right)\\= \frac{-4}{7}+ \frac{6}{7}+\frac{5}{7}\\=\frac{-4+6+5}{7}\\=\frac{7}{7}\\=\frac{1}{1}\)
2. \(+\left(\frac{8}{9}\right) +\left(\frac{3}{4}\right) -\left(\frac{11}{12}\right)\\= \frac{8}{9}+ \frac{3}{4}-\frac{11}{12}\\=\frac{32}{36}+\frac{27}{36}-\frac{33}{36}\\=\frac{32+27-33}{36}\\=\frac{26}{36}\\=\frac{13}{18}\)
3. \(+\left(\frac{-8}{7}\right) -\left(\frac{-7}{6}\right) -\left(\frac{8}{7}\right)\\= \frac{-8}{7}+ \frac{7}{6}-\frac{8}{7}\\=\frac{-48}{42}+\frac{49}{42}-\frac{48}{42}\\=\frac{-48+49-48}{42}\\=\frac{-47}{42}\)
4. \(+\left(\frac{2}{3}\right) +\left(\frac{3}{4}\right) -\left(\frac{-12}{-2}\right)\\= \frac{2}{3}+ \frac{3}{4}-\frac{12}{2}\\=\frac{2}{3}+\frac{3}{4}-\frac{6}{1}\\=\frac{8}{12}+\frac{9}{12}-\frac{72}{12}\\=\frac{8+9-72}{12}\\=\frac{-55}{12}\)
5. \(+\left(\frac{7}{9}\right) -\left(\frac{-10}{-2}\right) -\left(\frac{-5}{9}\right)\\= \frac{7}{9}- \frac{10}{2}+\frac{5}{9}\\=\frac{7}{9}-\frac{5}{1}+\frac{5}{9}\\=\frac{7-5+5}{9}\\=\frac{7}{9}\)
6. \(-\left(\frac{2}{3}\right) -\left(\frac{6}{5}\right) +\left(\frac{5}{8}\right)\\= \frac{-2}{3}- \frac{6}{5}+\frac{5}{8}\\=\frac{-80}{120}-\frac{144}{120}+\frac{75}{120}\\=\frac{-80-144+75}{120}\\=\frac{-149}{120}\)
7. \(-\left(\frac{9}{-2}\right) -\left(\frac{6}{10}\right) +\left(\frac{8}{-5}\right)\\= \frac{9}{2}- \frac{6}{10}-\frac{8}{5}\\=\frac{9}{2}-\frac{3}{5}-\frac{8}{5}\\=\frac{45}{10}-\frac{6}{10}-\frac{16}{10}\\=\frac{45-6-16}{10}\\=\frac{23}{10}\)
8. \(-\left(\frac{-8}{3}\right) +\left(\frac{6}{2}\right) -\left(\frac{-12}{-4}\right)\\= \frac{8}{3}+ \frac{6}{2}-\frac{12}{4}\\=\frac{8}{3}+\frac{3}{1}-\frac{3}{1}\\=\frac{8+3-3}{3}\\=\frac{8}{3}\)
9. \(+\left(\frac{4}{7}\right) -\left(\frac{6}{9}\right) -\left(\frac{10}{3}\right)\\= \frac{4}{7}- \frac{6}{9}-\frac{10}{3}\\=\frac{4}{7}-\frac{2}{3}-\frac{10}{3}\\=\frac{12}{21}-\frac{14}{21}-\frac{70}{21}\\=\frac{12-14-70}{21}\\=\frac{-72}{21}\\=\frac{-24}{7}\)
10. \(-\left(\frac{6}{7}\right) -\left(\frac{2}{-9}\right) -\left(\frac{-9}{-10}\right)\\= \frac{-6}{7}+ \frac{2}{9}-\frac{9}{10}\\=\frac{-540}{630}+\frac{140}{630}-\frac{567}{630}\\=\frac{-540+140-567}{630}\\=\frac{-967}{630}\)
11. \(+\left(\frac{7}{-8}\right) -\left(\frac{-7}{-5}\right) -\left(\frac{5}{-9}\right)\\= \frac{-7}{8}- \frac{7}{5}+\frac{5}{9}\\=\frac{-315}{360}-\frac{504}{360}+\frac{200}{360}\\=\frac{-315-504+200}{360}\\=\frac{-619}{360}\)
12. \(+\left(\frac{-8}{-5}\right) +\left(\frac{7}{-10}\right) +\left(\frac{7}{3}\right)\\= \frac{8}{5}- \frac{7}{10}+\frac{7}{3}\\=\frac{48}{30}-\frac{21}{30}+\frac{70}{30}\\=\frac{48-21+70}{30}\\=\frac{97}{30}\)