Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{7}{-3}\right) +\left(\frac{-7}{3}\right) +\left(\frac{2}{-9}\right)\\= \frac{7}{3}- \frac{7}{3}-\frac{2}{9}\\=\frac{21}{9}-\frac{21}{9}-\frac{2}{9}\\=\frac{21-21-2}{9}\\=\frac{-2}{9}\)
2. \(-\left(\frac{-3}{-2}\right) -\left(\frac{8}{-3}\right) -\left(\frac{-11}{5}\right)\\= \frac{-3}{2}+ \frac{8}{3}+\frac{11}{5}\\=\frac{-45}{30}+\frac{80}{30}+\frac{66}{30}\\=\frac{-45+80+66}{30}\\=\frac{101}{30}\)
3. \(-\left(\frac{-10}{7}\right) +\left(\frac{6}{9}\right) +\left(\frac{8}{2}\right)\\= \frac{10}{7}+ \frac{6}{9}+\frac{8}{2}\\=\frac{10}{7}+\frac{2}{3}+\frac{4}{1}\\=\frac{30}{21}+\frac{14}{21}+\frac{84}{21}\\=\frac{30+14+84}{21}\\=\frac{128}{21}\)
4. \(-\left(\frac{-10}{-7}\right) -\left(\frac{-6}{-7}\right) -\left(\frac{-11}{-7}\right)\\= \frac{-10}{7}- \frac{6}{7}-\frac{11}{7}\\=\frac{-10-6-11}{7}\\=\frac{-27}{7}\)
5. \(-\left(\frac{4}{-5}\right) -\left(\frac{6}{7}\right) +\left(\frac{-12}{3}\right)\\= \frac{4}{5}- \frac{6}{7}-\frac{12}{3}\\=\frac{4}{5}-\frac{6}{7}-\frac{4}{1}\\=\frac{28}{35}-\frac{30}{35}-\frac{140}{35}\\=\frac{28-30-140}{35}\\=\frac{-142}{35}\)
6. \(+\left(\frac{9}{-4}\right) +\left(\frac{-3}{-4}\right) -\left(\frac{8}{2}\right)\\= \frac{-9}{4}+ \frac{3}{4}-\frac{8}{2}\\=\frac{-9}{4}+\frac{3}{4}-\frac{4}{1}\\=\frac{-9+3-4}{4}\\=\frac{-10}{4}\\=\frac{-5}{2}\)
7. \(+\left(\frac{-4}{9}\right) +\left(\frac{9}{-5}\right) +\left(\frac{-5}{-12}\right)\\= \frac{-4}{9}- \frac{9}{5}+\frac{5}{12}\\=\frac{-80}{180}-\frac{324}{180}+\frac{75}{180}\\=\frac{-80-324+75}{180}\\=\frac{-329}{180}\)
8. \(-\left(\frac{-5}{-4}\right) -\left(\frac{7}{-7}\right) +\left(\frac{-7}{-6}\right)\\= \frac{-5}{4}+ \frac{7}{7}+\frac{7}{6}\\=\frac{-5}{4}+\frac{1}{1}+\frac{7}{6}\\=\frac{-15}{12}+\frac{12}{12}+\frac{14}{12}\\=\frac{-15+12+14}{12}\\=\frac{11}{12}\)
9. \(-\left(\frac{-4}{-3}\right) +\left(\frac{7}{7}\right) +\left(\frac{9}{5}\right)\\= \frac{-4}{3}+ \frac{7}{7}+\frac{9}{5}\\=\frac{-4}{3}+\frac{1}{1}+\frac{9}{5}\\=\frac{-20}{15}+\frac{15}{15}+\frac{27}{15}\\=\frac{-20+15+27}{15}\\=\frac{22}{15}\)
10. \(-\left(\frac{8}{3}\right) -\left(\frac{2}{2}\right) +\left(\frac{-9}{5}\right)\\= \frac{-8}{3}- \frac{2}{2}-\frac{9}{5}\\=\frac{-8}{3}-\frac{1}{1}-\frac{9}{5}\\=\frac{-40}{15}-\frac{15}{15}-\frac{27}{15}\\=\frac{-40-15-27}{15}\\=\frac{-82}{15}\)
11. \(+\left(\frac{7}{8}\right) +\left(\frac{3}{2}\right) +\left(\frac{11}{3}\right)\\= \frac{7}{8}+ \frac{3}{2}+\frac{11}{3}\\=\frac{21}{24}+\frac{36}{24}+\frac{88}{24}\\=\frac{21+36+88}{24}\\=\frac{145}{24}\)
12. \(+\left(\frac{7}{3}\right) +\left(\frac{-4}{7}\right) +\left(\frac{-9}{10}\right)\\= \frac{7}{3}- \frac{4}{7}-\frac{9}{10}\\=\frac{490}{210}-\frac{120}{210}-\frac{189}{210}\\=\frac{490-120-189}{210}\\=\frac{181}{210}\)