Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{-9}\right) +\left(\frac{4}{5}\right) +\left(\frac{-4}{-9}\right)\\= \frac{10}{9}+ \frac{4}{5}+\frac{4}{9}\\=\frac{50}{45}+\frac{36}{45}+\frac{20}{45}\\=\frac{50+36+20}{45}\\=\frac{106}{45}\)
2. \(+\left(\frac{3}{2}\right) -\left(\frac{-5}{6}\right) -\left(\frac{-11}{-7}\right)\\= \frac{3}{2}+ \frac{5}{6}-\frac{11}{7}\\=\frac{63}{42}+\frac{35}{42}-\frac{66}{42}\\=\frac{63+35-66}{42}\\=\frac{32}{42}\\=\frac{16}{21}\)
3. \(+\left(\frac{8}{7}\right) +\left(\frac{-3}{7}\right) +\left(\frac{-4}{10}\right)\\= \frac{8}{7}- \frac{3}{7}-\frac{4}{10}\\=\frac{8}{7}-\frac{3}{7}-\frac{2}{5}\\=\frac{40}{35}-\frac{15}{35}-\frac{14}{35}\\=\frac{40-15-14}{35}\\=\frac{11}{35}\)
4. \(-\left(\frac{3}{-8}\right) -\left(\frac{10}{10}\right) -\left(\frac{-4}{-11}\right)\\= \frac{3}{8}- \frac{10}{10}-\frac{4}{11}\\=\frac{3}{8}-\frac{1}{1}-\frac{4}{11}\\=\frac{33}{88}-\frac{88}{88}-\frac{32}{88}\\=\frac{33-88-32}{88}\\=\frac{-87}{88}\)
5. \(-\left(\frac{-8}{-3}\right) -\left(\frac{-2}{2}\right) +\left(\frac{-9}{-2}\right)\\= \frac{-8}{3}+ \frac{2}{2}+\frac{9}{2}\\=\frac{-8}{3}+\frac{1}{1}+\frac{9}{2}\\=\frac{-16}{6}+\frac{6}{6}+\frac{27}{6}\\=\frac{-16+6+27}{6}\\=\frac{17}{6}\)
6. \(+\left(\frac{-9}{-2}\right) +\left(\frac{7}{10}\right) +\left(\frac{-10}{12}\right)\\= \frac{9}{2}+ \frac{7}{10}-\frac{10}{12}\\=\frac{9}{2}+\frac{7}{10}-\frac{5}{6}\\=\frac{135}{30}+\frac{21}{30}-\frac{25}{30}\\=\frac{135+21-25}{30}\\=\frac{131}{30}\)
7. \(-\left(\frac{-10}{7}\right) -\left(\frac{-2}{8}\right) +\left(\frac{3}{-3}\right)\\= \frac{10}{7}+ \frac{2}{8}-\frac{3}{3}\\=\frac{10}{7}+\frac{1}{4}-\frac{1}{1}\\=\frac{40}{28}+\frac{7}{28}-\frac{28}{28}\\=\frac{40+7-28}{28}\\=\frac{19}{28}\)
8. \(+\left(\frac{6}{5}\right) -\left(\frac{-5}{10}\right) -\left(\frac{-2}{8}\right)\\= \frac{6}{5}+ \frac{5}{10}+\frac{2}{8}\\=\frac{6}{5}+\frac{1}{2}+\frac{1}{4}\\=\frac{24}{20}+\frac{10}{20}+\frac{5}{20}\\=\frac{24+10+5}{20}\\=\frac{39}{20}\)
9. \(-\left(\frac{4}{3}\right) -\left(\frac{-3}{7}\right) +\left(\frac{8}{8}\right)\\= \frac{-4}{3}+ \frac{3}{7}+\frac{8}{8}\\=\frac{-4}{3}+\frac{3}{7}+\frac{1}{1}\\=\frac{-28}{21}+\frac{9}{21}+\frac{21}{21}\\=\frac{-28+9+21}{21}\\=\frac{2}{21}\)
10. \(-\left(\frac{3}{2}\right) -\left(\frac{-6}{9}\right) +\left(\frac{-12}{-8}\right)\\= \frac{-3}{2}+ \frac{6}{9}+\frac{12}{8}\\=\frac{-3}{2}+\frac{2}{3}+\frac{3}{2}\\=\frac{-9}{6}+\frac{4}{6}+\frac{9}{6}\\=\frac{-9+4+9}{6}\\=\frac{4}{6}\\=\frac{2}{3}\)
11. \(+\left(\frac{4}{3}\right) +\left(\frac{10}{2}\right) +\left(\frac{12}{-4}\right)\\= \frac{4}{3}+ \frac{10}{2}-\frac{12}{4}\\=\frac{4}{3}+\frac{5}{1}-\frac{3}{1}\\=\frac{4+5-3}{3}\\=\frac{6}{3}\\=\frac{2}{1}\)
12. \(+\left(\frac{7}{8}\right) +\left(\frac{8}{-8}\right) -\left(\frac{-6}{-11}\right)\\= \frac{7}{8}- \frac{8}{8}-\frac{6}{11}\\=\frac{7}{8}-\frac{1}{1}-\frac{6}{11}\\=\frac{77}{88}-\frac{88}{88}-\frac{48}{88}\\=\frac{77-88-48}{88}\\=\frac{-59}{88}\)