Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{8}{3}\right) +\left(\frac{-8}{-2}\right) +\left(\frac{-10}{-9}\right)\\= \frac{-8}{3}+ \frac{8}{2}+\frac{10}{9}\\=\frac{-8}{3}+\frac{4}{1}+\frac{10}{9}\\=\frac{-24}{9}+\frac{36}{9}+\frac{10}{9}\\=\frac{-24+36+10}{9}\\=\frac{22}{9}\)
2. \(+\left(\frac{3}{2}\right) +\left(\frac{9}{-9}\right) -\left(\frac{-11}{7}\right)\\= \frac{3}{2}- \frac{9}{9}+\frac{11}{7}\\=\frac{3}{2}-\frac{1}{1}+\frac{11}{7}\\=\frac{21}{14}-\frac{14}{14}+\frac{22}{14}\\=\frac{21-14+22}{14}\\=\frac{29}{14}\)
3. \(-\left(\frac{2}{5}\right) +\left(\frac{8}{-3}\right) -\left(\frac{2}{-3}\right)\\= \frac{-2}{5}- \frac{8}{3}+\frac{2}{3}\\=\frac{-6}{15}-\frac{40}{15}+\frac{10}{15}\\=\frac{-6-40+10}{15}\\=\frac{-36}{15}\\=\frac{-12}{5}\)
4. \(+\left(\frac{-2}{9}\right) -\left(\frac{-4}{4}\right) +\left(\frac{-3}{2}\right)\\= \frac{-2}{9}+ \frac{4}{4}-\frac{3}{2}\\=\frac{-2}{9}+\frac{1}{1}-\frac{3}{2}\\=\frac{-4}{18}+\frac{18}{18}-\frac{27}{18}\\=\frac{-4+18-27}{18}\\=\frac{-13}{18}\)
5. \(+\left(\frac{-3}{4}\right) -\left(\frac{-9}{2}\right) +\left(\frac{4}{10}\right)\\= \frac{-3}{4}+ \frac{9}{2}+\frac{4}{10}\\=\frac{-3}{4}+\frac{9}{2}+\frac{2}{5}\\=\frac{-15}{20}+\frac{90}{20}+\frac{8}{20}\\=\frac{-15+90+8}{20}\\=\frac{83}{20}\)
6. \(+\left(\frac{7}{-9}\right) +\left(\frac{-9}{-5}\right) +\left(\frac{8}{4}\right)\\= \frac{-7}{9}+ \frac{9}{5}+\frac{8}{4}\\=\frac{-7}{9}+\frac{9}{5}+\frac{2}{1}\\=\frac{-35}{45}+\frac{81}{45}+\frac{90}{45}\\=\frac{-35+81+90}{45}\\=\frac{136}{45}\)
7. \(+\left(\frac{-10}{7}\right) +\left(\frac{3}{6}\right) +\left(\frac{-7}{-3}\right)\\= \frac{-10}{7}+ \frac{3}{6}+\frac{7}{3}\\=\frac{-10}{7}+\frac{1}{2}+\frac{7}{3}\\=\frac{-60}{42}+\frac{21}{42}+\frac{98}{42}\\=\frac{-60+21+98}{42}\\=\frac{59}{42}\)
8. \(+\left(\frac{-4}{3}\right) +\left(\frac{-4}{-8}\right) -\left(\frac{4}{5}\right)\\= \frac{-4}{3}+ \frac{4}{8}-\frac{4}{5}\\=\frac{-4}{3}+\frac{1}{2}-\frac{4}{5}\\=\frac{-40}{30}+\frac{15}{30}-\frac{24}{30}\\=\frac{-40+15-24}{30}\\=\frac{-49}{30}\)
9. \(-\left(\frac{-2}{3}\right) +\left(\frac{5}{5}\right) -\left(\frac{-9}{-7}\right)\\= \frac{2}{3}+ \frac{5}{5}-\frac{9}{7}\\=\frac{2}{3}+\frac{1}{1}-\frac{9}{7}\\=\frac{14}{21}+\frac{21}{21}-\frac{27}{21}\\=\frac{14+21-27}{21}\\=\frac{8}{21}\)
10. \(+\left(\frac{6}{-5}\right) -\left(\frac{-10}{4}\right) -\left(\frac{-8}{-6}\right)\\= \frac{-6}{5}+ \frac{10}{4}-\frac{8}{6}\\=\frac{-6}{5}+\frac{5}{2}-\frac{4}{3}\\=\frac{-36}{30}+\frac{75}{30}-\frac{40}{30}\\=\frac{-36+75-40}{30}\\=\frac{-1}{30}\)
11. \(-\left(\frac{2}{9}\right) +\left(\frac{7}{3}\right) +\left(\frac{-3}{11}\right)\\= \frac{-2}{9}+ \frac{7}{3}-\frac{3}{11}\\=\frac{-22}{99}+\frac{231}{99}-\frac{27}{99}\\=\frac{-22+231-27}{99}\\=\frac{182}{99}\)
12. \(+\left(\frac{-4}{5}\right) +\left(\frac{-9}{2}\right) +\left(\frac{-2}{6}\right)\\= \frac{-4}{5}- \frac{9}{2}-\frac{2}{6}\\=\frac{-4}{5}-\frac{9}{2}-\frac{1}{3}\\=\frac{-24}{30}-\frac{135}{30}-\frac{10}{30}\\=\frac{-24-135-10}{30}\\=\frac{-169}{30}\)