Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{9}{8}\right) -\left(\frac{2}{4}\right) +\left(\frac{5}{-4}\right)\\= \frac{9}{8}- \frac{2}{4}-\frac{5}{4}\\=\frac{9}{8}-\frac{1}{2}-\frac{5}{4}\\=\frac{9-1-5}{8}\\=\frac{3}{8}\)
2. \(+\left(\frac{5}{-8}\right) +\left(\frac{-2}{-2}\right) +\left(\frac{9}{11}\right)\\= \frac{-5}{8}+ \frac{2}{2}+\frac{9}{11}\\=\frac{-5}{8}+\frac{1}{1}+\frac{9}{11}\\=\frac{-55}{88}+\frac{88}{88}+\frac{72}{88}\\=\frac{-55+88+72}{88}\\=\frac{105}{88}\)
3. \(-\left(\frac{-5}{6}\right) +\left(\frac{-3}{10}\right) -\left(\frac{7}{-2}\right)\\= \frac{5}{6}- \frac{3}{10}+\frac{7}{2}\\=\frac{25}{30}-\frac{9}{30}+\frac{105}{30}\\=\frac{25-9+105}{30}\\=\frac{121}{30}\)
4. \(+\left(\frac{2}{-3}\right) -\left(\frac{-2}{-8}\right) -\left(\frac{11}{-3}\right)\\= \frac{-2}{3}- \frac{2}{8}+\frac{11}{3}\\=\frac{-2}{3}-\frac{1}{4}+\frac{11}{3}\\=\frac{-8}{12}-\frac{3}{12}+\frac{44}{12}\\=\frac{-8-3+44}{12}\\=\frac{33}{12}\\=\frac{11}{4}\)
5. \(-\left(\frac{-5}{2}\right) +\left(\frac{-8}{9}\right) +\left(\frac{-7}{3}\right)\\= \frac{5}{2}- \frac{8}{9}-\frac{7}{3}\\=\frac{45}{18}-\frac{16}{18}-\frac{42}{18}\\=\frac{45-16-42}{18}\\=\frac{-13}{18}\)
6. \(+\left(\frac{10}{7}\right) -\left(\frac{-2}{-4}\right) +\left(\frac{8}{-8}\right)\\= \frac{10}{7}- \frac{2}{4}-\frac{8}{8}\\=\frac{10}{7}-\frac{1}{2}-\frac{1}{1}\\=\frac{20}{14}-\frac{7}{14}-\frac{14}{14}\\=\frac{20-7-14}{14}\\=\frac{-1}{14}\)
7. \(+\left(\frac{-4}{3}\right) +\left(\frac{-6}{-5}\right) +\left(\frac{-9}{12}\right)\\= \frac{-4}{3}+ \frac{6}{5}-\frac{9}{12}\\=\frac{-4}{3}+\frac{6}{5}-\frac{3}{4}\\=\frac{-80}{60}+\frac{72}{60}-\frac{45}{60}\\=\frac{-80+72-45}{60}\\=\frac{-53}{60}\)
8. \(+\left(\frac{-10}{-3}\right) -\left(\frac{-5}{3}\right) +\left(\frac{11}{4}\right)\\= \frac{10}{3}+ \frac{5}{3}+\frac{11}{4}\\=\frac{40}{12}+\frac{20}{12}+\frac{33}{12}\\=\frac{40+20+33}{12}\\=\frac{93}{12}\\=\frac{31}{4}\)
9. \(+\left(\frac{6}{7}\right) -\left(\frac{-8}{-8}\right) +\left(\frac{-2}{-12}\right)\\= \frac{6}{7}- \frac{8}{8}+\frac{2}{12}\\=\frac{6}{7}-\frac{1}{1}+\frac{1}{6}\\=\frac{36}{42}-\frac{42}{42}+\frac{7}{42}\\=\frac{36-42+7}{42}\\=\frac{1}{42}\)
10. \(+\left(\frac{-9}{-5}\right) -\left(\frac{-7}{-3}\right) -\left(\frac{-4}{11}\right)\\= \frac{9}{5}- \frac{7}{3}+\frac{4}{11}\\=\frac{297}{165}-\frac{385}{165}+\frac{60}{165}\\=\frac{297-385+60}{165}\\=\frac{-28}{165}\)
11. \(-\left(\frac{10}{-9}\right) -\left(\frac{-3}{2}\right) -\left(\frac{10}{-5}\right)\\= \frac{10}{9}+ \frac{3}{2}+\frac{10}{5}\\=\frac{10}{9}+\frac{3}{2}+\frac{2}{1}\\=\frac{20}{18}+\frac{27}{18}+\frac{36}{18}\\=\frac{20+27+36}{18}\\=\frac{83}{18}\)
12. \(-\left(\frac{-5}{-3}\right) -\left(\frac{5}{-5}\right) -\left(\frac{10}{-9}\right)\\= \frac{-5}{3}+ \frac{5}{5}+\frac{10}{9}\\=\frac{-5}{3}+\frac{1}{1}+\frac{10}{9}\\=\frac{-15}{9}+\frac{9}{9}+\frac{10}{9}\\=\frac{-15+9+10}{9}\\=\frac{4}{9}\)