Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{8}{5}\right) +\left(\frac{-9}{-6}\right) -\left(\frac{5}{-2}\right)\\= \frac{-8}{5}+ \frac{9}{6}+\frac{5}{2}\\=\frac{-8}{5}+\frac{3}{2}+\frac{5}{2}\\=\frac{-16}{10}+\frac{15}{10}+\frac{25}{10}\\=\frac{-16+15+25}{10}\\=\frac{24}{10}\\=\frac{12}{5}\)
2. \(-\left(\frac{-9}{4}\right) +\left(\frac{8}{-8}\right) +\left(\frac{7}{6}\right)\\= \frac{9}{4}- \frac{8}{8}+\frac{7}{6}\\=\frac{9}{4}-\frac{1}{1}+\frac{7}{6}\\=\frac{27}{12}-\frac{12}{12}+\frac{14}{12}\\=\frac{27-12+14}{12}\\=\frac{29}{12}\)
3. \(+\left(\frac{5}{-6}\right) +\left(\frac{6}{-4}\right) -\left(\frac{-3}{3}\right)\\= \frac{-5}{6}- \frac{6}{4}+\frac{3}{3}\\=\frac{-5}{6}-\frac{3}{2}+\frac{1}{1}\\=\frac{-5-3+1}{6}\\=\frac{-7}{6}\)
4. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-2}{2}\right) -\left(\frac{-5}{7}\right)\\= \frac{6}{5}+ \frac{2}{2}+\frac{5}{7}\\=\frac{6}{5}+\frac{1}{1}+\frac{5}{7}\\=\frac{42}{35}+\frac{35}{35}+\frac{25}{35}\\=\frac{42+35+25}{35}\\=\frac{102}{35}\)
5. \(+\left(\frac{-10}{9}\right) -\left(\frac{6}{5}\right) -\left(\frac{10}{8}\right)\\= \frac{-10}{9}- \frac{6}{5}-\frac{10}{8}\\=\frac{-10}{9}-\frac{6}{5}-\frac{5}{4}\\=\frac{-200}{180}-\frac{216}{180}-\frac{225}{180}\\=\frac{-200-216-225}{180}\\=\frac{-641}{180}\)
6. \(-\left(\frac{2}{-7}\right) -\left(\frac{-7}{-4}\right) -\left(\frac{10}{-12}\right)\\= \frac{2}{7}- \frac{7}{4}+\frac{10}{12}\\=\frac{2}{7}-\frac{7}{4}+\frac{5}{6}\\=\frac{24}{84}-\frac{147}{84}+\frac{70}{84}\\=\frac{24-147+70}{84}\\=\frac{-53}{84}\)
7. \(-\left(\frac{9}{8}\right) +\left(\frac{-10}{-2}\right) +\left(\frac{-10}{-4}\right)\\= \frac{-9}{8}+ \frac{10}{2}+\frac{10}{4}\\=\frac{-9}{8}+\frac{5}{1}+\frac{5}{2}\\=\frac{-9+5+5}{8}\\=\frac{1}{8}\)
8. \(-\left(\frac{6}{-5}\right) -\left(\frac{-5}{5}\right) -\left(\frac{-4}{3}\right)\\= \frac{6}{5}+ \frac{5}{5}+\frac{4}{3}\\=\frac{6}{5}+\frac{1}{1}+\frac{4}{3}\\=\frac{18}{15}+\frac{15}{15}+\frac{20}{15}\\=\frac{18+15+20}{15}\\=\frac{53}{15}\)
9. \(+\left(\frac{5}{2}\right) -\left(\frac{-9}{2}\right) +\left(\frac{10}{8}\right)\\= \frac{5}{2}+ \frac{9}{2}+\frac{10}{8}\\=\frac{5}{2}+\frac{9}{2}+\frac{5}{4}\\=\frac{10}{4}+\frac{18}{4}+\frac{5}{4}\\=\frac{10+18+5}{4}\\=\frac{33}{4}\)
10. \(+\left(\frac{-8}{-5}\right) -\left(\frac{8}{9}\right) -\left(\frac{-10}{7}\right)\\= \frac{8}{5}- \frac{8}{9}+\frac{10}{7}\\=\frac{504}{315}-\frac{280}{315}+\frac{450}{315}\\=\frac{504-280+450}{315}\\=\frac{674}{315}\)
11. \(-\left(\frac{-7}{-3}\right) +\left(\frac{-3}{3}\right) +\left(\frac{6}{-3}\right)\\= \frac{-7}{3}- \frac{3}{3}-\frac{6}{3}\\=\frac{-7}{3}-\frac{1}{1}-\frac{2}{1}\\=\frac{-7-1-2}{3}\\=\frac{-10}{3}\)
12. \(-\left(\frac{3}{2}\right) +\left(\frac{-8}{4}\right) +\left(\frac{-8}{3}\right)\\= \frac{-3}{2}- \frac{8}{4}-\frac{8}{3}\\=\frac{-3}{2}-\frac{2}{1}-\frac{8}{3}\\=\frac{-9}{6}-\frac{12}{6}-\frac{16}{6}\\=\frac{-9-12-16}{6}\\=\frac{-37}{6}\)