Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-10}{-2}\right) +\left(\frac{-6}{2}\right)\\= \frac{6}{5}- \frac{10}{2}-\frac{6}{2}\\=\frac{6}{5}-\frac{5}{1}-\frac{3}{1}\\=\frac{6-5-3}{5}\\=\frac{-2}{5}\)
2. \(-\left(\frac{-5}{-4}\right) -\left(\frac{-6}{10}\right) +\left(\frac{-10}{-4}\right)\\= \frac{-5}{4}+ \frac{6}{10}+\frac{10}{4}\\=\frac{-5}{4}+\frac{3}{5}+\frac{5}{2}\\=\frac{-25}{20}+\frac{12}{20}+\frac{50}{20}\\=\frac{-25+12+50}{20}\\=\frac{37}{20}\)
3. \(+\left(\frac{-5}{8}\right) -\left(\frac{-5}{6}\right) -\left(\frac{9}{8}\right)\\= \frac{-5}{8}+ \frac{5}{6}-\frac{9}{8}\\=\frac{-15}{24}+\frac{20}{24}-\frac{27}{24}\\=\frac{-15+20-27}{24}\\=\frac{-22}{24}\\=\frac{-11}{12}\)
4. \(+\left(\frac{-7}{-3}\right) +\left(\frac{5}{9}\right) +\left(\frac{-12}{7}\right)\\= \frac{7}{3}+ \frac{5}{9}-\frac{12}{7}\\=\frac{147}{63}+\frac{35}{63}-\frac{108}{63}\\=\frac{147+35-108}{63}\\=\frac{74}{63}\)
5. \(-\left(\frac{-9}{7}\right) +\left(\frac{8}{-8}\right) -\left(\frac{5}{-10}\right)\\= \frac{9}{7}- \frac{8}{8}+\frac{5}{10}\\=\frac{9}{7}-\frac{1}{1}+\frac{1}{2}\\=\frac{18}{14}-\frac{14}{14}+\frac{7}{14}\\=\frac{18-14+7}{14}\\=\frac{11}{14}\)
6. \(+\left(\frac{9}{5}\right) -\left(\frac{-10}{-5}\right) +\left(\frac{-5}{4}\right)\\= \frac{9}{5}- \frac{10}{5}-\frac{5}{4}\\=\frac{9}{5}-\frac{2}{1}-\frac{5}{4}\\=\frac{36}{20}-\frac{40}{20}-\frac{25}{20}\\=\frac{36-40-25}{20}\\=\frac{-29}{20}\)
7. \(+\left(\frac{7}{6}\right) +\left(\frac{4}{-7}\right) +\left(\frac{-11}{4}\right)\\= \frac{7}{6}- \frac{4}{7}-\frac{11}{4}\\=\frac{98}{84}-\frac{48}{84}-\frac{231}{84}\\=\frac{98-48-231}{84}\\=\frac{-181}{84}\)
8. \(+\left(\frac{-9}{-4}\right) -\left(\frac{-4}{-9}\right) -\left(\frac{-6}{12}\right)\\= \frac{9}{4}- \frac{4}{9}+\frac{6}{12}\\=\frac{9}{4}-\frac{4}{9}+\frac{1}{2}\\=\frac{81}{36}-\frac{16}{36}+\frac{18}{36}\\=\frac{81-16+18}{36}\\=\frac{83}{36}\)
9. \(-\left(\frac{2}{-5}\right) +\left(\frac{7}{4}\right) -\left(\frac{-4}{6}\right)\\= \frac{2}{5}+ \frac{7}{4}+\frac{4}{6}\\=\frac{2}{5}+\frac{7}{4}+\frac{2}{3}\\=\frac{24}{60}+\frac{105}{60}+\frac{40}{60}\\=\frac{24+105+40}{60}\\=\frac{169}{60}\)
10. \(-\left(\frac{-4}{7}\right) +\left(\frac{-6}{-8}\right) -\left(\frac{-8}{-12}\right)\\= \frac{4}{7}+ \frac{6}{8}-\frac{8}{12}\\=\frac{4}{7}+\frac{3}{4}-\frac{2}{3}\\=\frac{48}{84}+\frac{63}{84}-\frac{56}{84}\\=\frac{48+63-56}{84}\\=\frac{55}{84}\)
11. \(+\left(\frac{-3}{2}\right) -\left(\frac{10}{9}\right) +\left(\frac{10}{-8}\right)\\= \frac{-3}{2}- \frac{10}{9}-\frac{10}{8}\\=\frac{-3}{2}-\frac{10}{9}-\frac{5}{4}\\=\frac{-54}{36}-\frac{40}{36}-\frac{45}{36}\\=\frac{-54-40-45}{36}\\=\frac{-139}{36}\)
12. \(-\left(\frac{7}{-2}\right) +\left(\frac{10}{-7}\right) +\left(\frac{-8}{-6}\right)\\= \frac{7}{2}- \frac{10}{7}+\frac{8}{6}\\=\frac{7}{2}-\frac{10}{7}+\frac{4}{3}\\=\frac{147}{42}-\frac{60}{42}+\frac{56}{42}\\=\frac{147-60+56}{42}\\=\frac{143}{42}\)