Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{3}{7}\right) -\left(\frac{-5}{-8}\right) +\left(\frac{-11}{9}\right)\\= \frac{3}{7}- \frac{5}{8}-\frac{11}{9}\\=\frac{216}{504}-\frac{315}{504}-\frac{616}{504}\\=\frac{216-315-616}{504}\\=\frac{-715}{504}\)
2. \(+\left(\frac{7}{-4}\right) +\left(\frac{-8}{2}\right) -\left(\frac{7}{-10}\right)\\= \frac{-7}{4}- \frac{8}{2}+\frac{7}{10}\\=\frac{-7}{4}-\frac{4}{1}+\frac{7}{10}\\=\frac{-35}{20}-\frac{80}{20}+\frac{14}{20}\\=\frac{-35-80+14}{20}\\=\frac{-101}{20}\)
3. \(+\left(\frac{6}{5}\right) +\left(\frac{-8}{2}\right) +\left(\frac{-9}{-8}\right)\\= \frac{6}{5}- \frac{8}{2}+\frac{9}{8}\\=\frac{6}{5}-\frac{4}{1}+\frac{9}{8}\\=\frac{48}{40}-\frac{160}{40}+\frac{45}{40}\\=\frac{48-160+45}{40}\\=\frac{-67}{40}\)
4. \(+\left(\frac{-3}{-4}\right) -\left(\frac{2}{-3}\right) -\left(\frac{6}{3}\right)\\= \frac{3}{4}+ \frac{2}{3}-\frac{6}{3}\\=\frac{3}{4}+\frac{2}{3}-\frac{2}{1}\\=\frac{9}{12}+\frac{8}{12}-\frac{24}{12}\\=\frac{9+8-24}{12}\\=\frac{-7}{12}\)
5. \(+\left(\frac{10}{7}\right) +\left(\frac{9}{6}\right) +\left(\frac{11}{-11}\right)\\= \frac{10}{7}+ \frac{9}{6}-\frac{11}{11}\\=\frac{10}{7}+\frac{3}{2}-\frac{1}{1}\\=\frac{20}{14}+\frac{21}{14}-\frac{14}{14}\\=\frac{20+21-14}{14}\\=\frac{27}{14}\)
6. \(+\left(\frac{-8}{3}\right) +\left(\frac{6}{-4}\right) -\left(\frac{11}{4}\right)\\= \frac{-8}{3}- \frac{6}{4}-\frac{11}{4}\\=\frac{-8}{3}-\frac{3}{2}-\frac{11}{4}\\=\frac{-32}{12}-\frac{18}{12}-\frac{33}{12}\\=\frac{-32-18-33}{12}\\=\frac{-83}{12}\)
7. \(-\left(\frac{8}{3}\right) +\left(\frac{-8}{3}\right) +\left(\frac{-9}{9}\right)\\= \frac{-8}{3}- \frac{8}{3}-\frac{9}{9}\\=\frac{-8}{3}-\frac{8}{3}-\frac{1}{1}\\=\frac{-8-8-1}{3}\\=\frac{-17}{3}\)
8. \(-\left(\frac{-4}{3}\right) -\left(\frac{-6}{-9}\right) +\left(\frac{-3}{7}\right)\\= \frac{4}{3}- \frac{6}{9}-\frac{3}{7}\\=\frac{4}{3}-\frac{2}{3}-\frac{3}{7}\\=\frac{28}{21}-\frac{14}{21}-\frac{9}{21}\\=\frac{28-14-9}{21}\\=\frac{5}{21}\)
9. \(-\left(\frac{-10}{9}\right) -\left(\frac{-9}{-2}\right) -\left(\frac{-4}{-9}\right)\\= \frac{10}{9}- \frac{9}{2}-\frac{4}{9}\\=\frac{20}{18}-\frac{81}{18}-\frac{8}{18}\\=\frac{20-81-8}{18}\\=\frac{-69}{18}\\=\frac{-23}{6}\)
10. \(+\left(\frac{-7}{8}\right) +\left(\frac{-5}{-3}\right) +\left(\frac{-3}{11}\right)\\= \frac{-7}{8}+ \frac{5}{3}-\frac{3}{11}\\=\frac{-231}{264}+\frac{440}{264}-\frac{72}{264}\\=\frac{-231+440-72}{264}\\=\frac{137}{264}\)
11. \(-\left(\frac{-3}{-7}\right) +\left(\frac{6}{-5}\right) -\left(\frac{-12}{-10}\right)\\= \frac{-3}{7}- \frac{6}{5}-\frac{12}{10}\\=\frac{-3}{7}-\frac{6}{5}-\frac{6}{5}\\=\frac{-15}{35}-\frac{42}{35}-\frac{42}{35}\\=\frac{-15-42-42}{35}\\=\frac{-99}{35}\)
12. \(+\left(\frac{-3}{-4}\right) -\left(\frac{-8}{-8}\right) +\left(\frac{-6}{-11}\right)\\= \frac{3}{4}- \frac{8}{8}+\frac{6}{11}\\=\frac{3}{4}-\frac{1}{1}+\frac{6}{11}\\=\frac{33}{44}-\frac{44}{44}+\frac{24}{44}\\=\frac{33-44+24}{44}\\=\frac{13}{44}\)